##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=1.5 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=10000 $glob_max_h=0.5 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=4 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=1.570796327 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb #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=10.0 $glob_subiter_method=3 #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) return(-ln(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 1.4 estimated_steps 1400000.0 step_error 7.142857142857143e-17 est_needed_step_err 7.142857142857143e-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 1.4727597895213286e-100 estimated_step_error 1.4727597895213286e-100 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 9.65188097658525e-96 estimated_step_error 9.65188097658525e-96 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 6.32545988873263e-91 estimated_step_error 6.32545988873263e-91 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 4.145457550185764e-86 estimated_step_error 4.145457550185764e-86 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 2.716772509442038e-81 estimated_step_error 2.716772509442038e-81 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 1.7804711744313894e-76 estimated_step_error 1.7804711744313894e-76 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 1.1668589510603357e-71 estimated_step_error 1.1668589510603357e-71 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 7.647249538401683e-67 estimated_step_error 7.647249538401683e-67 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 5.0118623170887115e-62 estimated_step_error 5.0118623170887115e-62 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 3.284784962340086e-57 estimated_step_error 3.284784962340086e-57 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 2.1529931547010194e-52 estimated_step_error 2.1529931547010194e-52 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 1.4113482062960053e-47 estimated_step_error 1.4113482062960053e-47 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 9.254170269628698e-43 estimated_step_error 9.254170269628698e-43 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 6.071065620364792e-38 estimated_step_error 6.071065620364792e-38 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 3.986969263894856e-33 estimated_step_error 3.986969263894856e-33 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 2.6238013200956174e-28 estimated_step_error 2.6238013200956174e-28 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 1.7341060289357585e-23 estimated_step_error 1.7341060289357585e-23 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 1.1563275615904211e-18 estimated_step_error 1.1563275615904211e-18 best_h 0.262144 opt_iter 19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.859664928848418e-14 estimated_step_error 7.859664928848418e-14 best_h 0.131072 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (analytic) 0.005008355623235254 y[1] (numeric) 0.005008355623235254 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.470796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11 y[1] (analytic) 0.006062240346532338 y[1] (numeric) 0.006062240346532248 absolute error 9.020562075079397e-17 relative error 1.4879914948009688e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 1.460796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12 y[1] (analytic) 0.007217346646627739 y[1] (numeric) 0.0072173466466276814 absolute error 5.724587470723463e-17 relative error 7.931706416510065e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.450796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13 y[1] (analytic) 0.008473908649082243 y[1] (numeric) 0.008473908649082238 absolute error 5.204170427930421e-18 relative error 6.141404921203691e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.4407963270000002 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14 y[1] (analytic) 0.009832181658295606 y[1] (numeric) 0.009832181658295495 absolute error 1.1102230246251565e-16 relative error 1.1291726121520948e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 1.430796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15000000000000002 y[1] (analytic) 0.011292442366641833 y[1] (numeric) 0.011292442366641732 absolute error 1.0061396160665481e-16 relative error 8.909849467451882e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.4207963270000001 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000003 y[1] (analytic) 0.012854989082009669 y[1] (numeric) 0.012854989082009594 absolute error 7.45931094670027e-17 relative error 5.802658329083644e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.410796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000004 y[1] (analytic) 0.014520141974147178 y[1] (numeric) 0.014520141974147064 absolute error 1.1449174941446927e-16 relative error 7.885029610476229e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.4007963270000001 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000005 y[1] (analytic) 0.016288243340248813 y[1] (numeric) 0.016288243340248795 absolute error 1.734723475976807e-17 relative error 1.0650156924474756e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.3907963269999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000006 y[1] (analytic) 0.01815965789025992 y[1] (numeric) 0.018159657890259858 absolute error 6.245004513516506e-17 relative error 3.438943922432627e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.380796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.20000000000000007 