##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.4 ## ## Trouble about Pi/2 ## $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 $glob_max_iter=20 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=10 $glob_display_interval=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=30.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y1 (x) return(1.0 + sin(x)) end def exact_soln_y2 (x) return(1.0 + sin(x)) end def exact_soln_y2p (x) return( cos(x)) end def exact_soln_y2pp (x) return( -sin(x)) end def exact_soln_y2ppp (x) return( -cos(x)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 estimated_h 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-10 range 1.2999999999999998 estimated_steps 1299999.9999999998 step_error 7.692307692307694e-17 est_needed_step_err 7.692307692307694e-17 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.4754661255148745e-184 estimated_step_error 2.4754661255148745e-184 best_h 2.0e-06 opt_iter 2 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6612575021518595e-176 estimated_step_error 1.6612575021518595e-176 best_h 4.0e-06 opt_iter 3 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1148514493392506e-168 estimated_step_error 1.1148514493392506e-168 best_h 8.0e-06 opt_iter 4 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.481646952858087e-161 estimated_step_error 7.481646952858087e-161 best_h 1.6e-05 opt_iter 5 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.020855692025619e-153 estimated_step_error 5.020855692025619e-153 best_h 3.2e-05 opt_iter 6 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.369449168191338e-145 estimated_step_error 3.369449168191338e-145 best_h 6.4e-05 opt_iter 7 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2612124147544466e-137 estimated_step_error 2.2612124147544466e-137 best_h 0.000128 opt_iter 8 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5174918888439645e-129 estimated_step_error 1.5174918888439645e-129 best_h 0.000256 opt_iter 9 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0183956259872493e-121 estimated_step_error 1.0183956259872493e-121 best_h 0.000512 opt_iter 10 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.834660258501093e-114 estimated_step_error 6.834660258501093e-114 best_h 0.001024 opt_iter 11 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.587096249794805e-106 estimated_step_error 4.587096249794805e-106 best_h 0.002048 opt_iter 12 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.078929872793795e-98 estimated_step_error 3.078929872793795e-98 best_h 0.004096 opt_iter 13 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.0670155907079864e-90 estimated_step_error 2.0670155907079864e-90 best_h 0.008192 opt_iter 14 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3881985593182528e-82 estimated_step_error 1.3881985593182528e-82 best_h 0.016384 opt_iter 15 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 9.33010720852238e-75 estimated_step_error 9.33010720852238e-75 best_h 0.032768 opt_iter 16 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.280205843940557e-67 estimated_step_error 6.280205843940557e-67 best_h 0.065536 opt_iter 17 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.239910926664728e-59 estimated_step_error 4.239910926664728e-59 best_h 0.131072 opt_iter 18 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.879361632773575e-51 estimated_step_error 2.879361632773575e-51 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y2[1] (analytic) 1.0998334166468282 y2[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.0998334166468282 y1[1] (numeric) 1.0998334166468282 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0993346653975307 Order of pole (three term test) 22.99003328892063 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.09933466539753073 Order of pole (three term test) 22.990033288920625 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11 y2[1] (analytic) 1.1097783008371749 y2[1] (numeric) 1.1097783008371749 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1097783008371749 y1[1] (numeric) 1.1097783008371749 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10911481154043486 Order of pole (three term test) 22.9879487246653 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.10911481154043486 Order of pole (three term test) 22.987948724665298 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12 y2[1] (analytic) 1.1197122072889194 y2[1] (numeric) 1.1197122072889194 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1197122072889194 y1[1] (numeric) 1.1197122072889194 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11885131321356744 Order of pole (three term test) 22.985668987426013 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.11885131321356741 Order of pole (three term test) 22.985668987426013 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.13 y2[1] (analytic) 1.129634142619695 y2[1] (numeric) 1.129634142619695 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.129634142619695 y1[1] (numeric) 1.129634142619695 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1285402759460777 Order of pole (three term test) 22.983194989067254 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.12854027594607773 Order of pole (three term test) 22.983194989067247 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.14 y2[1] (analytic) 1.1395431146442365 y2[1] (numeric) 1.1395431146442365 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1395431146442365 y1[1] (numeric) 1.1395431146442365 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13817782428205677 Order of pole (three term test) 22.98052771915538 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.13817782428205674 Order of pole (three term test) 22.980527719155383 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y2[1] (analytic) 1.1494381324735992 y2[1] (numeric) 1.1494381324735992 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1494381324735992 y1[1] (numeric) 1.1494381324735992 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1477601033306697 Order of pole (three term test) 22.977668244562803 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1477601033306697 Order of pole (three term test) 22.977668244562807 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16000000000000003 y2[1] (analytic) 1.159318206614246 y2[1] (numeric) 1.159318206614246 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.159318206614246 y1[1] (numeric) 1.159318206614246 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15728328030805896 Order of pole (three term test) 22.97461770904122 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.15728328030805902 Order of pole (three term test) 22.974617709041222 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17000000000000004 y2[1] (analytic) 1.1691823490669961 y2[1] (numeric) 1.1691823490669961 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1691823490669961 y1[1] (numeric) 1.1691823490669961 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1667435460704073 Order of pole (three term test) 22.971377332764174 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1667435460704074 Order of pole (three term test) 22.97137733276417 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.18000000000000005 y2[1] (analytic) 1.1790295734258243 y2[1] (numeric) 1.1790295734258243 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1790295734258243 y1[1] (numeric) 1.1790295734258243 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17613711663754517 Order of pole (three term test) 22.967948411838965 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1761371166375452 Order of pole (three term test) 22.967948411838968 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.19000000000000006 y2[1] (analytic) 1.1888588949765007 y2[1] (numeric) 1.1888588949765007 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1888588949765007 y1[1] (numeric) 1.1888588949765007 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18546023470649134 Order of pole (three term test) 22.964332317788255 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.18546023470649134 Order of pole (three term test) 22.964332317788262 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.20000000000000007 y2[1] (analytic) 1.1986693307950613 y2[1] (numeric) 1.1986693307950613 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.1986693307950613 y1[1] (numeric) 1.1986693307950613 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19470917115432534 Order of pole (three term test) 22.960530497001447 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1947091711543253 Order of pole (three term test) 22.96053049700144 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.21000000000000008 y2[1] (analytic) 1.2084598998460996 y2[1] (numeric) 1.2084598998460996 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2084598998460996 y1[1] (numeric) 1.2084598998460996 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20388022652978496 Order of pole (three term test) 22.956544470156153 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.203880226529785 Order of pole (three term test) 22.95654447015615 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.22000000000000008 y2[1] (analytic) 1.2182296230808694 y2[1] (numeric) 1.2182296230808694 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2182296230808694 y1[1] (numeric) 1.2182296230808694 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21296973253299986 Order of pole (three term test) 22.952375831609974 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2129697325329999 Order of pole (three term test) 22.952375831609988 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2300000000000001 y2[1] (analytic) 1.2279775235351884 y2[1] (numeric) 1.2279775235351884 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2279775235351884 y1[1] (numeric) 1.2279775235351884 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22197405348276 Order of pole (three term test) 22.948026248762766 