##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(1.4) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) $array_y2_init[1 + 1] = exact_soln_y2p(x_start) $array_y2_init[2 + 1] = exact_soln_y2pp(x_start) $array_y2_init[3 + 1] = exact_soln_y2ppp(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=true $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) x = c(x) return(c(1.0) + sin(c(x))) end def exact_soln_y2 (x) x = c(x) return(c(1.0) + sin(c(x))) end def exact_soln_y2p (x) x = c(x) return( cos(c(x))) end def exact_soln_y2pp (x) x = c(x) return(neg(sin(c(x)))) end def exact_soln_y2ppp (x) x = c(x) return( neg(cos(c(x)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y2[1] (closed_form) 1.0998334166468282 y2[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 1.0998334166468282 y1[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0993346653975306 Order of pole (three term test) 32.990033288920614 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.09933466539753054 Order of pole (three term test) 32.990033288920614 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11000000000000001 y2[1] (closed_form) 1.1097783008371749 y2[1] (numeric) 1.1097783008371749 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1097783008371749 y1[1] (numeric) 1.1097783008371749 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10911481154043474 Order of pole (three term test) 32.9879487246653 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.10911481154043469 Order of pole (three term test) 32.9879487246653 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12000000000000002 y2[1] (closed_form) 1.1197122072889194 y2[1] (numeric) 1.1197122072889192 absolute error 2.220446049250313e-16 relative error 1.983050675696859e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1197122072889194 y1[1] (numeric) 1.1197122072889192 absolute error 2.220446049250313e-16 relative error 1.983050675696859e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11885131321356723 Order of pole (three term test) 32.98566898742602 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.11885131321356723 Order of pole (three term test) 32.98566898742602 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.13000000000000003 y2[1] (closed_form) 1.129634142619695 y2[1] (numeric) 1.1296341426196943 absolute error 6.661338147750939e-16 relative error 5.896898735995057e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 1.129634142619695 y1[1] (numeric) 1.1296341426196943 absolute error 6.661338147750939e-16 relative error 5.896898735995057e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12854027594607695 Order of pole (three term test) 32.98319498906726 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.128540275946077 Order of pole (three term test) 32.983194989067265 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.14000000000000004 y2[1] (closed_form) 1.1395431146442365 y2[1] (numeric) 1.1395431146442359 absolute error 6.661338147750939e-16 relative error 5.84562186559356e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1395431146442365 y1[1] (numeric) 1.1395431146442359 absolute error 6.661338147750939e-16 relative error 5.84562186559356e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13817782428205624 Order of pole (three term test) 32.98052771915539 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1381778242820562 Order of pole (three term test) 32.98052771915539 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15000000000000005 y2[1] (closed_form) 1.1494381324735992 y2[1] (numeric) 1.1494381324735985 absolute error 6.661338147750939e-16 relative error 5.79529942461165e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1494381324735992 y1[1] (numeric) 1.1494381324735985 absolute error 6.661338147750939e-16 relative error 5.79529942461165e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14776010333066927 Order of pole (three term test) 32.97766824456281 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.14776010333066916 Order of pole (three term test) 32.9776682445628 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16000000000000006 y2[1] (closed_form) 1.159318206614246 y2[1] (numeric) 1.1593182066142451 absolute error 8.881784197001252e-16 relative error 7.66121341520223e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.159318206614246 y1[1] (numeric) 1.1593182066142451 absolute error 8.881784197001252e-16 relative error 7.66121341520223e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15728328030805838 Order of pole (three term test) 32.97461770904122 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1572832803080584 Order of pole (three term test) 32.97461770904121 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17000000000000007 y2[1] (closed_form) 1.1691823490669961 y2[1] (numeric) 1.169182349066995 absolute error 1.1102230246251565e-15 relative error 9.49572173674287e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1691823490669961 y1[1] (numeric) 1.169182349066995 absolute error 1.1102230246251565e-15 relative error 9.49572173674287e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1667435460704062 Order of pole (three term test) 32.97137733276418 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.16674354607040615 Order of pole (three term test) 32.97137733276418 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18000000000000008 y2[1] (closed_form) 1.1790295734258243 y2[1] (numeric) 1.1790295734258234 absolute error 8.881784197001252e-16 relative error 7.533130972443778e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1790295734258243 y1[1] (numeric) 1.1790295734258234 absolute error 8.881784197001252e-16 relative error 7.533130972443778e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1761371166375442 Order of pole (three term test) 32.96794841183897 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1761371166375442 Order of pole (three term test) 32.96794841183897 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19000000000000009 y2[1] (closed_form) 1.1888588949765007 y2[1] (numeric) 1.1888588949764995 absolute error 1.1102230246251565e-15 relative error 9.338560104284719e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1888588949765007 y1[1] (numeric) 1.1888588949764995 absolute error 1.1102230246251565e-15 relative error 9.338560104284719e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1854602347064905 Order of pole (three term test) 32.964332317788255 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.18546023470649053 Order of pole (three term test) 32.964332317788255 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2000000000000001 y2[1] (closed_form) 1.1986693307950613 y2[1] (numeric) 1.1986693307950602 absolute error 1.1102230246251565e-15 relative error 9.262129230325435e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.1986693307950613 y1[1] (numeric) 1.1986693307950602 absolute error 1.1102230246251565e-15 relative error 9.262129230325435e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1947091711543246 Order of pole (three term test) 32.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1947091711543246 Order of pole (three term test) 32.96053049700144 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2100000000000001 y2[1] (closed_form) 1.2084598998460996 y2[1] (numeric) 1.2084598998460985 absolute error 1.1102230246251565e-15 relative error 9.187090318566187e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2084598998460996 y1[1] (numeric) 1.2084598998460985 absolute error 1.1102230246251565e-15 relative error 9.187090318566187e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20388022652978402 Order of pole (three term test) 32.95654447015616 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.20388022652978402 Order of pole (three term test) 32.95654447015616 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2200000000000001 y2[1] (closed_form) 1.2182296230808694 y2[1] (numeric) 1.2182296230808682 absolute error 1.1102230246251565e-15 relative error 9.113413461556065e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2182296230808694 y1[1] (numeric) 1.2182296230808682 absolute error 1.1102230246251565e-15 relative error 9.113413461556065e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21296973253299897 Order of pole (three term test) 32.952375831609984 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.212969732532999 Order of pole (three term test) 32.952375831609984 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.23000000000000012 y2[1] (closed_form) 1.2279775235351886 y2[1] (numeric) 1.2279775235351873 absolute error 1.3322676295501878e-15 relative error 1.0849283508990958e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.2279775235351886 y1[1] (numeric) 1.2279775235351873 absolute error 1.3322676295501878e-15 relative error 1.0849283508990958e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22197405348275906 Order of pole (three term test) 32.948026248762766 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.22197405348275911 Order of pole (three term test) 32.94802624876276 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.24000000000000013 y2[1] (closed_form) 1.2377026264271347 y2[1] (numeric) 1.2377026264271338 absolute error 8.881784197001252e-16 relative error 7.176024359453951e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2377026264271347 y1[1] (numeric) 1.2377026264271338 absolute error 8.881784197001252e-16 relative error 7.176024359453951e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23088958777074098 Order of pole (three term test) 32.94349746138964 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.23088958777074095 Order of pole (three term test) 32.94349746138964 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y2[1] (closed_form) 1.247403959254523 y2[1] (numeric) 1.247403959254522 absolute error 8.881784197001252e-16 relative error 7.120214851898666e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.247403959254523 y1[1] (numeric) 1.247403959254522 absolute error 8.881784197001252e-16 relative error 7.120214851898666e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23971276930210095 Order of pole (three term