y[1] (analytic) 0.020134773052408354 y[1] (numeric) 0.020134773052408298 absolute error 5.551115123125783e-17 relative error 2.756979236208379e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.3707963269999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.21000000000000008 y[1] (analytic) 0.02221399929951903 y[1] (numeric) 0.022213999299519005 absolute error 2.42861286636753e-17 relative error 1.0932803380524611e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.360796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.22000000000000008 y[1] (analytic) 0.024397770496703126 y[1] (numeric) 0.0243977704967031 absolute error 2.42861286636753e-17 relative error 9.954240969254584e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.3507963269999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2300000000000001 y[1] (analytic) 0.026686544271060854 y[1] (numeric) 0.02668654427106074 absolute error 1.1449174941446927e-16 relative error 4.2902426125897923e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.340796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2400000000000001 y[1] (analytic) 0.029080802404080987 y[1] (numeric) 0.029080802404080883 absolute error 1.0408340855860843e-16 relative error 3.5791106143619383e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.3307963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2500000000000001 y[1] (analytic) 0.03158105124746966 y[1] (numeric) 0.03158105124746956 absolute error 1.0408340855860843e-16 relative error 3.295755031807176e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.320796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.2600000000000001 y[1] (analytic) 0.034187822163188435 y[1] (numeric) 0.03418782216318837 absolute error 6.245004513516506e-17 relative error 1.82667514874369e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.3107963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.27000000000000013 y[1] (analytic) 0.036901671988538005 y[1] (numeric) 0.03690167198853797 absolute error 3.469446951953614e-17 relative error 9.401869251429193e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.300796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.28000000000000014 y[1] (analytic) 0.03972318352717689 y[1] (numeric) 0.03972318352717678 absolute error 1.1102230246251565e-16 relative error 2.794899416522318e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.2907963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.29000000000000015 y[1] (analytic) 0.042652966067024164 y[1] (numeric) 0.04265296606702402 absolute error 1.457167719820518e-16 relative error 3.4163338547915956e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.280796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.30000000000000016 y[1] (analytic) 0.04569165592605806 y[1] (numeric) 0.04569165592605797 absolute error 9.020562075079397e-17 relative error 1.9742252479702642e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.2707963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.31000000000000016 y[1] (analytic) 0.04883991702708585 y[1] (numeric) 0.04883991702708579 absolute error 6.245004513516506e-17 relative error 1.2786681251020808e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.260796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3200000000000002 y[1] (analytic) 0.05209844150263039 y[1] (numeric) 0.05209844150263031 absolute error 8.326672684688674e-17 relative error 1.5982575379473242e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.2507963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3300000000000002 y[1] (analytic) 0.05546795033115276 y[1] (numeric) 0.05546795033115264 absolute error 1.1796119636642288e-16 relative error 2.1266550442584448e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.240796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3400000000000002 y[1] (analytic) 0.058949194005906855 y[1] (numeric) 0.05894919400590678 absolute error 7.632783294297951e-17 relative error 1.2948070661548193e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.2307963269999997 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3500000000000002 y[1] (analytic) 0.06254295323780479 y[1] (numeric) 0.06254295323780472 absolute error 6.938893903907228e-17 relative error 1.109460545862573e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.220796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3600000000000002 y[1] (analytic) 0.0662500396937582 y[1] (numeric) 0.06625003969375812 absolute error 8.326672684688674e-17 relative error 1.2568555012463151e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.2107963269999997 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3700000000000002 y[1] (analytic) 0.07007129677205522 y[1] (numeric) 0.07007129677205513 absolute error 8.326672684688674e-17 relative error 1.1883143410026618e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.200796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.3800000000000002 y[1] (analytic) 0.07400760041643002 y[1] (numeric) 0.07400760041642987 absolute error 1.5265566588595902e-16 relative error 2.0627025471301293e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.1907963269999997 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.39000000000000024 y[1] (analytic) 0.07805985997058702 y[1] (numeric) 0.07805985997058694 absolute error 8.326672684688674e-17 relative error 1.0667035128971749e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.180796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.40000000000000024 