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.22197405348276003 Order of pole (three term test) 22.948026248762766 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2400000000000001 y2[1] (analytic) 1.2377026264271347 y2[1] (numeric) 1.2377026264271347 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.2377026264271347 y1[1] (numeric) 1.2377026264271347 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23088958777074187 Order of pole (three term test) 22.943497461389647 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2308895877707418 Order of pole (three term test) 22.943497461389647 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y2[1] (analytic) 1.247403959254523 y2[1] (numeric) 1.247403959254523 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.247403959254523 y1[1] (numeric) 1.247403959254523 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23971276930210164 Order of pole (three term test) 22.938791280945185 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.23971276930210159 Order of pole (three term test) 22.938791280945182 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y2[1] (analytic) 1.2570805518921553 y2[1] (numeric) 1.257080551892155 absolute error 2.220446049250313e-16 relative error 1.7663514449476623e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2570805518921553 y1[1] (numeric) 1.257080551892155 absolute error 2.220446049250313e-16 relative error 1.7663514449476623e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24844006892186826 Order of pole (three term test) 22.933909589838827 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2484400689218683 Order of pole (three term test) 22.933909589838827 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y2[1] (analytic) 1.2667314366888314 y2[1] (numeric) 1.2667314366888311 absolute error 2.220446049250313e-16 relative error 1.7528940902062405e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2667314366888314 y1[1] (numeric) 1.2667314366888311 absolute error 2.220446049250313e-16 relative error 1.7528940902062405e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.25706799582655654 Order of pole (three term test) 22.928854340681912 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2570679958265565 Order of pole (three term test) 22.928854340681905 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y2[1] (analytic) 1.2763556485641139 y2[1] (numeric) 1.2763556485641137 absolute error 2.220446049250313e-16 relative error 1.7396765954287822e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2763556485641139 y1[1] (numeric) 1.2763556485641137 absolute error 2.220446049250313e-16 relative error 1.7396765954287822e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2655930989604418 Order of pole (three term test) 22.92362755550671 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.26559309896044186 Order of pole (three term test) 22.92362755550671 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y2[1] (analytic) 1.2859522251048356 y2[1] (numeric) 1.2859522251048354 absolute error 2.220446049250313e-16 relative error 1.726694045005672e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2859522251048356 y1[1] (numeric) 1.2859522251048354 absolute error 2.220446049250313e-16 relative error 1.726694045005672e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.27401196839593656 Order of pole (three term test) 22.918231324957592 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.27401196839593667 Order of pole (three term test) 22.918231324957603 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y2[1] (analytic) 1.2955202066613398 y2[1] (numeric) 1.2955202066613394 absolute error 4.440892098500626e-16 relative error 3.427883313333386e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.2955202066613398 y1[1] (numeric) 1.2955202066613394 absolute error 4.440892098500626e-16 relative error 3.427883313333386e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2823212366975176 Order of pole (three term test) 22.912667807454845 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2823212366975175 Order of pole (three term test) 22.912667807454838 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y2[1] (analytic) 1.3050586364434436 y2[1] (numeric) 1.3050586364434433 absolute error 2.220446049250313e-16 relative error 1.7014147772712272e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3050586364434436 y1[1] (numeric) 1.3050586364434433 absolute error 2.220446049250313e-16 relative error 1.7014147772712272e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2905175802686523 Order of pole (three term test) 22.906939228331268 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29051758026865243 Order of pole (three term test) 22.906939228331268 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y2[1] (analytic) 1.3145665606161179 y2[1] (numeric) 1.3145665606161177 absolute error 2.220446049250313e-16 relative error 1.6891088787543956e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3145665606161179 y1[1] (numeric) 1.3145665606161177 absolute error 2.220446049250313e-16 relative error 1.6891088787543956e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29859772068119583 Order of pole (three term test) 22.90104787894215 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29859772068119567 Order of pole (three term test) 22.901047878942144 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y2[1] (analytic) 1.3240430283948685 y2[1] (numeric) 1.3240430283948683 absolute error 2.220446049250313e-16 relative error 1.677019554222607e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3240430283948685 y1[1] (numeric) 1.3240430283948683 absolute error 2.220446049250313e-16 relative error 1.677019554222607e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30655842598671673 Order of pole (three term test) 22.89499611574868 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3065584259867167 Order of pole (three term test) 22.894996115748686 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y2[1] (analytic) 1.3334870921408146 y2[1] (numeric) 1.3334870921408144 absolute error 2.220446049250313e-16 relative error 1.6651425141922832e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3334870921408146 y1[1] (numeric) 1.3334870921408144 absolute error 2.220446049250313e-16 relative error 1.6651425141922832e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3143965120092342 Order of pole (three term test) 22.888786359375462 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.31439651200923413 Order of pole (three term test) 22.888786359375462 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y2[1] (analytic) 1.3428978074554516 y2[1] (numeric) 1.3428978074554514 absolute error 2.220446049250313e-16 relative error 1.653473582965823e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3428978074554516 y1[1] (numeric) 1.3428978074554514 absolute error 2.220446049250313e-16 relative error 1.653473582965823e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.32210884361884573 Order of pole (three term test) 22.882421093642243 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.32210884361884573 Order of pole (three term test) 22.882421093642243 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y2[1] (analytic) 1.35227423327509 y2[1] (numeric) 1.35227423327509 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.35227423327509 y1[1] (numeric) 1.35227423327509 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3296923359857367 Order of pole (three term test) 22.87590286457045 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3296923359857367 Order of pole (three term test) 22.875902864570445 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y2[1] (analytic) 1.3616154319649623 y2[1] (numeric) 1.361615431964962 absolute error 2.220446049250313e-16 relative error 1.630743892235389e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3616154319649623 y1[1] (numeric) 1.361615431964962 absolute error 2.220446049250313e-16 relative error 1.630743892235389e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33714395581407275 Order of pole (three term test) 22.86923427936479 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.33714395581407286 Order of pole (three term test) 22.86923427936479 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y2[1] (analytic) 1.3709204694129828 y2[1] (numeric) 1.3709204694129828 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.3709204694129828 y1[1] (numeric) 1.3709204694129828 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34446072255527593 Order of pole (three term test) 22.862418005370447 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3444607225552758 Order of pole (three term test) 22.86241800537045 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y2[1] (analytic) 1.3801884151231616 y2[1] (numeric) 1.3801884151231616 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.3801884151231616 y1[1] (numeric) 1.3801884151231616 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35163970960020513 Order of pole (three term test) 22.85545676900614 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35163970960020513 Order of pole (three term test) 22.85545676900614 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y2[1] (analytic) 1.3894183423086508 y2[1] (numeric) 1.3894183423086506 absolute error 2.220446049250313e-16 relative error 1.5981119448594803e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3894183423086508 y1[1] (numeric) 1.3894183423086506 absolute error 2.220446049250313e-16 relative error 1.5981119448594803e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35867804544976106 Order of pole (three term test) 22.84835335467358 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35867804544976106 Order of pole (three term test) 22.848353354673574 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y2[1] (analytic) 1.3986093279844232 y2[1] (numeric) 1.398609327984423 absolute error 2.220446049250313e-16 relative error 