test) 32.93879128094518 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2397127693021008 Order of pole (three term test) 32.93879128094518 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y2[1] (closed_form) 1.2570805518921553 y2[1] (numeric) 1.2570805518921544 absolute error 8.881784197001252e-16 relative error 7.065405779790649e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2570805518921553 y1[1] (numeric) 1.2570805518921544 absolute error 8.881784197001252e-16 relative error 7.065405779790649e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24844006892186787 Order of pole (three term test) 32.93390958983882 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.24844006892186787 Order of pole (three term test) 32.93390958983882 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y2[1] (closed_form) 1.2667314366888314 y2[1] (numeric) 1.2667314366888303 absolute error 1.1102230246251565e-15 relative error 8.764470451031203e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2667314366888314 y1[1] (numeric) 1.2667314366888303 absolute error 1.1102230246251565e-15 relative error 8.764470451031203e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2570679958265555 Order of pole (three term test) 32.928854340681916 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.25706799582655526 Order of pole (three term test) 32.92885434068191 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y2[1] (closed_form) 1.2763556485641139 y2[1] (numeric) 1.2763556485641128 absolute error 1.1102230246251565e-15 relative error 8.698382977143912e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2763556485641139 y1[1] (numeric) 1.2763556485641128 absolute error 1.1102230246251565e-15 relative error 8.698382977143912e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2655930989604408 Order of pole (three term test) 32.92362755550671 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2655930989604408 Order of pole (three term test) 32.92362755550671 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y2[1] (closed_form) 1.2859522251048356 y2[1] (numeric) 1.2859522251048348 absolute error 8.881784197001252e-16 relative error 6.906776180022688e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2859522251048356 y1[1] (numeric) 1.2859522251048348 absolute error 8.881784197001252e-16 relative error 6.906776180022688e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2740119683959356 Order of pole (three term test) 32.918231324957596 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2740119683959357 Order of pole (three term test) 32.918231324957596 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y2[1] (closed_form) 1.2955202066613398 y2[1] (numeric) 1.2955202066613387 absolute error 1.1102230246251565e-15 relative error 8.569708283333465e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.2955202066613398 y1[1] (numeric) 1.2955202066613387 absolute error 1.1102230246251565e-15 relative error 8.569708283333465e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28232123669751696 Order of pole (three term test) 32.91266780745484 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2823212366975169 Order of pole (three term test) 32.91266780745484 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y2[1] (closed_form) 1.3050586364434436 y2[1] (numeric) 1.3050586364434427 absolute error 8.881784197001252e-16 relative error 6.805659109084909e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3050586364434436 y1[1] (numeric) 1.3050586364434427 absolute error 8.881784197001252e-16 relative error 6.805659109084909e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2905175802686519 Order of pole (three term test) 32.90693922833127 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29051758026865193 Order of pole (three term test) 32.90693922833127 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y2[1] (closed_form) 1.3145665606161179 y2[1] (numeric) 1.3145665606161172 absolute error 6.661338147750939e-16 relative error 5.0673266362631866e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3145665606161179 y1[1] (numeric) 1.3145665606161172 absolute error 6.661338147750939e-16 relative error 5.0673266362631866e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2985977206811952 Order of pole (three term test) 32.901047878942144 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29859772068119517 Order of pole (three term test) 32.901047878942144 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y2[1] (closed_form) 1.3240430283948685 y2[1] (numeric) 1.3240430283948676 absolute error 8.881784197001252e-16 relative error 6.708078216890428e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3240430283948685 y1[1] (numeric) 1.3240430283948676 absolute error 8.881784197001252e-16 relative error 6.708078216890428e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30655842598671645 Order of pole (three term test) 32.89499611574868 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3065584259867165 Order of pole (three term test) 32.894996115748675 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y2[1] (closed_form) 1.3334870921408146 y2[1] (numeric) 1.3334870921408135 absolute error 1.1102230246251565e-15 relative error 8.325712570961417e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3334870921408146 y1[1] (numeric) 1.3334870921408135 absolute error 1.1102230246251565e-15 relative error 8.325712570961417e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3143965120092336 Order of pole (three term test) 32.88878635937546 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.31439651200923335 Order of pole (three term test) 32.888786359375466 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y2[1] (closed_form) 1.3428978074554516 y2[1] (numeric) 1.3428978074554505 absolute error 1.1102230246251565e-15 relative error 8.267367914829114e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3428978074554516 y1[1] (numeric) 1.3428978074554505 absolute error 1.1102230246251565e-15 relative error 8.267367914829114e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.322108843618845 Order of pole (three term test) 32.88242109364224 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.32210884361884495 Order of pole (three term test) 32.88242109364224 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y2[1] (closed_form) 1.35227423327509 y2[1] (numeric) 1.3522742332750892 absolute error 8.881784197001252e-16 relative error 6.568034780556565e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.35227423327509 y1[1] (numeric) 1.3522742332750892 absolute error 8.881784197001252e-16 relative error 6.568034780556565e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.32969233598573583 Order of pole (three term test) 32.87590286457044 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.32969233598573583 Order of pole (three term test) 32.87590286457045 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y2[1] (closed_form) 1.3616154319649623 y2[1] (numeric) 1.3616154319649612 absolute error 1.1102230246251565e-15 relative error 8.153719461176946e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3616154319649623 y1[1] (numeric) 1.3616154319649612 absolute error 1.1102230246251565e-15 relative error 8.153719461176946e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.337143955814072 Order of pole (three term test) 32.8692342793648 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.33714395581407214 Order of pole (three term test) 32.8692342793648 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y2[1] (closed_form) 1.3709204694129828 y2[1] (numeric) 1.370920469412982 absolute error 8.881784197001252e-16 relative error 6.478701277838795e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3709204694129828 y1[1] (numeric) 1.370920469412982 absolute error 8.881784197001252e-16 relative error 6.478701277838795e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34446072255527516 Order of pole (three term test) 32.86241800537045 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.34446072255527516 Order of pole (three term test) 32.86241800537045 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y2[1] (closed_form) 1.3801884151231616 y2[1] (numeric) 1.3801884151231607 absolute error 8.881784197001252e-16 relative error 6.435196890280146e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3801884151231616 y1[1] (numeric) 1.3801884151231607 absolute error 8.881784197001252e-16 relative error 6.435196890280146e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35163970960020485 Order of pole (three term test) 32.85545676900614 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35163970960020474 Order of pole (three term test) 32.85545676900614 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y2[1] (closed_form) 1.3894183423086508 y2[1] (numeric) 1.3894183423086495 absolute error 1.3322676295501878e-15 relative error 9.588671669156882e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3894183423086508 y1[1] (numeric) 1.3894183423086495 absolute error 1.3322676295501878e-15 relative error 9.588671669156882e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35867804544976084 Order of pole (three term test) 32.848353354673584 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35867804544976084 Order of pole (three term test) 32.848353354673584 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y2[1] (closed_form) 1.3986093279844232 y2[1] (numeric) 1.3986093279844218 absolute error 1.3322676295501878e-15 relative error 9.525659545472629e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.3986093279844232 y1[1] (numeric) 1.3986093279844218 absolute error 1.3322676295501878e-15 relative error 9.525659545472629e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3655729148634475 Order of pole (three term test) 32.841110603643806 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3655729148634474 Order of pole (three term test) 32.841110603643806 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y2[1] (closed_form) 1.4077604530595704 y2[1] (numeric) 1.4077604530595693 absolute error 1.1102230246251565e-15 relative error 7.88644845230765e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.4077604530595704 