y[1] (analytic) 0.08222901907505553 y[1] (numeric) 0.08222901907505542 absolute error 1.1102230246251565e-16 relative error 1.3501596359939392e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.1707963269999997 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.41000000000000025 y[1] (analytic) 0.08651605660836616 y[1] (numeric) 0.08651605660836603 absolute error 1.249000902703301e-16 relative error 1.4436636985862366e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.160796327 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.42000000000000026 y[1] (analytic) 0.09092198767467256 y[1] (numeric) 0.0909219876746724 absolute error 1.6653345369377348e-16 relative error 1.831608150600995e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.1507963269999997 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.43000000000000027 y[1] (analytic) 0.09544786464007339 y[1] (numeric) 0.09544786464007321 absolute error 1.8041124150158794e-16 relative error 1.890154820979023e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.1407963269999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4400000000000003 y[1] (analytic) 0.10009477822003766 y[1] (numeric) 0.10009477822003748 absolute error 1.8041124150158794e-16 relative error 1.802404128465035e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.1307963269999997 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4500000000000003 y[1] (analytic) 0.10486385862049037 y[1] (numeric) 0.10486385862049022 absolute error 1.5265566588595902e-16 relative error 1.4557509888934236e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.1207963269999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4600000000000003 y[1] (analytic) 0.10975627673528227 y[1] (numeric) 0.10975627673528209 absolute error 1.8041124150158794e-16 relative error 1.6437441836398677e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.1107963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4700000000000003 y[1] (analytic) 0.11477324540294474 y[1] (numeric) 0.11477324540294467 absolute error 6.938893903907228e-17 relative error 6.045741653071001e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.1007963269999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4800000000000003 y[1] (analytic) 0.11991602072582375 y[1] (numeric) 0.11991602072582361 absolute error 1.3877787807814457e-16 relative error 1.1572922219913101e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0907963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.4900000000000003 y[1] (analytic) 0.12518590345488673 y[1] (numeric) 0.1251859034548866 absolute error 1.3877787807814457e-16 relative error 1.108574322253112e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0807963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5000000000000003 y[1] (analytic) 0.1305842404437229 y[1] (numeric) 0.13058424044372274 absolute error 1.6653345369377348e-16 relative error 1.2752951897403224e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0707963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5100000000000003 y[1] (analytic) 0.13611242617548622 y[1] (numeric) 0.13611242617548602 absolute error 1.942890293094024e-16 relative error 1.427415811829778e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0607963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5200000000000004 y[1] (analytic) 0.1417719043667884 y[1] (numeric) 0.1417719043667883 absolute error 1.1102230246251565e-16 relative error 7.831051078730083e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 1.0507963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5300000000000004 y[1] (analytic) 0.1475641696528218 y[1] (numeric) 0.1475641696528216 absolute error 1.942890293094024e-16 relative error 1.316640955365462e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0407963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5400000000000004 y[1] (analytic) 0.15349076935828165 y[1] (numeric) 0.15349076935828146 absolute error 1.942890293094024e-16 relative error 1.2658026936843904e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0307963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5500000000000004 y[1] (analytic) 0.159553305358981 y[1] (numeric) 0.15955330535898082 absolute error 1.6653345369377348e-16 relative error 1.0437480647554607e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0207963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5600000000000004 y[1] (analytic) 0.1657534360393848 y[1] (numeric) 0.16575343603938458 absolute error 2.220446049250313e-16 relative error 1.339607855081032e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0107963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5700000000000004 y[1] (analytic) 0.17209287835166318 y[1] (numeric) 0.17209287835166293 absolute error 2.498001805406602e-16 relative error 1.451542811842603e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 1.0007963269999998 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5800000000000004 y[1] (analytic) 0.17857340998225993 y[1] (numeric) 0.17857340998225973 absolute error 1.942890293094024e-16 relative error 1.0880064917207086e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.9907963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.5900000000000004 y[1] (analytic) 0.18519687163240187 y[1] (numeric) 0.18519687163240162 absolute error 2.498001805406602e-16 relative error 1.3488358541848903e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.9807963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6000000000000004 