1.587609924245438e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.3986093279844232 y1[1] (numeric) 1.398609327984423 absolute error 2.220446049250313e-16 relative error 1.587609924245438e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.36557291486344784 Order of pole (three term test) 22.84111060364381 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3655729148634479 Order of pole (three term test) 22.841110603643806 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y2[1] (analytic) 1.4077604530595704 y2[1] (numeric) 1.4077604530595702 absolute error 2.220446049250313e-16 relative error 1.57728969046153e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4077604530595704 y1[1] (numeric) 1.4077604530595702 absolute error 2.220446049250313e-16 relative error 1.57728969046153e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37232155998542954 Order of pole (three term test) 22.833731412920653 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37232155998542954 Order of pole (three term test) 22.833731412920653 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y2[1] (analytic) 1.416870802429211 y2[1] (numeric) 1.4168708024292107 absolute error 2.220446049250313e-16 relative error 1.567147862348056e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.416870802429211 y1[1] (numeric) 1.4168708024292107 absolute error 2.220446049250313e-16 relative error 1.567147862348056e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37892128144763815 Order of pole (three term test) 22.826218734082023 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37892128144763826 Order of pole (three term test) 22.82621873408202 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y2[1] (analytic) 1.4259394650659998 y2[1] (numeric) 1.4259394650659996 absolute error 2.220446049250313e-16 relative error 1.5571811452371433e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4259394650659998 y1[1] (numeric) 1.4259394650659996 absolute error 2.220446049250313e-16 relative error 1.5571811452371433e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3853694394494845 Order of pole (three term test) 22.818575572099288 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.38536943944948443 Order of pole (three term test) 22.818575572099288 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y2[1] (analytic) 1.4349655341112304 y2[1] (numeric) 1.4349655341112302 absolute error 2.220446049250313e-16 relative error 1.5473863284288448e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4349655341112304 y1[1] (numeric) 1.4349655341112302 absolute error 2.220446049250313e-16 relative error 1.5473863284288448e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3916634548137414 Order of pole (three term test) 22.81080498413533 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.39166345481374143 Order of pole (three term test) 22.810804984135327 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y2[1] (analytic) 1.44394810696552 y2[1] (numeric) 1.4439481069655198 absolute error 2.220446049250313e-16 relative error 1.5377602827546315e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.44394810696552 y1[1] (numeric) 1.4439481069655198 absolute error 2.220446049250313e-16 relative error 1.5377602827546315e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.39780081001818285 Order of pole (three term test) 22.80291007832173 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3978008100181831 Order of pole (three term test) 22.802910078321734 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y2[1] (analytic) 1.4528862853790685 y2[1] (numeric) 1.4528862853790683 absolute error 2.220446049250313e-16 relative error 1.5282999582248675e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4528862853790685 y1[1] (numeric) 1.4528862853790683 absolute error 2.220446049250313e-16 relative error 1.5282999582248675e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4037790502025567 Order of pole (three term test) 22.794894012515545 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.403779050202557 Order of pole (three term test) 22.79489401251555 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y2[1] (analytic) 1.461779175541483 y2[1] (numeric) 1.4617791755414828 absolute error 2.220446049250313e-16 relative error 1.5190023817570114e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.461779175541483 y1[1] (numeric) 1.4617791755414828 absolute error 2.220446049250313e-16 relative error 1.5190023817570114e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4095957841504992 Order of pole (three term test) 22.786759993036227 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.40959578415049913 Order of pole (three term test) 22.786759993036224 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y2[1] (analytic) 1.4706258881711582 y2[1] (numeric) 1.470625888171158 absolute error 2.220446049250313e-16 relative error 1.5098646549814355e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4706258881711582 y1[1] (numeric) 1.470625888171158 absolute error 2.220446049250313e-16 relative error 1.5098646549814355e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4152486852459853 Order of pole (three term test) 22.77851127338311 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4152486852459853 Order of pole (three term test) 22.77851127338311 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y2[1] (analytic) 1.4794255386042032 y2[1] (numeric) 1.479425538604203 absolute error 2.220446049250313e-16 relative error 1.500883952121877e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4794255386042032 y1[1] (numeric) 1.479425538604203 absolute error 2.220446049250313e-16 relative error 1.500883952121877e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4207354924039483 Order of pole (three term test) 22.77015115293407 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.42073549240394825 Order of pole (three term test) 22.77015115293407 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y2[1] (analytic) 1.4881772468829078 y2[1] (numeric) 1.4881772468829075 absolute error 2.220446049250313e-16 relative error 1.492057517947673e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.4881772468829078 y1[1] (numeric) 1.4881772468829075 absolute error 2.220446049250313e-16 relative error 1.492057517947673e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4260540109746813 Order of pole (three term test) 22.761682975625824 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.42605401097468115 Order of pole (three term test) 22.761682975625824 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y2[1] (analytic) 1.496880137843737 y2[1] (numeric) 1.4968801378437369 absolute error 2.220446049250313e-16 relative error 1.4833826657950556e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.496880137843737 y1[1] (numeric) 1.4968801378437369 absolute error 2.220446049250313e-16 relative error 1.4833826657950556e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4312021136216693 Order of pole (three term test) 22.753110128616385 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.43120211362166955 Order of pole (three term test) 22.753110128616388 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y2[1] (analytic) 1.5055333412048473 y2[1] (numeric) 1.505533341204847 absolute error 2.220446049250313e-16 relative error 1.474856775654889e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5055333412048473 y1[1] (numeric) 1.505533341204847 absolute error 2.220446049250313e-16 relative error 1.474856775654889e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4361777411724931 Order of pole (three term test) 22.744436040930264 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4361777411724932 Order of pole (three term test) 22.744436040930267 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y2[1] (analytic) 1.5141359916531134 y2[1] (numeric) 1.5141359916531132 absolute error 2.220446049250313e-16 relative error 1.4664772923243572e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5141359916531134 y1[1] (numeric) 1.5141359916531132 absolute error 2.220446049250313e-16 relative error 1.4664772923243572e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.44097890344247376 Order of pole (three term test) 22.73566418208686 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4409789034424739 Order of pole (three term test) 22.735664182086865 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y2[1] (analytic) 1.5226872289306594 y2[1] (numeric) 1.5226872289306592 absolute error 2.220446049250313e-16 relative error 1.4582417236202013e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5226872289306594 y1[1] (numeric) 1.5226872289306592 absolute error 2.220446049250313e-16 relative error 1.4582417236202013e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.44560368003071765 Order of pole (three term test) 22.726798060712788 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4456036800307178 Order of pole (three term test) 22.72679806071279 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y2[1] (analytic) 1.5311861979208836 y2[1] (numeric) 1.5311861979208834 absolute error 2.220446049250313e-16 relative error 1.4501476386512227e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5311861979208836 y1[1] (numeric) 1.5311861979208834 absolute error 2.220446049250313e-16 relative error 1.4501476386512227e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45005022108825243 Order of pole (three term test) 22.717841223138354 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4500502210882525 Order of pole (three term test) 22.71784122313836 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y2[1] (analytic) 1.5396320487339694 y2[1] (numeric) 1.5396320487339692 absolute error 2.220446049250313e-16 relative error 1.4421926661478455e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5396320487339694 y1[1] (numeric) 1.5396320487339692 absolute error 2.220446049250313e-16 relative error 1.4421926661478455e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4543167480579415 Order of pole (three term test) 22.708797251979178 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4543167480579414 Order of pole (three term test) 22.708797251979178 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y2[1] (analytic) 1.548023936791874 y2[1] (numeric) 1.5480239367918736 absolute error 4.440892098500626e-16 relative error 2.8687489856932924e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.548023936791874 y1[1] (numeric) 1.5480239367918736 absolute error 4.440892098500626e-16 relative error 2.8687489856932924e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45840155438588354 Order of pole (three term test) 22.699669764703142 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4584015543858836 Order of pole (three term test) 22.69966976470314 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y2[1] (analytic) 1.556361022912784 y2[1] (numeric) 1.5563610229127838 absolute error 2.220446049250313e-16 relative error 1.4266908619278262e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.556361022912784 y1[1] (numeric) 1.5563610229127838 absolute error 2.220446049250313e-16 relative error 1.4266908619278262e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4623030062040103 Order of pole (three term test) 22.690462412183443 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46230300620401044 Order of pole (three term test) 22.690462412183443 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y2[1] (analytic) 1.5646424733950357 y2[1] (numeric) 1.5646424733950353 absolute error 4.440892098500626e-16 relative error 2.838279143007391e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5646424733950357 y1[1] (numeric) 1.5646424733950353 absolute error 4.440892098500626e-16 relative error 2.838279143007391e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4660195429836131 Order of pole (three term test) 22.681178877238334 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46601954298361303 Order of pole (three term test) 22.681178877238334 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y2[1] (analytic) 1.5728674601004817 y2[1] (numeric) 1.572867460100481 absolute error 6.661338147750939e-16 relative error 4.2351554194689636e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5728674601004817 y1[1] (numeric) 1.572867460100481 absolute error 6.661338147750939e-16 relative error 4.2351554194689636e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46954967815953363 Order of pole (three term test) 22.671822873158018 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46954967815953363 Order of pole (three term test) 22.671822873158018 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y2[1] (analytic) 1.5810351605373054 y2[1] (numeric) 1.581035160537305 absolute error 4.440892098500626e-16 relative error 2.8088509410451158e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5810351605373054 y1[1] (numeric) 1.581035160537305 absolute error 4.440892098500626e-16 relative error 2.8088509410451158e-14% Correct digits 16 h 0.01 NO INFO (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) 22.662398142219388 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47289199972476925 Order of pole (three term test) 22.662398142219388 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y2[1] (analytic) 1.58914475794227 y2[1] (numeric) 1.5891447579422695 absolute error 4.440892098500626e-16 relative error 2.7945170358495143e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.58914475794227 y1[1] (numeric) 1.5891447579422695 absolute error 4.440892098500626e-16 relative error 2.7945170358495143e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4760451707952578 Order of pole (three term test) 22.65290845418915 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4760451707952578 Order of pole (three term test) 22.65290845418915 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y2[1] (analytic) 1.5971954413623926 y2[1] (numeric) 1.597195441362392 absolute error 4.440892098500626e-16 relative error 2.780431238091055e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.5971954413623926 y1[1] (numeric) 1.597195441362392 absolute error 4.440892098500626e-16 relative error 2.780431238091055e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.47900793014461235 Order of pole (three term test) 22.643357604815975 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47900793014461235 Order of pole (three term test) 22.643357604815975 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y2[1] (analytic) 1.6051864057360399 y2[1] (numeric) 1.6051864057360397 absolute error 2.220446049250313e-16 relative error 1.3832948256449711e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6051864057360399 y1[1] (numeric) 1.6051864057360397 absolute error 2.220446049250313e-16 relative error 1.3832948256449711e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4817790927085964 Order of pole (three term test) 22.633749414312287 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.48177909270859665 Order of pole (three term test) 22.633749414312295 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y2[1] (analytic) 1.6131168519734342 y2[1] (numeric) 1.6131168519734338 absolute error 4.440892098500626e-16 relative error 2.7529884726377908e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6131168519734342 y1[1] (numeric) 1.6131168519734338 absolute error 4.440892098500626e-16 relative error 2.7529884726377908e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4843575500591326 Order of pole (three term test) 22.624087725826186 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4843575500591326 Order of pole (three term test) 22.62408772582619 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y2[1] (analytic) 1.6209859870365602 y2[1] (numeric) 1.6209859870365597 absolute error 4.440892098500626e-16 relative error 2.7396239905931187e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6209859870365602 y1[1] (numeric) 1.6209859870365597 absolute error 4.440892098500626e-16 relative error 2.7396239905931187e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4867422708476597 Order of pole (three term test) 22.614376403904227 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4867422708476597 Order of pole (three term test) 22.61437640390423 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y2[1] (analytic) 1.628793024018469 y2[1] (numeric) 1.6287930240184685 absolute error 4.440892098500626e-16 relative error 2.726492582553123e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.628793024018469 y1[1] (numeric) 1.6287930240184685 absolute error 4.440892098500626e-16 relative error 2.726492582553123e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48893230121765796 Order of pole (three term test) 22.60461933294571 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.488932301217658 Order of pole (three term test) 22.60461933294571 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y2[1] (analytic) 1.6365371822219683 y2[1] (numeric) 1.6365371822219679 absolute error 4.440892098500626e-16 relative error 2.713590712599095e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6365371822219683 y1[1] (numeric) 1.6365371822219679 absolute error 4.440892098500626e-16 relative error 2.713590712599095e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49092676518617967 Order of pole (three term test) 22.594820415648915 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49092676518617967 Order of pole (three term test) 22.594820415648915 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y2[1] (analytic) 1.6442176872376915 y2[1] (numeric) 1.644217687237691 absolute error 4.440892098500626e-16 relative error 2.7009149293129102e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6442176872376915 y1[1] (numeric) 1.644217687237691 absolute error 4.440892098500626e-16 relative error 2.7009149293129102e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49272486499423007 Order of pole (three term test) 22.584983571450124 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49272486499423007 Order of pole (three term test) 22.58498357145012 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y2[1] (analytic) 1.6518337710215372 y2[1] (numeric) 1.6518337710215367 absolute error 4.440892098500626e-16 relative error 2.6884618636621422e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6518337710215372 y1[1] (numeric) 1.6518337710215367 absolute error 4.440892098500626e-16 relative error 2.6884618636621422e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4943258814258598 Order of pole (three term test) 22.575112734955844 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4943258814258599 Order of pole (three term test) 22.575112734955844 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y2[1] (analytic) 1.6593846719714735 y2[1] (numeric) 1.659384671971473 absolute error 4.440892098500626e-16 relative error 2.6762282269514477e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6593846719714735 y1[1] (numeric) 1.659384671971473 absolute error 4.440892098500626e-16 relative error 2.6762282269514477e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49572917409584316 Order of pole (three term test) 22.565211854369075 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4957291740958434 Order of pole (three term test) 22.56521185436908 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y2[1] (analytic) 1.6668696350036982 y2[1] (numeric) 1.6668696350036978 absolute error 4.440892098500626e-16 relative error 2.664210808837953e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6668696350036982 y1[1] (numeric) 1.6668696350036978 absolute error 4.440892098500626e-16 relative error 2.664210808837953e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4969341817058225 Order of pole (three term test) 22.55528488991004 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49693418170582243 Order of pole (three term test) 22.555284889910038 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y2[1] (analytic) 1.6742879116281455 y2[1] (numeric) 