y1[1] (numeric) 1.4077604530595693 absolute error 1.1102230246251565e-15 relative error 7.88644845230765e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3723215599854291 Order of pole (three term test) 32.833731412920656 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.372321559985429 Order of pole (three term test) 32.833731412920656 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y2[1] (closed_form) 1.416870802429211 y2[1] (numeric) 1.4168708024292098 absolute error 1.1102230246251565e-15 relative error 7.835739311740281e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.416870802429211 y1[1] (numeric) 1.4168708024292098 absolute error 1.1102230246251565e-15 relative error 7.835739311740281e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3789212814476377 Order of pole (three term test) 32.82621873408203 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37892128144763765 Order of pole (three term test) 32.82621873408203 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y2[1] (closed_form) 1.4259394650659998 y2[1] (numeric) 1.4259394650659987 absolute error 1.1102230246251565e-15 relative error 7.785905726185717e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.4259394650659998 y1[1] (numeric) 1.4259394650659987 absolute error 1.1102230246251565e-15 relative error 7.785905726185717e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.385369439449484 Order of pole (three term test) 32.81857557209929 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.38536943944948393 Order of pole (three term test) 32.81857557209929 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y2[1] (closed_form) 1.4349655341112304 y2[1] (numeric) 1.434965534111229 absolute error 1.3322676295501878e-15 relative error 9.284317970573069e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.4349655341112304 y1[1] (numeric) 1.434965534111229 absolute error 1.3322676295501878e-15 relative error 9.284317970573069e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3916634548137409 Order of pole (three term test) 32.81080498413534 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3916634548137409 Order of pole (three term test) 32.81080498413534 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y2[1] (closed_form) 1.44394810696552 y2[1] (numeric) 1.443948106965519 absolute error 1.1102230246251565e-15 relative error 7.688801413773159e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.44394810696552 y1[1] (numeric) 1.443948106965519 absolute error 1.1102230246251565e-15 relative error 7.688801413773159e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3978008100181823 Order of pole (three term test) 32.80291007832174 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.39780081001818224 Order of pole (three term test) 32.80291007832173 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y2[1] (closed_form) 1.4528862853790685 y2[1] (numeric) 1.4528862853790674 absolute error 1.1102230246251565e-15 relative error 7.641499791124336e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.4528862853790685 y1[1] (numeric) 1.4528862853790674 absolute error 1.1102230246251565e-15 relative error 7.641499791124336e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.40377905020255683 Order of pole (three term test) 32.79489401251555 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.40377905020255667 Order of pole (three term test) 32.794894012515556 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y2[1] (closed_form) 1.461779175541483 y2[1] (numeric) 1.4617791755414824 absolute error 6.661338147750939e-16 relative error 4.5570071452710337e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.461779175541483 y1[1] (numeric) 1.4617791755414824 absolute error 6.661338147750939e-16 relative error 4.5570071452710337e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.40959578415049913 Order of pole (three term test) 32.786759993036235 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.409595784150499 Order of pole (three term test) 32.78675999303623 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y2[1] (closed_form) 1.4706258881711582 y2[1] (numeric) 1.4706258881711576 absolute error 6.661338147750939e-16 relative error 4.529593964944307e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.4706258881711582 y1[1] (numeric) 1.4706258881711576 absolute error 6.661338147750939e-16 relative error 4.529593964944307e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.41524868524598463 Order of pole (three term test) 32.77851127338311 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4152486852459847 Order of pole (three term test) 32.77851127338311 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y2[1] (closed_form) 1.4794255386042032 y2[1] (numeric) 1.479425538604202 absolute error 1.3322676295501878e-15 relative error 9.005303712731262e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.4794255386042032 y1[1] (numeric) 1.479425538604202 absolute error 1.3322676295501878e-15 relative error 9.005303712731262e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4207354924039475 Order of pole (three term test) 32.770151152934076 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4207354924039476 Order of pole (three term test) 32.770151152934076 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y2[1] (closed_form) 1.4881772468829078 y2[1] (numeric) 1.4881772468829064 absolute error 1.3322676295501878e-15 relative error 8.95234510768604e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.4881772468829078 y1[1] (numeric) 1.4881772468829064 absolute error 1.3322676295501878e-15 relative error 8.95234510768604e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.42605401097468076 Order of pole (three term test) 32.761682975625824 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.42605401097468065 Order of pole (three term test) 32.761682975625824 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y2[1] (closed_form) 1.496880137843737 y2[1] (numeric) 1.4968801378437357 absolute error 1.3322676295501878e-15 relative error 8.900295994770334e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.496880137843737 y1[1] (numeric) 1.4968801378437357 absolute error 1.3322676295501878e-15 relative error 8.900295994770334e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.43120211362166866 Order of pole (three term test) 32.753110128616385 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.43120211362166866 Order of pole (three term test) 32.75311012861639 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y2[1] (closed_form) 1.5055333412048473 y2[1] (numeric) 1.505533341204846 absolute error 1.3322676295501878e-15 relative error 8.849140653929334e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.5055333412048473 y1[1] (numeric) 1.505533341204846 absolute error 1.3322676295501878e-15 relative error 8.849140653929334e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.43617774117249264 Order of pole (three term test) 32.744436040930275 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.43617774117249275 Order of pole (three term test) 32.74443604093027 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y2[1] (closed_form) 1.5141359916531134 y2[1] (numeric) 1.514135991653112 absolute error 1.3322676295501878e-15 relative error 8.798863753946143e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.5141359916531134 y1[1] (numeric) 1.514135991653112 absolute error 1.3322676295501878e-15 relative error 8.798863753946143e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4409789034424731 Order of pole (three term test) 32.73566418208688 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.44097890344247315 Order of pole (three term test) 32.73566418208687 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y2[1] (closed_form) 1.5226872289306594 y2[1] (numeric) 1.5226872289306579 absolute error 1.5543122344752192e-15 relative error 1.020769206534141e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.5226872289306594 y1[1] (numeric) 1.522687228930658 absolute error 1.3322676295501878e-15 relative error 8.749450341721209e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4456036800307172 Order of pole (three term test) 32.726798060712795 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4456036800307171 Order of pole (three term test) 32.726798060712795 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y2[1] (closed_form) 1.5311861979208836 y2[1] (numeric) 1.531186197920882 absolute error 1.5543122344752192e-15 relative error 1.0151033470558558e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.5311861979208836 y1[1] (numeric) 1.5311861979208823 absolute error 1.3322676295501878e-15 relative error 8.700885831907336e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.450050221088252 Order of pole (three term test) 32.71784122313836 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.45005022108825193 Order of pole (three term test) 32.717841223138365 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y2[1] (closed_form) 1.5396320487339694 y2[1] (numeric) 1.5396320487339679 absolute error 1.5543122344752192e-15 relative error 1.009534866303492e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.5396320487339694 y1[1] (numeric) 1.539632048733968 absolute error 1.3322676295501878e-15 relative error 8.653155996887074e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45431674805794103 Order of pole (three term test) 32.70879725197918 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.454316748057941 Order of pole (three term test) 32.708797251979185 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y2[1] (closed_form) 1.548023936791874 y2[1] (numeric) 1.548023936791872 absolute error 1.9984014443252818e-15 relative error 1.2909370435619816e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.548023936791874 y1[1] (numeric) 1.5480239367918722 absolute error 1.7763568394002505e-15 relative error 1.147499594277317e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45840155438588276 Order of pole (three term test) 32.69966976470314 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4584015543858827 Order of pole (three term test) 