y[1] (analytic) 0.19196516941943795 y[1] (numeric) 0.1919651694194378 absolute error 1.3877787807814457e-16 relative error 7.229325950007067e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.9707963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6100000000000004 y[1] (analytic) 0.19888027740640507 y[1] (numeric) 0.19888027740640485 absolute error 2.220446049250313e-16 relative error 1.116473728922304e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.9607963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6200000000000004 y[1] (analytic) 0.20594424026775485 y[1] (numeric) 0.20594424026775462 absolute error 2.220446049250313e-16 relative error 1.0781782711492385e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.9507963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6300000000000004 y[1] (analytic) 0.21315917609977578 y[1] (numeric) 0.2131591760997756 absolute error 1.6653345369377348e-16 relative error 7.812633579322071e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.9407963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6400000000000005 y[1] (analytic) 0.22052727938487904 y[1] (numeric) 0.2205272793848788 absolute error 2.498001805406602e-16 relative error 1.1327404992136693e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.9307963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6500000000000005 y[1] (analytic) 0.22805082411961658 y[1] (numeric) 0.2280508241196163 absolute error 2.7755575615628914e-16 relative error 1.2170785053190878e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.9207963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6600000000000005 y[1] (analytic) 0.23573216711705908 y[1] (numeric) 0.23573216711705877 absolute error 3.0531133177191805e-16 relative error 1.2951619437677658e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.9107963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6700000000000005 y[1] (analytic) 0.2435737514949815 y[1] (numeric) 0.24357375149498128 absolute error 2.220446049250313e-16 relative error 9.116113848975481e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.9007963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6800000000000005 y[1] (analytic) 0.2515781103622067 y[1] (numeric) 0.2515781103622064 absolute error 2.7755575615628914e-16 relative error 1.1032587682476884e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.8907963269999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.6900000000000005 y[1] (analytic) 0.259747870716431 y[1] (numeric) 0.25974787071643085 absolute error 1.6653345369377348e-16 relative error 6.411350100173852e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8807963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7000000000000005 y[1] (analytic) 0.26808575756793157 y[1] (numeric) 0.2680857575679313 absolute error 2.7755575615628914e-16 relative error 1.0353245121048921e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.8707963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7100000000000005 y[1] (analytic) 0.2765945983047113 y[1] (numeric) 0.2765945983047111 absolute error 1.6653345369377348e-16 relative error 6.020849818271266e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8607963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7200000000000005 y[1] (analytic) 0.28527732731592603 y[1] (numeric) 0.2852773273159258 absolute error 2.220446049250313e-16 relative error 7.783464848544778e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8507963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7300000000000005 y[1] (analytic) 0.29413699089182177 y[1] (numeric) 0.2941369908918215 absolute error 2.7755575615628914e-16 relative error 9.43627509463334e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8407963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7400000000000005 y[1] (analytic) 0.3031767524199507 y[1] (numeric) 0.3031767524199504 absolute error 2.7755575615628914e-16 relative error 9.154915538241132e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8307963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7500000000000006 y[1] (analytic) 0.3123998978991059 y[1] (numeric) 0.3123998978991056 absolute error 2.7755575615628914e-16 relative error 8.884630181471117e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8207963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7600000000000006 y[1] (analytic) 0.32180984179426003 y[1] (numeric) 0.32180984179425975 absolute error 2.7755575615628914e-16 relative error 8.624837407357371e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8107963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7700000000000006 y[1] (analytic) 0.3314101332578185 y[1] (numeric) 0.33141013325781826 absolute error 2.220446049250313e-16 relative error 6.699994437173503e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8007963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7800000000000006 y[1] (analytic) 0.3412044627447259 y[1] (numeric) 0.34120446274472566 absolute error 2.220446049250313e-16 relative error 6.507670009320929e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7907963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.7900000000000006 y[1] (analytic) 0.351196669051421 y[1] (numeric) 0.35119666905142066 absolute error 3.3306690738754696e-16 relative error 9.483771821844371e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7807963269999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8000000000000006 y[1] (analytic) 0.36139074681134437 y[1] (numeric) 0.36139074681134403 absolute