1.674287911628145 absolute error 4.440892098500626e-16 relative error 2.6524064754084752e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6742879116281455 y1[1] (numeric) 1.674287911628145 absolute error 4.440892098500626e-16 relative error 2.6524064754084752e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49794042226882007 Order of pole (three term test) 22.54533581223216 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49794042226882007 Order of pole (three term test) 22.545335812232157 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y2[1] (analytic) 1.6816387600233345 y2[1] (numeric) 1.6816387600233342 absolute error 2.220446049250313e-16 relative error 1.3204060836582419e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6816387600233345 y1[1] (numeric) 1.6816387600233342 absolute error 2.220446049250313e-16 relative error 1.3204060836582419e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49874749330202717 Order of pole (three term test) 22.535368600833852 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49874749330202717 Order of pole (three term test) 22.535368600833852 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y2[1] (analytic) 1.6889214451105516 y2[1] (numeric) 1.6889214451105514 absolute error 2.220446049250313e-16 relative error 1.3147124489883954e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6889214451105516 y1[1] (numeric) 1.6889214451105514 absolute error 2.220446049250313e-16 relative error 1.3147124489883954e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49935507198779144 Order of pole (three term test) 22.52538724246679 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4993550719877915 Order of pole (three term test) 22.52538724246679 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y2[1] (analytic) 1.6961352386273572 y2[1] (numeric) 1.696135238627357 absolute error 2.220446049250313e-16 relative error 1.3091208759080252e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.6961352386273572 y1[1] (numeric) 1.696135238627357 absolute error 2.220446049250313e-16 relative error 1.3091208759080252e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49976291530273953 Order of pole (three term test) 22.515395729541233 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49976291530273964 Order of pole (three term test) 22.515395729541233 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y2[1] (analytic) 1.7032794192004106 y2[1] (numeric) 1.7032794192004104 absolute error 2.220446049250313e-16 relative error 1.3036299412886006e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7032794192004106 y1[1] (numeric) 1.7032794192004104 absolute error 2.220446049250313e-16 relative error 1.3036299412886006e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4999708601149832 Order of pole (three term test) 22.50539805852914 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4999708601149832 Order of pole (three term test) 22.50539805852914 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y2[1] (analytic) 1.7103532724176083 y2[1] (numeric) 1.710353272417608 absolute error 2.220446049250313e-16 relative error 1.298238255838036e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7103532724176083 y1[1] (numeric) 1.710353272417608 absolute error 2.220446049250313e-16 relative error 1.298238255838036e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4999788232493701 Order of pole (three term test) 22.495398228365598 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4999788232493701 Order of pole (three term test) 22.495398228365598 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y2[1] (analytic) 1.7173560908995231 y2[1] (numeric) 1.717356090899523 absolute error 2.220446049250313e-16 relative error 1.2929444633042176e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7173560908995231 y1[1] (numeric) 1.717356090899523 absolute error 2.220446049250313e-16 relative error 1.2929444633042176e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4997868015207526 Order of pole (three term test) 22.485400238849355 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4997868015207526 Order of pole (three term test) 22.48540023884935 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y2[1] (analytic) 1.724287174370143 y2[1] (numeric) 1.7242871743701427 absolute error 2.220446049250313e-16 relative error 1.2877472397029281e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.724287174370143 y1[1] (numeric) 1.7242871743701427 absolute error 2.220446049250313e-16 relative error 1.2877472397029281e-14% Correct digits 16 h 0.01 NO INFO (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) 22.47540808904291 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49939487173526187 Order of pole (three term test) 22.47540808904291 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y2[1] (analytic) 1.7311458297268962 y2[1] (numeric) 1.731145829726896 absolute error 2.220446049250313e-16 relative error 1.2826452925693777e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7311458297268962 y1[1] (numeric) 1.731145829726896 absolute error 2.220446049250313e-16 relative error 1.2826452925693777e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4988031906595867 Order of pole (three term test) 22.46542577567297 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4988031906595868 Order of pole (three term test) 22.46542577567297 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y2[1] (analytic) 1.737931371109963 y2[1] (numeric) 1.7379313711099629 absolute error 2.220446049250313e-16 relative error 1.2776373602325751e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.737931371109963 y1[1] (numeric) 1.7379313711099629 absolute error 2.220446049250313e-16 relative error 1.2776373602325751e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4980119949582684 Order of pole (three term test) 22.45545729153177 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49801199495826837 Order of pole (three term test) 22.45545729153177 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y2[1] (analytic) 1.7446431199708599 y2[1] (numeric) 1.7446431199708594 absolute error 4.440892098500626e-16 relative error 2.5454444222236127e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7446431199708599 y1[1] (numeric) 1.7446431199708594 absolute error 4.440892098500626e-16 relative error 2.5454444222236127e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4970216010990381 Order of pole (three term test) 22.445506623880064 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4970216010990381 Order of pole (three term test) 22.445506623880068 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y2[1] (analytic) 1.7512804051402933 y2[1] (numeric) 1.7512804051402928 absolute error 4.440892098500626e-16 relative error 2.5357972860690295e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7512804051402933 y1[1] (numeric) 1.7512804051402928 absolute error 4.440892098500626e-16 relative error 2.5357972860690295e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49583240522623423 Order of pole (three term test) 22.435577752852236 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49583240522623423 Order of pole (three term test) 22.43557775285224 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y2[1] (analytic) 1.7578425628952774 y2[1] (numeric) 1.7578425628952772 absolute error 2.220446049250313e-16 relative error 1.2631654825749006e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7578425628952774 y1[1] (numeric) 1.7578425628952772 absolute error 2.220446049250313e-16 relative error 1.2631654825749006e-14% Correct digits 16 h 0.01 NO INFO (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) 22.425674649864316 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4944448830023508 Order of pole (three term test) 22.42567464986432 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y2[1] (analytic) 1.7643289370255055 y2[1] (numeric) 1.7643289370255053 absolute error 2.220446049250313e-16 relative error 1.258521584412586e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7643289370255055 y1[1] (numeric) 1.7643289370255053 absolute error 2.220446049250313e-16 relative error 1.258521584412586e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.49285958941777663 Order of pole (three term test) 22.415801276025455 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49285958941777663 Order of pole (three term test) 22.41580127602546 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y2[1] (analytic) 1.7707388788989697 y2[1] (numeric) 1.7707388788989695 absolute error 2.220446049250313e-16 relative error 1.2539658307107185e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7707388788989697 y1[1] (numeric) 1.7707388788989695 absolute error 2.220446049250313e-16 relative error 1.2539658307107185e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4910771585688092 Order of pole (three term test) 22.40596158055356 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.49107715856880924 Order of pole (three term test) 22.40596158055356 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y2[1] (analytic) 1.7770717475268243 y2[1] (numeric) 1.777071747526824 absolute error 2.220446049250313e-16 relative error 1.2494971305129008e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7770717475268243 y1[1] (numeric) 1.777071747526824 absolute error 2.220446049250313e-16 relative error 1.2494971305129008e-14% Correct digits 16 h 0.01 NO INFO (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) 22.396159499195612 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4890983034040222 Order of pole (three term test) 22.39615949919561 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y2[1] (analytic) 1.7833269096274837 y2[1] (numeric) 1.7833269096274835 absolute error 2.220446049250313e-16 relative error 1.2451144191583686e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7833269096274837 y1[1] (numeric) 1.7833269096274835 absolute error 2.220446049250313e-16 relative error 