32.69966976470314 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y2[1] (closed_form) 1.556361022912784 y2[1] (numeric) 1.5563610229127822 absolute error 1.7763568394002505e-15 relative error 1.141352689542261e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.556361022912784 y1[1] (numeric) 1.5563610229127824 absolute error 1.5543122344752192e-15 relative error 9.986836033494783e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46230300620400966 Order of pole (three term test) 32.69046241218344 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46230300620400955 Order of pole (three term test) 32.69046241218344 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y2[1] (closed_form) 1.5646424733950357 y2[1] (numeric) 1.5646424733950337 absolute error 1.9984014443252818e-15 relative error 1.277225614353326e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.5646424733950357 y1[1] (numeric) 1.564642473395034 absolute error 1.7763568394002505e-15 relative error 1.1353116572029564e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4660195429836127 Order of pole (three term test) 32.681178877238345 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46601954298361253 Order of pole (three term test) 32.68117887723834 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y2[1] (closed_form) 1.5728674601004817 y2[1] (numeric) 1.5728674601004797 absolute error 1.9984014443252818e-15 relative error 1.270546625840689e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.5728674601004817 y1[1] (numeric) 1.57286746010048 absolute error 1.7763568394002505e-15 relative error 1.129374778525057e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46954967815953347 Order of pole (three term test) 32.67182287315802 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4695496781595334 Order of pole (three term test) 32.67182287315802 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y2[1] (closed_form) 1.5810351605373054 y2[1] (numeric) 1.5810351605373036 absolute error 1.7763568394002505e-15 relative error 1.1235403764180463e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.5810351605373054 y1[1] (numeric) 1.5810351605373039 absolute error 1.5543122344752192e-15 relative error 9.830978293657906e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.47289199972476914 Order of pole (three term test) 32.66239814221938 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47289199972476914 Order of pole (three term test) 32.66239814221938 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y2[1] (closed_form) 1.58914475794227 y2[1] (numeric) 1.5891447579422677 absolute error 2.220446049250313e-15 relative error 1.3972585179247573e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.58914475794227 y1[1] (numeric) 1.589144757942268 absolute error 1.9984014443252818e-15 relative error 1.2575326661322816e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4760451707952576 Order of pole (three term test) 32.65290845418915 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4760451707952575 Order of pole (three term test) 32.652908454189145 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y2[1] (closed_form) 1.5971954413623926 y2[1] (numeric) 1.5971954413623908 absolute error 1.7763568394002505e-15 relative error 1.112172495236422e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.5971954413623926 y1[1] (numeric) 1.597195441362391 absolute error 1.5543122344752192e-15 relative error 9.731509333318693e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.479007930144612 Order of pole (three term test) 32.643357604815975 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.479007930144612 Order of pole (three term test) 32.64335760481598 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y2[1] (closed_form) 1.6051864057360399 y2[1] (numeric) 1.6051864057360385 absolute error 1.3322676295501878e-15 relative error 8.299768953869826e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6051864057360399 y1[1] (numeric) 1.6051864057360388 absolute error 1.1102230246251565e-15 relative error 6.916474128224855e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4817790927085961 Order of pole (three term test) 32.63374941431229 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4817790927085963 Order of pole (three term test) 32.6337494143123 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y2[1] (closed_form) 1.6131168519734342 y2[1] (numeric) 1.613116851973433 absolute error 1.3322676295501878e-15 relative error 8.258965417913373e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6131168519734342 y1[1] (numeric) 1.6131168519734331 absolute error 1.1102230246251565e-15 relative error 6.882471181594477e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4843575500591325 Order of pole (three term test) 32.624087725826186 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4843575500591323 Order of pole (three term test) 32.624087725826186 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y2[1] (closed_form) 1.6209859870365602 y2[1] (numeric) 1.620985987036559 absolute error 1.1102230246251565e-15 relative error 6.849059976482797e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6209859870365602 y1[1] (numeric) 1.6209859870365593 absolute error 8.881784197001252e-16 relative error 5.4792479811862374e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48674227084765953 Order of pole (three term test) 32.61437640390423 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.48674227084765975 Order of pole (three term test) 32.61437640390423 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y2[1] (closed_form) 1.628793024018469 y2[1] (numeric) 1.628793024018468 absolute error 8.881784197001252e-16 relative error 5.452985165106246e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.628793024018469 y1[1] (numeric) 1.6287930240184683 absolute error 6.661338147750939e-16 relative error 4.0897388738296844e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4889323012176579 Order of pole (three term test) 32.60461933294572 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4889323012176579 Order of pole (three term test) 32.60461933294572 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y2[1] (closed_form) 1.6365371822219683 y2[1] (numeric) 1.6365371822219679 absolute error 4.440892098500626e-16 relative error 2.713590712599095e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6365371822219683 y1[1] (numeric) 1.636537182221968 absolute error 2.220446049250313e-16 relative error 1.3567953562995475e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4909267651861798 Order of pole (three term test) 32.59482041564892 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4909267651861798 Order of pole (three term test) 32.59482041564892 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y2[1] (closed_form) 1.6442176872376915 y2[1] (numeric) 1.6442176872376908 absolute error 6.661338147750939e-16 relative error 4.0513723939693655e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6442176872376915 y1[1] (numeric) 1.6442176872376912 absolute error 2.220446049250313e-16 relative error 1.3504574646564551e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49272486499423 Order of pole (three term test) 32.584983571450124 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49272486499423 Order of pole (three term test) 32.58498357145012 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y2[1] (closed_form) 1.6518337710215372 y2[1] (numeric) 1.6518337710215363 absolute error 8.881784197001252e-16 relative error 5.3769237273242844e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6518337710215372 y1[1] (numeric) 1.6518337710215367 absolute error 4.440892098500626e-16 relative error 2.6884618636621422e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49432588142585976 Order of pole (three term test) 32.57511273495584 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49432588142585976 Order of pole (three term test) 32.575112734955844 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y2[1] (closed_form) 1.6593846719714735 y2[1] (numeric) 1.6593846719714729 absolute error 6.661338147750939e-16 relative error 4.0143423404271715e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6593846719714735 y1[1] (numeric) 1.6593846719714733 absolute error 2.220446049250313e-16 relative error 1.3381141134757238e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4957291740958431 Order of pole (three term test) 32.565211854369075 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49572917409584316 Order of pole (three term test) 32.565211854369075 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y2[1] (closed_form) 1.6668696350036982 y2[1] (numeric) 1.6668696350036976 absolute error 6.661338147750939e-16 relative error 3.996316213256929e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6668696350036982 y1[1] (numeric) 1.666869635003698 absolute error 2.220446049250313e-16 relative error 1.3321054044189765e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4969341817058222 Order of pole (three term test) 32.555284889910034 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4969341817058222 Order of pole (three term test) 32.555284889910034 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y2[1] (closed_form) 1.6742879116281455 y2[1] (numeric) 1.6742879116281448 absolute error 6.661338147750939e-16 relative error 3.978609713112713e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6742879116281455 y1[1] (numeric) 1.6742879116281453 absolute error 2.220446049250313e-16 relative error 1.3262032377042376e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49794042226881996 Order of pole (three term test) 32.54533581223215 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49794042226881996 Order of pole (three term test) 32.54533581223216 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y2[1] (closed_form) 1.6816387600233345 y2[1] (numeric) 1.6816387600233342 absolute error 2.220446049250313e-16 relative error 1.3204060836582419e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6816387600233345 y1[1] (numeric) 1.6816387600233347 absolute error 2.220446049250313e-16 relative error 