error 3.3306690738754696e-16 relative error 9.2162544372343e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8100000000000006 y[1] (analytic) 0.37179085448269517 y[1] (numeric) 0.37179085448269494 absolute error 2.220446049250313e-16 relative error 5.972298733221429e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7607963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8200000000000006 y[1] (analytic) 0.3824013228674413 y[1] (numeric) 0.38240132286744105 absolute error 2.220446049250313e-16 relative error 5.806585690133783e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7507963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8300000000000006 y[1] (analytic) 0.3932266642042512 y[1] (numeric) 0.3932266642042508 absolute error 3.885780586188048e-16 relative error 9.881783052661155e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7407963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8400000000000006 y[1] (analytic) 0.4042715818820776 y[1] (numeric) 0.40427158188207735 absolute error 2.7755575615628914e-16 relative error 6.865576721077804e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7307963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8500000000000006 y[1] (analytic) 0.41554098082563534 y[1] (numeric) 0.415540980825635 absolute error 3.3306690738754696e-16 relative error 8.01526017303465e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7207963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8600000000000007 y[1] (analytic) 0.4270399786090209 y[1] (numeric) 0.42703997860902054 absolute error 3.3306690738754696e-16 relative error 7.799431530331928e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7107963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8700000000000007 y[1] (analytic) 0.43877391735931565 y[1] (numeric) 0.4387739173593153 absolute error 3.3306690738754696e-16 relative error 7.590854747977093e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.7007963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8800000000000007 y[1] (analytic) 0.4507483765182265 y[1] (numeric) 0.4507483765182262 absolute error 3.3306690738754696e-16 relative error 7.389198158855244e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6907963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.8900000000000007 y[1] (analytic) 0.4629691865367751 y[1] (numeric) 0.4629691865367747 absolute error 3.885780586188048e-16 relative error 8.393173237414555e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6807963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9000000000000007 y[1] (analytic) 0.4754424435858151 y[1] (numeric) 0.47544244358581483 absolute error 2.7755575615628914e-16 relative error 5.837841360206446e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9100000000000007 y[1] (analytic) 0.48817452537386696 y[1] (numeric) 0.48817452537386663 absolute error 3.3306690738754696e-16 relative error 6.822701515046666e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6607963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9200000000000007 y[1] (analytic) 0.5011721081735231 y[1] (numeric) 0.5011721081735226 absolute error 4.440892098500626e-16 relative error 8.861012067660868e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6507963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9300000000000007 y[1] (analytic) 0.5144421851686615 y[1] (numeric) 0.5144421851686611 absolute error 3.3306690738754696e-16 relative error 6.474331168590888e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6407963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9400000000000007 y[1] (analytic) 0.5279920862470625 y[1] (numeric) 0.5279920862470622 absolute error 3.3306690738754696e-16 relative error 6.308179915251523e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6307963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9500000000000007 y[1] (analytic) 0.5418294993769632 y[1] (numeric) 0.541829499376963 absolute error 2.220446049250313e-16 relative error 4.098053080911155e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6207963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9600000000000007 y[1] (analytic) 0.5559624937218419 y[1] (numeric) 0.5559624937218415 absolute error 4.440892098500626e-16 relative error 7.987754837150012e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6107963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9700000000000008 y[1] (analytic) 0.5703995446655491 y[1] (numeric) 0.5703995446655488 absolute error 3.3306690738754696e-16 relative error 5.83918606707232e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.6007963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9800000000000008 y[1] (analytic) 0.5851495609401413 y[1] (numeric) 0.5851495609401408 absolute error 4.440892098500626e-16 relative error 7.589328258856736e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5907963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.9900000000000008 y[1] (analytic) 0.6002219140717494 y[1] (numeric) 0.6002219140717491 absolute error 3.3306690738754696e-16 relative error 5.549062764604972e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5807963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0000000000000007 y[1] (analytic) 0.6156264703860153 y[1] (numeric) 0.615626470386015 absolute error 2.220446049250313e-16 relative error 3.606807302905657e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5707963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0100000000000007 y[1] (analytic) 0.6313736258445042 y[1] (numeric) 0.631373625844504 