1.2451144191583686e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48692381543909763 Order of pole (three term test) 22.386398952653458 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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) 22.386398952653458 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y2[1] (analytic) 1.789503739689951 y2[1] (numeric) 1.7895037396899505 absolute error 4.440892098500626e-16 relative error 2.4816333154297037e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.789503739689951 y1[1] (numeric) 1.7895037396899505 absolute error 4.440892098500626e-16 relative error 2.4816333154297037e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4845545644402282 Order of pole (three term test) 22.376683845015588 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4845545644402282 Order of pole (three term test) 22.376683845015588 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y2[1] (analytic) 1.7956016200363665 y2[1] (numeric) 1.795601620036366 absolute error 4.440892098500626e-16 relative error 2.473205664857155e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.7956016200363665 y1[1] (numeric) 1.795601620036366 absolute error 4.440892098500626e-16 relative error 2.473205664857155e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.48199149807622393 Order of pole (three term test) 22.367018062195505 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.48199149807622393 Order of pole (three term test) 22.367018062195505 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y2[1] (analytic) 1.8016199408837776 y2[1] (numeric) 1.8016199408837772 absolute error 4.440892098500626e-16 relative error 2.464943908381789e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8016199408837776 y1[1] (numeric) 1.8016199408837772 absolute error 4.440892098500626e-16 relative error 2.464943908381789e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.47923564153945714 Order of pole (three term test) 22.35740547037749 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4792356415394571 Order of pole (three term test) 22.357405470377486 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y2[1] (analytic) 1.8075581004051147 y2[1] (numeric) 1.8075581004051142 absolute error 4.440892098500626e-16 relative error 2.4568461160420358e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8075581004051147 y1[1] (numeric) 1.8075581004051142 absolute error 4.440892098500626e-16 relative error 2.4568461160420358e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.47628809713579795 Order of pole (three term test) 22.34784991447009 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.47628809713579784 Order of pole (three term test) 22.347849914470086 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y2[1] (analytic) 1.8134155047893743 y2[1] (numeric) 1.8134155047893736 absolute error 6.661338147750939e-16 relative error 3.673365607693227e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8134155047893743 y1[1] (numeric) 1.8134155047893736 absolute error 6.661338147750939e-16 relative error 3.673365607693227e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4731500438437073 Order of pole (three term test) 22.338355216568246 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4731500438437074 Order of pole (three term test) 22.33835521656825 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y2[1] (analytic) 1.8191915683009987 y2[1] (numeric) 1.8191915683009983 absolute error 4.440892098500626e-16 relative error 2.4411349392126512e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8191915683009987 y1[1] (numeric) 1.8191915683009983 absolute error 4.440892098500626e-16 relative error 2.4411349392126512e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46982273684266257 Order of pole (three term test) 22.32892517442455 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.46982273684266285 Order of pole (three term test) 22.32892517442455 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y2[1] (analytic) 1.8248857133384506 y2[1] (numeric) 1.82488571333845 absolute error 6.661338147750939e-16 relative error 3.650276890800285e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8248857133384506 y1[1] (numeric) 1.82488571333845 absolute error 6.661338147750939e-16 relative error 3.650276890800285e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.46630750701110035 Order of pole (three term test) 22.31956355993012 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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) 22.319563559930117 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y2[1] (analytic) 1.830497370491971 y2[1] (numeric) 1.8304973704919705 absolute error 4.440892098500626e-16 relative error 2.4260576224193518e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.830497370491971 y1[1] (numeric) 1.8304973704919705 absolute error 4.440892098500626e-16 relative error 2.4260576224193518e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4626057603940843 Order of pole (three term test) 22.310274117605925 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4626057603940843 Order of pole (three term test) 22.310274117605925 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y2[1] (analytic) 1.8360259786005209 y2[1] (numeric) 1.8360259786005206 absolute error 2.220446049250313e-16 relative error 1.209376160866095e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8360259786005209 y1[1] (numeric) 1.8360259786005206 absolute error 2.220446049250313e-16 relative error 1.209376160866095e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45871897764090497 Order of pole (three term test) 22.301060563105043 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4587189776409049 Order of pole (three term test) 22.301060563105043 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y2[1] (analytic) 1.8414709848078967 y2[1] (numeric) 1.8414709848078967 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.8414709848078967 y1[1] (numeric) 1.8414709848078967 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4546487134128411 Order of pole (three term test) 22.29192658172643 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4546487134128411 Order of pole (three term test) 22.29192658172643 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0100000000000007 y2[1] (analytic) 1.8468318446180154 y2[1] (numeric) 1.8468318446180154 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.8468318446180154 y1[1] (numeric) 1.8468318446180154 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.45039659576131386 Order of pole (three term test) 22.282875826940852 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.45039659576131386 Order of pole (three term test) 22.28287582694085 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0200000000000007 y2[1] (analytic) 1.8521080219493633 y2[1] (numeric) 1.852108021949363 absolute error 2.220446049250313e-16 relative error 1.198875023991997e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8521080219493633 y1[1] (numeric) 1.852108021949363 absolute error 2.220446049250313e-16 relative error 1.198875023991997e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4459643254766899 Order of pole (three term test) 22.273911918929546 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.44596432547668996 Order of pole (three term test) 22.27391191892955 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0300000000000007 y2[1] (analytic) 1.8572989891886036 y2[1] (numeric) 1.8572989891886036 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.8572989891886036 y1[1] (numeric) 1.8572989891886036 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4413536754079872 Order of pole (three term test) 22.265038443136202 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.44135367540798726 Order of pole (three term test) 22.2650384431362 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0400000000000007 y2[1] (analytic) 1.8624042272433388 y2[1] (numeric) 1.8624042272433385 absolute error 2.220446049250313e-16 relative error 1.19224710552603e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8624042272433388 y1[1] (numeric) 1.8624042272433385 absolute error 2.220446049250313e-16 relative error 1.19224710552603e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4365664897537585 Order of pole (three term test) 22.25625894883282 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4365664897537584 Order of pole (three term test) 22.256258948832823 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0500000000000007 y2[1] (analytic) 1.8674232255940173 y2[1] (numeric) 1.867423225594017 absolute error 2.220446049250313e-16 relative error 1.1890427508975643e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8674232255940173 y1[1] (numeric) 1.867423225594017 absolute error 2.220446049250313e-16 relative error 1.1890427508975643e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.43160468332443697 Order of pole (three term test) 22.247576947700068 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.431604683324437 Order of pole (three term test) 22.24757694770007 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0600000000000007 y2[1] (analytic) 1.8723554823449866 y2[1] (numeric) 1.8723554823449864 absolute error 2.220446049250313e-16 relative error 1.1859105122865712e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8723554823449866 y1[1] (numeric) 1.8723554823449864 absolute error 2.220446049250313e-16 relative error 1.1859105122865712e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4264702407764381 Order of pole (three term test) 22.23899591242265 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.42647024077643814 Order of pole (three term test) 22.238995912422645 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0700000000000007 y2[1] (analytic) 1.877200504274682 y2[1] (numeric) 1.8772005042746818 absolute error 2.220446049250313e-16 relative error 1.1828496978314287e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.877200504274682 y1[1] (numeric) 1.8772005042746818 absolute