1.3204060836582419e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4987474933020271 Order of pole (three term test) 32.53536860083385 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49874749330202706 Order of pole (three term test) 32.53536860083385 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y2[1] (closed_form) 1.6889214451105516 y2[1] (numeric) 1.6889214451105514 absolute error 2.220446049250313e-16 relative error 1.3147124489883954e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6889214451105516 y1[1] (numeric) 1.6889214451105519 absolute error 2.220446049250313e-16 relative error 1.3147124489883954e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4993550719877915 Order of pole (three term test) 32.52538724246679 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49935507198779144 Order of pole (three term test) 32.52538724246679 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y2[1] (closed_form) 1.6961352386273572 y2[1] (numeric) 1.6961352386273567 absolute error 4.440892098500626e-16 relative error 2.6182417518160505e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.6961352386273572 y1[1] (numeric) 1.6961352386273572 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4997629153027395 Order of pole (three term test) 32.51539572954123 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49976291530273953 Order of pole (three term test) 32.51539572954124 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y2[1] (closed_form) 1.7032794192004106 y2[1] (numeric) 1.70327941920041 absolute error 6.661338147750939e-16 relative error 3.910889823865802e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7032794192004106 y1[1] (numeric) 1.7032794192004104 absolute error 2.220446049250313e-16 relative error 1.3036299412886006e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4999708601149831 Order of pole (three term test) 32.50539805852913 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4999708601149831 Order of pole (three term test) 32.50539805852913 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y2[1] (closed_form) 1.7103532724176083 y2[1] (numeric) 1.7103532724176078 absolute error 4.440892098500626e-16 relative error 2.596476511676072e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7103532724176083 y1[1] (numeric) 1.7103532724176083 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49997882324937 Order of pole (three term test) 32.495398228365595 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49997882324937004 Order of pole (three term test) 32.495398228365595 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y2[1] (closed_form) 1.7173560908995231 y2[1] (numeric) 1.7173560908995227 absolute error 4.440892098500626e-16 relative error 2.5858889266084353e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7173560908995231 y1[1] (numeric) 1.7173560908995231 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49978680152075255 Order of pole (three term test) 32.48540023884936 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4997868015207525 Order of pole (three term test) 32.48540023884936 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y2[1] (closed_form) 1.724287174370143 y2[1] (numeric) 1.7242871743701427 absolute error 2.220446049250313e-16 relative error 1.2877472397029281e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.724287174370143 y1[1] (numeric) 1.7242871743701431 absolute error 2.220446049250313e-16 relative error 1.2877472397029281e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.499394871735262 Order of pole (three term test) 32.475408089042915 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4993948717352619 Order of pole (three term test) 32.475408089042915 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y2[1] (closed_form) 1.7311458297268962 y2[1] (numeric) 1.731145829726896 absolute error 2.220446049250313e-16 relative error 1.2826452925693777e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7311458297268962 y1[1] (numeric) 1.7311458297268965 absolute error 2.220446049250313e-16 relative error 1.2826452925693777e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.498803190659587 Order of pole (three term test) 32.465425775672976 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4988031906595869 Order of pole (three term test) 32.465425775672976 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y2[1] (closed_form) 1.737931371109963 y2[1] (numeric) 1.7379313711099629 absolute error 2.220446049250313e-16 relative error 1.2776373602325751e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.737931371109963 y1[1] (numeric) 1.7379313711099633 absolute error 2.220446049250313e-16 relative error 1.2776373602325751e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4980119949582685 Order of pole (three term test) 32.45545729153178 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4980119949582684 Order of pole (three term test) 32.45545729153177 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y2[1] (closed_form) 1.7446431199708599 y2[1] (numeric) 1.7446431199708592 absolute error 6.661338147750939e-16 relative error 3.818166633335419e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7446431199708599 y1[1] (numeric) 1.7446431199708596 absolute error 2.220446049250313e-16 relative error 1.2727222111118063e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49702160109903804 Order of pole (three term test) 32.44550662388007 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.497021601099038 Order of pole (three term test) 32.445506623880064 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y2[1] (closed_form) 1.7512804051402933 y2[1] (numeric) 1.7512804051402924 absolute error 8.881784197001252e-16 relative error 5.071594572138059e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7512804051402933 y1[1] (numeric) 1.751280405140293 absolute error 2.220446049250313e-16 relative error 1.2678986430345148e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4958324052262343 Order of pole (three term test) 32.43557775285223 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49583240522623434 Order of pole (three term test) 32.43557775285224 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y2[1] (closed_form) 1.7578425628952774 y2[1] (numeric) 1.7578425628952765 absolute error 8.881784197001252e-16 relative error 5.0526619302996024e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7578425628952774 y1[1] (numeric) 1.7578425628952774 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49444488300235073 Order of pole (three term test) 32.42567464986432 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49444488300235084 Order of pole (three term test) 32.42567464986433 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y2[1] (closed_form) 1.7643289370255055 y2[1] (numeric) 1.7643289370255044 absolute error 1.1102230246251565e-15 relative error 6.292607922062931e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7643289370255055 y1[1] (numeric) 1.7643289370255053 absolute error 2.220446049250313e-16 relative error 1.258521584412586e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49285958941777674 Order of pole (three term test) 32.41580127602546 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49285958941777674 Order of pole (three term test) 32.41580127602546 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y2[1] (closed_form) 1.7707388788989697 y2[1] (numeric) 1.7707388788989686 absolute error 1.1102230246251565e-15 relative error 6.269829153553593e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7707388788989697 y1[1] (numeric) 1.7707388788989695 absolute error 2.220446049250313e-16 relative error 1.2539658307107185e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49107715856880935 Order of pole (three term test) 32.40596158055356 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49107715856880935 Order of pole (three term test) 32.40596158055356 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y2[1] (closed_form) 1.7770717475268243 y2[1] (numeric) 1.7770717475268232 absolute error 1.1102230246251565e-15 relative error 6.247485652564504e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7770717475268243 y1[1] (numeric) 1.777071747526824 absolute error 2.220446049250313e-16 relative error 1.2494971305129008e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4890983034040224 Order of pole (three term test) 32.39615949919561 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4890983034040224 Order of pole (three term test) 32.39615949919561 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y2[1] (closed_form) 1.7833269096274837 y2[1] (numeric) 1.7833269096274824 absolute error 1.3322676295501878e-15 relative error 7.470686514950212e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7833269096274837 y1[1] (numeric) 1.7833269096274835 absolute error 2.220446049250313e-16 relative error 1.2451144191583686e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4869238154390977 Order of pole (three term test) 32.38639895265346 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4869238154390976 Order of pole (three term test) 32.38639895265346 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y2[1] (closed_form) 1.789503739689951 y2[1] (numeric) 1.7895037396899494 absolute error 1.5543122344752192e-15 relative error 8.685716604003963e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.789503739689951 y1[1] (numeric) 1.7895037396899505 absolute error 4.440892098500626e-16 relative error 2.4816333154297037e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4845545644402284 Order of pole (three term test) 32.376683845015584 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4845545644402283 Order of pole (three term test) 32.376683845015584 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y2[1] (closed_form) 1.7956016200363665 y2[1] (numeric) 1.7956016200363651 absolute error 1.3322676295501878e-15 relative error 7.419616994571464e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.7956016200363665 y1[1] (numeric) 1.7956016200363663 absolute error 2.220446049250313e-16 relative error 1.2366028324285775e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4819914980762244 