absolute error 2.220446049250313e-16 relative error 3.5168495457508524e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5607963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0200000000000007 y[1] (analytic) 0.647474344017704 y[1] (numeric) 0.6474743440177037 absolute error 3.3306690738754696e-16 relative error 5.144094286745049e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5507963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0300000000000007 y[1] (analytic) 0.6639401975394195 y[1] (numeric) 0.6639401975394192 absolute error 2.220446049250313e-16 relative error 3.344346459936222e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5407963269999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0400000000000007 y[1] (analytic) 0.6807834134324346 y[1] (numeric) 0.6807834134324342 absolute error 4.440892098500626e-16 relative error 6.523208425584489e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5307963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0500000000000007 y[1] (analytic) 0.6980169227472273 y[1] (numeric) 0.6980169227472268 absolute error 4.440892098500626e-16 relative error 6.36215534864447e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5207963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0600000000000007 y[1] (analytic) 0.7156544150154999 y[1] (numeric) 0.7156544150154995 absolute error 3.3306690738754696e-16 relative error 4.654018761001192e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5107963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0700000000000007 y[1] (analytic) 0.7337103980897428 y[1] (numeric) 0.7337103980897425 absolute error 3.3306690738754696e-16 relative error 4.539487354339066e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.5007963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0800000000000007 y[1] (analytic) 0.7522002640207198 y[1] (numeric) 0.7522002640207195 absolute error 3.3306690738754696e-16 relative error 4.4279020271438305e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.4907963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.0900000000000007 y[1] (analytic) 0.7711403617187269 y[1] (numeric) 0.7711403617187266 absolute error 3.3306690738754696e-16 relative error 4.3191476405826226e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.4807963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1000000000000008 y[1] (analytic) 0.790548077254233 y[1] (numeric) 0.7905480772542327 absolute error 3.3306690738754696e-16 relative error 4.2131138759374367e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.4707963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1100000000000008 y[1] (analytic) 0.8104419227821352 y[1] (numeric) 0.8104419227821348 absolute error 4.440892098500626e-16 relative error 5.479593260989827e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.4607963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1200000000000008 y[1] (analytic) 0.8308416352250594 y[1] (numeric) 0.8308416352250589 absolute error 4.440892098500626e-16 relative error 5.345052426624807e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.4507963269999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1300000000000008 y[1] (analytic) 0.8517682860294862 y[1] (numeric) 0.8517682860294857 absolute error 4.440892098500626e-16 relative error 5.213732621112044e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.44079632699999927 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1400000000000008 y[1] (analytic) 0.8732444035195741 y[1] (numeric) 0.8732444035195738 absolute error 3.3306690738754696e-16 relative error 3.8141315998720984e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.43079632699999926 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1500000000000008 y[1] (analytic) 0.8952941096243293 y[1] (numeric) 0.8952941096243289 absolute error 4.440892098500626e-16 relative error 4.960260601249851e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.42079632699999925 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1600000000000008 y[1] (analytic) 0.9179432730528062 y[1] (numeric) 0.9179432730528058 absolute error 4.440892098500626e-16 relative error 4.8378720438045595e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.41079632699999924 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1700000000000008 y[1] (analytic) 0.9412196813500504 y[1] (numeric) 0.9412196813500499 absolute error 5.551115123125783e-16 relative error 5.897789042366253e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.40079632699999923 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1800000000000008 y[1] (analytic) 0.9651532346969017 y[1] (numeric) 0.9651532346969012 absolute error 5.551115123125783e-16 relative error 5.751537604149525e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.3907963269999992 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.39079632636477624 Order of pole (three term test) 1.4169817082294083e-08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.1900000000000008 y[1] (analytic) 0.989776164836492 y[1] (numeric) 0.9897761648364913 absolute error 6.661338147750939e-16 relative error 6.730146051608923e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.3807963269999992 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3807963265023142 Order of pole (three term test) 9.8948806775717e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2000000000000008 y[1] (analytic) 1.0151232831406618 y[1] (numeric) 1.0151232831406611 absolute error 6.661338147750939e-16 relative error 