error 2.220446049250313e-16 relative error 1.1828496978314287e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.421165215818323 Order of pole (three term test) 22.23051927530025 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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) 22.230519275300242 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0800000000000007 y2[1] (analytic) 1.8819578068849478 y2[1] (numeric) 1.8819578068849476 absolute error 2.220446049250313e-16 relative error 1.1798596340082871e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8819578068849478 y1[1] (numeric) 1.8819578068849476 absolute error 2.220446049250313e-16 relative error 1.1798596340082871e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4156917303893417 Order of pole (three term test) 22.22215042687469 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.4156917303893417 Order of pole (three term test) 22.2221504268747 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.0900000000000007 y2[1] (analytic) 1.8866269144494876 y2[1] (numeric) 1.8866269144494874 absolute error 2.220446049250313e-16 relative error 1.1769396653064461e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8866269144494876 y1[1] (numeric) 1.8866269144494874 absolute error 2.220446049250313e-16 relative error 1.1769396653064461e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4100519738106871 Order of pole (three term test) 22.21389271457378 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.41005197381068703 Order of pole (three term test) 22.21389271457378 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1000000000000008 y2[1] (analytic) 1.8912073600614356 y2[1] (numeric) 1.8912073600614354 absolute error 2.220446049250313e-16 relative error 1.174089153913922e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.8912073600614356 y1[1] (numeric) 1.8912073600614354 absolute error 2.220446049250313e-16 relative error 1.174089153913922e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.4042482019097956 Order of pole (three term test) 22.20574944137233 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.40424820190979555 Order of pole (three term test) 22.20574944137233 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1100000000000008 y2[1] (analytic) 1.895698685680048 y2[1] (numeric) 1.8956986856800477 absolute error 2.220446049250313e-16 relative error 1.1713074794129362e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.895698685680048 y1[1] (numeric) 1.8956986856800477 absolute error 2.220446049250313e-16 relative error 1.1713074794129362e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.39828273611804405 Order of pole (three term test) 22.197723864471037 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.39828273611804405 Order of pole (three term test) 22.197723864471033 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1200000000000008 y2[1] (analytic) 1.9001004421765053 y2[1] (numeric) 1.900100442176505 absolute error 2.220446049250313e-16 relative error 1.1685940384850719e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9001004421765053 y1[1] (numeric) 1.900100442176505 absolute error 2.220446049250313e-16 relative error 1.1685940384850719e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3921579625422104 Order of pole (three term test) 22.189819193993664 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3921579625422104 Order of pole (three term test) 22.189819193993664 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1300000000000008 y2[1] (analytic) 1.9044121893788262 y2[1] (numeric) 1.904412189378826 absolute error 2.220446049250313e-16 relative error 1.1659482446258494e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9044121893788262 y1[1] (numeric) 1.904412189378826 absolute error 2.220446049250313e-16 relative error 1.1659482446258494e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.385876331010063 Order of pole (three term test) 22.182038591703 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3858763310100631 Order of pole (three term test) 22.182038591702998 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1400000000000008 y2[1] (analytic) 1.9086334961158835 y2[1] (numeric) 1.9086334961158833 absolute error 2.220446049250313e-16 relative error 1.1633695278684859e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9086334961158835 y1[1] (numeric) 1.9086334961158833 absolute error 2.220446049250313e-16 relative error 1.1633695278684859e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.37944035409046106 Order of pole (three term test) 22.174385169736226 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.37944035409046095 Order of pole (three term test) 22.174385169736222 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1500000000000008 y2[1] (analytic) 1.9127639402605214 y2[1] (numeric) 1.912763940260521 absolute error 4.440892098500626e-16 relative error 2.3217146690332157e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9127639402605214 y1[1] (numeric) 1.9127639402605212 absolute error 2.220446049250313e-16 relative error 1.1608573345166078e-14% Correct digits 16 h 0.01 NO INFO (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) 22.166861989360086 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (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) 22.166861989360093 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1600000000000008 y2[1] (analytic) 1.9168031087717674 y2[1] (numeric) 1.9168031087717667 absolute error 6.661338147750939e-16 relative error 3.475233380657095e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9168031087717674 y1[1] (numeric) 1.916803108771767 absolute error 4.440892098500626e-16 relative error 2.3168222537713968e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3661157220151261 Order of pole (three term test) 22.15947205974643 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.366115722015126 Order of pole (three term test) 22.159472059746427 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1700000000000008 y2[1] (analytic) 1.920750597736136 y2[1] (numeric) 1.9207505977361354 absolute error 6.661338147750939e-16 relative error 3.468091149159201e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.920750597736136 y1[1] (numeric) 1.9207505977361357 absolute error 4.440892098500626e-16 relative error 2.3120607661061344e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.35923239653456346 Order of pole (three term test) 22.15221833676855 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.35923239653456346 Order of pole (three term test) 22.152218336768552 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1800000000000008 y2[1] (analytic) 1.9246060124080206 y2[1] (numeric) 1.9246060124080202 absolute error 4.440892098500626e-16 relative error 2.3074291932322755e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9246060124080206 y1[1] (numeric) 1.9246060124080204 absolute error 2.220446049250313e-16 relative error 1.1537145966161378e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3522053828850883 Order of pole (three term test) 22.145103721818938 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3522053828850883 Order of pole (three term test) 22.145103721818934 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.1900000000000008 y2[1] (analytic) 1.9283689672491668 y2[1] (numeric) 1.9283689672491666 absolute error 2.220446049250313e-16 relative error 1.1514632764588596e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9283689672491668 y1[1] (numeric) 1.9283689672491668 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3450374917784681 Order of pole (three term test) 22.138131060648714 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3450374917784681 Order of pole (three term test) 22.138131060648714 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2000000000000008 y2[1] (analytic) 1.9320390859672267 y2[1] (numeric) 1.9320390859672263 absolute error 4.440892098500626e-16 relative error 2.2985518930521042e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9320390859672267 y1[1] (numeric) 1.9320390859672265 absolute error 2.220446049250313e-16 relative error 1.1492759465260521e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33773159027557564 Order of pole (three term test) 22.131303142229374 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3377315902755757 Order of pole (three term test) 22.131303142229378 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2100000000000009 y2[1] (analytic) 1.9356160015533863 y2[1] (numeric) 1.9356160015533859 absolute error 4.440892098500626e-16 relative error 2.2943042912110074e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9356160015533863 y1[1] (numeric) 1.935616001553386 absolute error 2.220446049250313e-16 relative error 1.1471521456055037e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3302906006396005 Order of pole (three term test) 22.124622697637253 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.33029060063960053 Order of pole (three term test) 22.124622697637253 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2200000000000009 y2[1] (analytic) 1.9390993563190677 y2[1] (numeric) 1.9390993563190675 absolute error 2.220446049250313e-16 relative error 1.1450914271176476e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9390993563190677 y1[1] (numeric) 1.9390993563190677 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3227174991671857 Order of pole (three term test) 22.11809239896111 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.32271749916718556 Order of pole (three term test) 22.118092398961114 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2300000000000009 y2[1] (analytic) 1.942488801931698 y2[1] (numeric) 1.9424888019316975 absolute error 4.440892098500626e-16 relative error 2.2861867178252993e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.942488801931698 y1[1] (numeric) 1.9424888019316977 absolute error 2.220446049250313e-16 relative error 1.1430933589126497e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3150153149979463 