Order of pole (three term test) 32.36701806219551 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4819914980762243 Order of pole (three term test) 32.36701806219551 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y2[1] (closed_form) 1.8016199408837776 y2[1] (numeric) 1.801619940883776 absolute error 1.5543122344752192e-15 relative error 8.62730367933626e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8016199408837776 y1[1] (numeric) 1.8016199408837772 absolute error 4.440892098500626e-16 relative error 2.464943908381789e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.47923564153945725 Order of pole (three term test) 32.35740547037749 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47923564153945714 Order of pole (three term test) 32.35740547037749 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y2[1] (closed_form) 1.8075581004051147 y2[1] (numeric) 1.8075581004051129 absolute error 1.7763568394002505e-15 relative error 9.827384464168143e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8075581004051147 y1[1] (numeric) 1.807558100405114 absolute error 6.661338147750939e-16 relative error 3.685269174063054e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4762880971357983 Order of pole (three term test) 32.34784991447009 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4762880971357982 Order of pole (three term test) 32.34784991447009 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y2[1] (closed_form) 1.8134155047893743 y2[1] (numeric) 1.813415504789372 absolute error 2.220446049250313e-15 relative error 1.2244552025644088e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8134155047893743 y1[1] (numeric) 1.8134155047893732 absolute error 1.1102230246251565e-15 relative error 6.122276012822044e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.47315004384370746 Order of pole (three term test) 32.33835521656825 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47315004384370746 Order of pole (three term test) 32.33835521656825 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y2[1] (closed_form) 1.8191915683009987 y2[1] (numeric) 1.8191915683009963 absolute error 2.4424906541753444e-15 relative error 1.3426242165669582e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8191915683009987 y1[1] (numeric) 1.8191915683009976 absolute error 1.1102230246251565e-15 relative error 6.102837348031628e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46982273684266285 Order of pole (three term test) 32.328925174424555 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4698227368426629 Order of pole (three term test) 32.328925174424555 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y2[1] (closed_form) 1.8248857133384506 y2[1] (numeric) 1.8248857133384484 absolute error 2.220446049250313e-15 relative error 1.2167589636000948e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8248857133384506 y1[1] (numeric) 1.8248857133384497 absolute error 8.881784197001252e-16 relative error 4.8670358544003795e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4663075070111004 Order of pole (three term test) 32.31956355993012 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46630750701110035 Order of pole (three term test) 32.31956355993011 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y2[1] (closed_form) 1.830497370491971 y2[1] (numeric) 1.8304973704919691 absolute error 1.7763568394002505e-15 relative error 9.704230489677407e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.830497370491971 y1[1] (numeric) 1.8304973704919705 absolute error 4.440892098500626e-16 relative error 2.4260576224193518e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46260576039408424 Order of pole (three term test) 32.31027411760592 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.462605760394084 Order of pole (three term test) 32.31027411760592 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y2[1] (closed_form) 1.8360259786005209 y2[1] (numeric) 1.8360259786005193 absolute error 1.5543122344752192e-15 relative error 8.465633126062666e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8360259786005209 y1[1] (numeric) 1.8360259786005206 absolute error 2.220446049250313e-16 relative error 1.209376160866095e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4587189776409051 Order of pole (three term test) 32.30106056310505 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.458718977640905 Order of pole (three term test) 32.30106056310504 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y2[1] (closed_form) 1.8414709848078967 y2[1] (numeric) 1.8414709848078952 absolute error 1.5543122344752192e-15 relative error 8.440601276361495e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8414709848078967 y1[1] (numeric) 1.8414709848078967 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4546487134128412 Order of pole (three term test) 32.29192658172643 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.45464871341284124 Order of pole (three term test) 32.29192658172643 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0099999999999996 y2[1] (closed_form) 1.846831844618015 y2[1] (numeric) 1.846831844618014 absolute error 8.881784197001252e-16 relative error 4.809200265245748e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.846831844618015 y1[1] (numeric) 1.8468318446180156 absolute error 6.661338147750939e-16 relative error 3.6069001989343115e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4503965957613137 Order of pole (three term test) 32.28287582694085 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.45039659576131363 Order of pole (three term test) 32.28287582694085 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0199999999999985 y2[1] (closed_form) 1.8521080219493622 y2[1] (numeric) 1.8521080219493617 absolute error 4.440892098500626e-16 relative error 2.3977500479839954e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8521080219493622 y1[1] (numeric) 1.8521080219493633 absolute error 1.1102230246251565e-15 relative error 5.994375119959989e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.44596432547669 Order of pole (three term test) 32.27391191892956 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4459643254766899 Order of pole (three term test) 32.27391191892954 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0299999999999974 y2[1] (closed_form) 1.857298989188602 y2[1] (numeric) 1.8572989891886023 absolute error 2.220446049250313e-16 relative error 1.1955242867064496e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.857298989188602 y1[1] (numeric) 1.8572989891886038 absolute error 1.7763568394002505e-15 relative error 9.564194293651596e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.44135367540798726 Order of pole (three term test) 32.2650384431362 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.44135367540798714 Order of pole (three term test) 32.2650384431362 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0399999999999963 y2[1] (closed_form) 1.8624042272433365 y2[1] (numeric) 1.862404227243337 absolute error 4.440892098500626e-16 relative error 2.3844942110520627e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8624042272433365 y1[1] (numeric) 1.8624042272433388 absolute error 2.220446049250313e-15 relative error 1.1922471055260314e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4365664897537584 Order of pole (three term test) 32.25625894883282 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.43656648975375834 Order of pole (three term test) 32.25625894883282 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0499999999999952 y2[1] (closed_form) 1.8674232255940146 y2[1] (numeric) 1.8674232255940155 absolute error 8.881784197001252e-16 relative error 4.756171003590264e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8674232255940146 y1[1] (numeric) 1.8674232255940173 absolute error 2.6645352591003757e-15 relative error 1.4268513010770791e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.43160468332443713 Order of pole (three term test) 32.247576947700075 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4316046833244371 Order of pole (three term test) 32.247576947700075 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.059999999999994 y2[1] (closed_form) 1.8723554823449833 y2[1] (numeric) 1.8723554823449848 absolute error 1.5543122344752192e-15 relative error 8.301373586006013e-14% Desired digits 8 Estimated correct digits 12 Correct digits 16 h 0.001 y1[1] (closed_form) 1.8723554823449833 y1[1] (numeric) 1.8723554823449866 absolute error 3.3306690738754696e-15 relative error 1.77886576842986e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.42647024077643825 Order of pole (three term test) 32.238995912422645 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4264702407764383 Order of pole (three term test) 32.23899591242265 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.069999999999993 y2[1] (closed_form) 1.8772005042746782 y2[1] (numeric) 1.8772005042746804 absolute error 2.220446049250313e-15 relative error 1.182849697831431e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8772005042746782 y1[1] (numeric) 1.8772005042746822 absolute error 3.9968028886505635e-15 relative error 2.1291294560965757e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4211652158183231 Order of pole (three term test) 32.230519275300246 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.421165215818323 Order of pole (three term test) 32.230519275300246 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0799999999999919 y2[1] (closed_form) 1.8819578068849436 y2[1] (numeric) 1.881957806884946 absolute error 2.4424906541753444e-15 relative error 1.2978455974091187e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8819578068849436 y1[1] (numeric) 1.8819578068849478 absolute error 4.218847493575595e-15 relative error 2.2417333046157505e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.41569173038934193 Order of pole (three term test) 32.22215042687469 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.415691730389342 Order of pole (three term test) 32.22215042687469 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0899999999999908 y2[1] (closed_form) 