Order of pole (three term test) 22.111714858233352 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3150153149979464 Order of pole (three term test) 22.111714858233352 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2400000000000009 y2[1] (analytic) 1.9457839994495392 y2[1] (numeric) 1.945783999449539 absolute error 2.220446049250313e-16 relative error 1.1411575230747481e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9457839994495392 y1[1] (numeric) 1.9457839994495392 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30718712890285604 Order of pole (three term test) 22.105492626385235 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.3071871289028559 Order of pole (three term test) 22.10549262638523 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.2500000000000009 y2[1] (analytic) 1.9489846193555866 y2[1] (numeric) 1.9489846193555862 absolute error 4.440892098500626e-16 relative error 2.2785670314673725e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9489846193555866 y1[1] (numeric) 1.9489846193555864 absolute error 2.220446049250313e-16 relative error 1.1392835157336862e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29923607205197866 Order of pole (three term test) 22.099428192226533 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2992360720519786 Order of pole (three term test) 22.099428192226537 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.260000000000001 y2[1] (analytic) 1.952090341590516 y2[1] (numeric) 1.9520903415905158 absolute error 2.220446049250313e-16 relative error 1.1374709468830974e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.952090341590516 y1[1] (numeric) 1.952090341590516 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29116532476204127 Order of pole (three term test) 22.093523981450055 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.29116532476204127 Order of pole (three term test) 22.093523981450055 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.270000000000001 y2[1] (analytic) 1.9551008555846925 y2[1] (numeric) 1.9551008555846923 absolute error 2.220446049250313e-16 relative error 1.1357194402056903e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9551008555846925 y1[1] (numeric) 1.9551008555846925 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2829781152243516 Order of pole (three term test) 22.08778235566139 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2829781152243516 Order of pole (three term test) 22.08778235566139 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.280000000000001 y2[1] (analytic) 1.9580158602892253 y2[1] (numeric) 1.958015860289225 absolute error 2.220446049250313e-16 relative error 1.13402863290511e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9580158602892253 y1[1] (numeric) 1.9580158602892253 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (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) 22.0822056114343 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.27467771821356357 Order of pole (three term test) 22.082205611434297 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.290000000000001 y2[1] (analytic) 1.9608350642060728 y2[1] (numeric) 1.9608350642060728 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.9608350642060728 y1[1] (numeric) 1.960835064206073 absolute error 2.220446049250313e-16 relative error 1.1323981755443336e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.26626745377781075 Order of pole (three term test) 22.07679597939211 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2662674537778107 Order of pole (three term test) 22.076795979392113 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.300000000000001 y2[1] (analytic) 1.963558185417193 y2[1] (numeric) 1.963558185417193 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 y1[1] (analytic) 1.963558185417193 y1[1] (numeric) 1.9635581854171933 absolute error 2.220446049250313e-16 relative error 1.130827731890481e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2577506859107323 Order of pole (three term test) 22.071555623315525 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2577506859107322 Order of pole (three term test) 22.071555623315525 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.310000000000001 y2[1] (analytic) 1.9661849516127343 y2[1] (numeric) 1.966184951612734 absolute error 2.220446049250313e-16 relative error 1.1293169787659217e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9661849516127343 y1[1] (numeric) 1.9661849516127343 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24913082120591987 Order of pole (three term test) 22.0664866392771 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.24913082120591973 Order of pole (three term test) 22.066486639277098 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.320000000000001 y2[1] (analytic) 1.9687151001182654 y2[1] (numeric) 1.9687151001182652 absolute error 2.220446049250313e-16 relative error 1.1278656059055602e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9687151001182654 y1[1] (numeric) 1.9687151001182657 absolute error 2.220446049250313e-16 relative error 1.1278656059055602e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24041130749432482 Order of pole (three term test) 22.061591054802864 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2404113074943248 Order of pole (three term test) 22.06159105480286 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.330000000000001 y2[1] (analytic) 1.9711483779210448 y2[1] (numeric) 1.9711483779210446 absolute error 2.220446049250313e-16 relative error 1.1264733158201925e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9711483779210448 y1[1] (numeric) 1.971148377921045 absolute error 2.220446049250313e-16 relative error 1.1264733158201925e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23159563246517295 Order of pole (three term test) 22.056870828061324 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.23159563246517295 Order of pole (three term test) 22.056870828061324 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.340000000000001 y2[1] (analytic) 1.9734845416953197 y2[1] (numeric) 1.9734845416953193 absolute error 4.440892098500626e-16 relative error 2.2502796473316597e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9734845416953197 y1[1] (numeric) 1.97348454169532 absolute error 2.220446049250313e-16 relative error 1.1251398236658299e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22268732227093596 Order of pole (three term test) 22.052327847080253 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.22268732227093604 Order of pole (three term test) 22.052327847080253 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.350000000000001 y2[1] (analytic) 1.9757233578266593 y2[1] (numeric) 1.9757233578266589 absolute error 4.440892098500626e-16 relative error 2.247729714237781e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9757233578266593 y1[1] (numeric) 1.9757233578266598 absolute error 4.440892098500626e-16 relative error 2.247729714237781e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2136899401169152 Order of pole (three term test) 22.04796392899147 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.2136899401169151 Order of pole (three term test) 22.047963928991464 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.360000000000001 y2[1] (analytic) 1.9778646024353164 y2[1] (numeric) 1.977864602435316 absolute error 4.440892098500626e-16 relative error 2.2452963125143245e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9778646024353164 y1[1] (numeric) 1.9778646024353168 absolute error 4.440892098500626e-16 relative error 2.2452963125143245e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20460708483600895 Order of pole (three term test) 22.043780819304022 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.20460708483600898 Order of pole (three term test) 22.043780819304025 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.370000000000001 y2[1] (analytic) 1.9799080613986144 y2[1] (numeric) 1.979908061398614 absolute error 4.440892098500626e-16 relative error 2.2429789468928992e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9799080613986144 y1[1] (numeric) 1.9799080613986149 absolute error 4.440892098500626e-16 relative error 2.2429789468928992e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.1954423894492264 Order of pole (three term test) 22.039780191206006 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.19544238944922648 Order of pole (three term test) 22.03978019120601 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.380000000000001 y2[1] (analytic) 1.98185353037236 y2[1] (numeric) 1.9818535303723595 absolute error 4.440892098500626e-16 relative error 2.2407771464656374e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.98185353037236 y1[1] (numeric) 1.9818535303723603 absolute error 4.440892098500626e-16 relative error 2.2407771464656374e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18619951971252788 Order of pole (three term test) 22.035963644895332 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.18619951971252788 Order of pole (three term test) 22.035963644895343 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 1.390000000000001 y2[1] (analytic) 1.9837008148112767 y2[1] (numeric) 1.9837008148112762 absolute error 4.440892098500626e-16 relative error 2.238690464480713e-14% Correct digits 16 h 0.01 y1[1] (analytic) 1.9837008148112767 y1[1] (numeric) 1.9837008148112771 absolute error 4.440892098500626e-16 relative error 2.238690464480713e-14% Correct digits 16 h 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17688217265057177 Order of pole (three term test) 22.032332706939634 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.17688217265057182 Order of pole (three term test) 22.032332706939627 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations 130 Total Elapsed Time 3 Seconds Elapsed Time(since restart) 3 Seconds Time to Timeout 29 Minutes 57.0 Seconds Percent Done 100.76923076923084%