1.886626914449483 y2[1] (numeric) 1.8866269144494858 absolute error 2.886579864025407e-15 relative error 1.5300215648983837e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.886626914449483 y1[1] (numeric) 1.8866269144494876 absolute error 4.6629367034256575e-15 relative error 2.471573297143543e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4100519738106877 Order of pole (three term test) 32.21389271457378 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4100519738106877 Order of pole (three term test) 32.21389271457378 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0999999999999897 y2[1] (closed_form) 1.8912073600614305 y2[1] (numeric) 1.8912073600614339 absolute error 3.3306690738754696e-15 relative error 1.761133730870888e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8912073600614305 y1[1] (numeric) 1.8912073600614356 absolute error 5.10702591327572e-15 relative error 2.700405054002028e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4042482019097961 Order of pole (three term test) 32.20574944137233 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4042482019097962 Order of pole (three term test) 32.205749441372326 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1099999999999886 y2[1] (closed_form) 1.8956986856800424 y2[1] (numeric) 1.8956986856800464 absolute error 3.9968028886505635e-15 relative error 2.1083534629432913e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.8956986856800424 y1[1] (numeric) 1.8956986856800484 absolute error 5.995204332975845e-15 relative error 3.1625301944149373e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3982827361180434 Order of pole (three term test) 32.19772386447104 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.39828273611804316 Order of pole (three term test) 32.19772386447104 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1199999999999875 y2[1] (closed_form) 1.9001004421764995 y2[1] (numeric) 1.900100442176504 absolute error 4.440892098500626e-15 relative error 2.3371880769701506e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9001004421764995 y1[1] (numeric) 1.900100442176506 absolute error 6.439293542825908e-15 relative error 3.3889227116067187e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3921579625422102 Order of pole (three term test) 32.18981919399366 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.39215796254221036 Order of pole (three term test) 32.189819193993664 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1299999999999863 y2[1] (closed_form) 1.90441218937882 y2[1] (numeric) 1.9044121893788246 absolute error 4.6629367034256575e-15 relative error 2.4484913137142916e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.90441218937882 y1[1] (numeric) 1.9044121893788266 absolute error 6.661338147750939e-15 relative error 3.49784473387756e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.38587633101006313 Order of pole (three term test) 32.182038591703 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.38587633101006313 Order of pole (three term test) 32.182038591703 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1399999999999852 y2[1] (closed_form) 1.908633496115877 y2[1] (numeric) 1.9086334961158822 absolute error 5.10702591327572e-15 relative error 2.6757499140975266e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.908633496115877 y1[1] (numeric) 1.9086334961158842 absolute error 7.105427357601002e-15 relative error 3.7227824891791675e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3794403540904613 Order of pole (three term test) 32.174385169736226 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3794403540904612 Order of pole (three term test) 32.174385169736226 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1499999999999841 y2[1] (closed_form) 1.9127639402605146 y2[1] (numeric) 1.9127639402605199 absolute error 5.329070518200751e-15 relative error 2.786057602839869e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9127639402605146 y1[1] (numeric) 1.9127639402605219 absolute error 7.327471962526033e-15 relative error 3.8308292039048196e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3728526060883603 Order of pole (three term test) 32.16686198936009 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37285260608836046 Order of pole (three term test) 32.166861989360086 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.159999999999983 y2[1] (closed_form) 1.9168031087717603 y2[1] (numeric) 1.9168031087717656 absolute error 5.329070518200751e-15 relative error 2.780186704525687e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9168031087717603 y1[1] (numeric) 1.9168031087717676 absolute error 7.327471962526033e-15 relative error 3.822756718722819e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.36611572201512615 Order of pole (three term test) 32.15947205974643 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.36611572201512604 Order of pole (three term test) 32.15947205974642 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.169999999999982 y2[1] (closed_form) 1.9207505977361286 y2[1] (numeric) 1.920750597736134 absolute error 5.551115123125783e-15 relative error 2.890075957632679e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9207505977361286 y1[1] (numeric) 1.920750597736136 absolute error 7.549516567451064e-15 relative error 3.9305033023804435e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35923239653456385 Order of pole (three term test) 32.15221833676855 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35923239653456385 Order of pole (three term test) 32.15221833676855 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1799999999999808 y2[1] (closed_form) 1.924606012408013 y2[1] (numeric) 1.9246060124080189 absolute error 5.773159728050814e-15 relative error 2.99965795120197e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.924606012408013 y1[1] (numeric) 1.9246060124080209 absolute error 7.771561172376096e-15 relative error 4.0380010881564983e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35220538288508835 Order of pole (three term test) 32.14510372181894 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35220538288508824 Order of pole (three term test) 32.145103721818934 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1899999999999797 y2[1] (closed_form) 1.9283689672491593 y2[1] (numeric) 1.9283689672491648 absolute error 5.551115123125783e-15 relative error 2.8786581911471604e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9283689672491593 y1[1] (numeric) 1.928368967249167 absolute error 7.771561172376096e-15 relative error 4.0301214676060244e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34503749177846843 Order of pole (three term test) 32.13813106064872 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3450374917784685 Order of pole (three term test) 32.13813106064872 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1999999999999786 y2[1] (closed_form) 1.9320390859672187 y2[1] (numeric) 1.9320390859672243 absolute error 5.551115123125783e-15 relative error 2.8731898663151423e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9320390859672187 y1[1] (numeric) 1.9320390859672267 absolute error 7.993605777301127e-15 relative error 4.1373934074938045e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3377315902755761 Order of pole (three term test) 32.13130314222938 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3377315902755762 Order of pole (three term test) 32.13130314222938 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2099999999999775 y2[1] (closed_form) 1.9356160015533779 y2[1] (numeric) 1.9356160015533834 absolute error 5.551115123125783e-15 relative error 2.867880364013772e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9356160015533779 y1[1] (numeric) 1.9356160015533859 absolute error 7.993605777301127e-15 relative error 4.129747724179831e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3302906006396014 Order of pole (three term test) 32.12462269763726 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3302906006396014 Order of pole (three term test) 32.12462269763726 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2199999999999764 y2[1] (closed_form) 1.9390993563190595 y2[1] (numeric) 1.939099356319065 absolute error 5.551115123125783e-15 relative error 2.862728567794131e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9390993563190595 y1[1] (numeric) 1.9390993563190675 absolute error 7.993605777301127e-15 relative error 4.122329137623549e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3227174991671861 Order of pole (three term test) 32.11809239896112 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3227174991671861 Order of pole (three term test) 32.11809239896111 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2299999999999753 y2[1] (closed_form) 1.9424888019316893 y2[1] (numeric) 1.9424888019316953 absolute error 5.995204332975845e-15 relative error 3.086352069064168e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9424888019316893 y1[1] (numeric) 1.9424888019316977 absolute error 8.43769498715119e-15 relative error 4.3437547638680876e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.31501531499794694 Order of pole (three term test) 32.111714858233356 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.315015314997947 Order of pole (three term test) 32.111714858233356 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2399999999999742 y2[1] (closed_form) 1.9457839994495307 y2[1] (numeric) 1.9457839994495372 absolute error 6.439293542825908e-15 relative error 3.309356816916784e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9457839994495307 y1[1] (numeric) 1.9457839994495396 absolute error 8.881784197001252e-15 relative error 4.564630092299012e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3071871289028566 Order of pole (three term test) 32.105492626385235 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3071871289028564 Order of pole (three term test) 32.10549262638523 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2499999999999731 y2[1] (closed_form) 1.9489846193555778 y2[1] (numeric) 1.9489846193555844 absolute error 6.661338147750939e-15 relative error 3.4178505472010747e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9489846193555778 y1[1] (numeric) 1.9489846193555869 absolute error 9.103828801926284e-15 relative error 4.671062414508135e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29923607205197905 Order of pole (three term test) 32.09942819222653 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29923607205197905 Order of pole (three term test) 32.09942819222653 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.259999999999972 y2[1] (closed_form) 1.952090341590507 y2[1] (numeric) 1.9520903415905142 absolute error 7.105427357601002e-15 relative error 3.639907030025928e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.952090341590507 y1[1] (numeric) 1.9520903415905166 absolute error 9.547918011776346e-15 relative error 4.89112507159734e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2911653247620413 Order of pole (three term test) 32.093523981450055 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2911653247620413 Order of pole (three term test) 32.093523981450055 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.269999999999971 y2[1] (closed_form) 1.9551008555846836 y2[1] (numeric) 1.9551008555846905 absolute error 6.8833827526759706e-15 relative error 3.520730264637656e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9551008555846836 y1[1] (numeric) 1.9551008555846932 absolute error 9.547918011776346e-15 relative error 4.88359359288449e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28297811522435246 Order of pole (three term test) 32.08778235566139 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2829781152243526 Order of pole (three term test) 32.08778235566139 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2799999999999698 y2[1] (closed_form) 1.9580158602892164 y2[1] (numeric) 1.9580158602892233 absolute error 6.8833827526759706e-15 relative error 3.515488762005857e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9580158602892164 y1[1] (numeric) 1.958015860289226 absolute error 9.547918011776346e-15 relative error 4.876323121491995e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.27467771821356374 Order of pole (three term test) 32.0822056114343 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2746777182135638 Order of pole (three term test) 32.0822056114343 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2899999999999687 y2[1] (closed_form) 1.960835064206064 y2[1] (numeric) 1.960835064206071 absolute error 7.105427357601002e-15 relative error 3.6236741617418837e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.960835064206064 y1[1] (numeric) 1.9608350642060737 absolute error 9.769962616701378e-15 relative error 4.982551972395091e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.26626745377781125 Order of pole (three term test) 32.07679597939211 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2662674537778113 Order of pole (three term test) 32.07679597939211 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2999999999999676 y2[1] (closed_form) 1.9635581854171842 y2[1] (numeric) 1.9635581854171913 absolute error 7.105427357601002e-15 relative error 3.6186487420495556e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9635581854171842 y1[1] (numeric) 1.963558185417194 absolute error 9.769962616701378e-15 relative error 4.975642020318139e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2577506859107328 Order of pole (three term test) 32.07155562331553 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.25775068591073275 Order of pole (three term test) 32.07155562331553 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3099999999999665 y2[1] (closed_form) 1.9661849516127254 y2[1] (numeric) 1.9661849516127323 absolute error 6.8833827526759706e-15 relative error 3.500882634174373e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9661849516127254 y1[1] (numeric) 1.9661849516127352 absolute error 9.769962616701378e-15 relative error 4.968994706570078e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2491308212059201 Order of pole (three term test) 32.0664866392771 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.24913082120591995 Order of pole (three term test) 32.066486639277095 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3199999999999654 y2[1] (closed_form) 1.9687151001182568 y2[1] (numeric) 1.9687151001182637 absolute error 6.8833827526759706e-15 relative error 3.496383378307252e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9687151001182568 y1[1] (numeric) 1.9687151001182666 absolute error 9.769962616701378e-15 relative error 4.962608665984486e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24041130749432466 Order of pole (three term test) 32.061591054802854 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.24041130749432468 Order of pole (three term test) 32.061591054802854 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3299999999999643 y2[1] (closed_form) 1.9711483779210361 y2[1] (numeric) 1.9711483779210428 absolute error 6.661338147750939e-15 relative error 3.379419947460592e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9711483779210361 y1[1] (numeric) 1.9711483779210457 absolute error 9.547918011776346e-15 relative error 4.843835258026849e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23159563246517353 Order of pole (three term test) 32.05687082806133 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.23159563246517356 Order of pole (three term test) 32.05687082806133 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3399999999999632 y2[1] (closed_form) 1.9734845416953108 y2[1] (numeric) 1.9734845416953177 absolute error 6.8833827526759706e-15 relative error 3.487933453364088e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9734845416953108 y1[1] (numeric) 1.9734845416953206 absolute error 9.769962616701378e-15 relative error 4.950615224129674e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22268732227093643 Order of pole (three term test) 32.05232784708025 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2226873222709363 Order of pole (three term test) 32.05232784708025 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3499999999999621 y2[1] (closed_form) 1.9757233578266509 y2[1] (numeric) 1.9757233578266575 absolute error 6.661338147750939e-15 relative error 3.371594571356686e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9757233578266509 y1[1] (numeric) 1.9757233578266604 absolute error 9.547918011776346e-15 relative error 4.83261888561125e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21368994011691553 Order of pole (three term test) 32.04796392899147 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.21368994011691553 Order of pole (three term test) 32.04796392899147 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.359999999999961 y2[1] (closed_form) 1.9778646024353082 y2[1] (numeric) 1.9778646024353146 absolute error 6.439293542825908e-15 relative error 3.255679653145784e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9778646024353082 y1[1] (numeric) 1.9778646024353175 absolute error 9.325873406851315e-15 relative error 4.715122256280101e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2046070848360093 Order of pole (three term test) 32.043780819304025 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2046070848360093 Order of pole (three term test) 32.043780819304025 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.36999999999996 y2[1] (closed_form) 1.9799080613986062 y2[1] (numeric) 1.9799080613986122 absolute error 5.995204332975845e-15 relative error 3.028021578305427e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9799080613986062 y1[1] (numeric) 1.9799080613986153 absolute error 9.103828801926284e-15 relative error 4.598106841130463e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19544238944922673 Order of pole (three term test) 32.03978019120601 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.19544238944922668 Order of pole (three term test) 32.03978019120601 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3799999999999588 y2[1] (closed_form) 1.981853530372352 y2[1] (numeric) 1.9818535303723575 absolute error 5.551115123125783e-15 relative error 2.800971433082058e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.981853530372352 y1[1] (numeric) 1.9818535303723608 absolute error 8.881784197001252e-15 relative error 4.481554292931293e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18619951971252843 Order of pole (three term test) 32.03596364489533 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.18619951971252838 Order of pole (three term test) 32.03596364489533 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3899999999999577 y2[1] (closed_form) 1.983700814811269 y2[1] (numeric) 1.983700814811274 absolute error 5.10702591327572e-15 relative error 2.5744940341528303e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.983700814811269 y1[1] (numeric) 1.9837008148112774 absolute error 8.43769498715119e-15 relative error 4.2535118825133716e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1768821726505725 Order of pole (three term test) 32.032332706939634 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1768821726505725 Order of pole (three term test) 32.032332706939634 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.3999999999999566 y2[1] (closed_form) 1.9854497299884528 y2[1] (numeric) 1.9854497299884575 absolute error 4.6629367034256575e-15 relative error 2.3485544020561914e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 y1[1] (closed_form) 1.9854497299884528 y1[1] (numeric) 1.9854497299884608 absolute error 7.993605777301127e-15 relative error 4.0260932606677567e-13% Desired digits 8 Estimated correct digits 12 Correct digits 15 h 0.001 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16749407507795308 Order of pole (three term test) 32.02888882966567 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1674940750779531 Order of pole (three term test) 32.028888829665675 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = neg ( diff ( y2 , x , 3 ) ) ; Iterations 1301 Total Elapsed Time 8 Seconds Elapsed Time(since restart) 8 Seconds Time to Timeout 2 Minutes 52.0 Seconds Percent Done 100.15384615384282%