6.562097686442192e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.3707963269999992 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3707963265975613 Order of pole (three term test) 6.8557215960837035e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2100000000000009 y[1] (analytic) 1.041232262597865 y[1] (numeric) 1.0412322625978645 absolute error 4.440892098500626e-16 relative error 4.2650350531980645e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.3607963269999992 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.36079632666299866 Order of pole (three term test) 4.7108023495306336e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2200000000000009 y[1] (analytic) 1.06814395944531 y[1] (numeric) 1.0681439594453093 absolute error 6.661338147750939e-16 relative error 6.236367381799538e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.3507963269999992 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3507963267075674 Order of pole (three term test) 3.2088719677189785e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2300000000000009 y[1] (analytic) 1.0959027813271431 y[1] (numeric) 1.0959027813271425 absolute error 6.661338147750939e-16 relative error 6.078402447052857e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.3407963269999992 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.34079632673765853 Order of pole (three term test) 2.1655324792742275e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2400000000000009 y[1] (analytic) 1.1245571102958363 y[1] (numeric) 1.1245571102958356 absolute error 6.661338147750939e-16 relative error 5.923521435028361e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.33079632699999917 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.33079632675777504 Order of pole (three term test) 1.4473355666817805e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.2500000000000009 y[1] (analytic) 1.154159790761956 y[1] (numeric) 1.1541597907619554 absolute error 6.661338147750939e-16 relative error 5.77159090194369e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.32079632699999916 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.3207963267710962 Order of pole (three term test) 9.571858657719876e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.260000000000001 y[1] (analytic) 1.184768694738796 y[1] (numeric) 1.1847686947387954 absolute error 6.661338147750939e-16 relative error 5.622479879264157e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.31079632699999915 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.31079632677981917 Order of pole (three term test) 6.260737624566418e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.270000000000001 y[1] (analytic) 1.2164473795563955 y[1] (numeric) 1.2164473795563948 absolute error 6.661338147750939e-16 relative error 5.476059433150445e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.30079632699999914 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.30079632678546864 Order of pole (three term test) 4.0461779129230486e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.280000000000001 y[1] (analytic) 1.2492658568129797 y[1] (numeric) 1.249265856812979 absolute error 6.661338147750939e-16 relative error 5.332202198133211e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.29079632699999913 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.29079632678908024 Order of pole (three term test) 2.5826173136708217e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.290000000000001 y[1] (analytic) 1.2833014959320592 y[1] (numeric) 1.2833014959320588 absolute error 4.440892098500626e-16 relative error 3.460521251302069e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.2807963269999991 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28079632679136235 Order of pole (three term test) 1.6257769934724253e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.300000000000001 y[1] (analytic) 1.3186400916291718 y[1] (numeric) 1.3186400916291714 absolute error 4.440892098500626e-16 relative error 3.367781797847456e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.2707963269999991 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.27079632679278154 Order of pole (three term test) 1.008974657882947e-10 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.310000000000001 y[1] (analytic) 1.3553771323162076 y[1] (numeric) 1.3553771323162072 absolute error 4.440892098500626e-16 relative error 3.2764992064692534e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.2607963269999991 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.26079632679365145 Order of pole (three term test) 6.166403276125234e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.320000000000001 y[1] (analytic) 1.393619316613288 y[1] (numeric) 1.3936193166132873 absolute error 6.661338147750939e-16 relative error 4.779883622694775e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.2507963269999991 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2507963267941782 Order of pole (three term test) 3.6956695195506625e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.330000000000001 y[1] (analytic) 1.433486378584703 y[1] (numeric) 1.4334863785847023 absolute error 6.661338147750939e-16 relative error 4.6469490378609336e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.2407963269999991 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2407963267944883 Order of pole (three term test) 2.1863987314320684e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.340000000000001 y[1] (analytic) 1.475113300329342 y[1] (numeric) 1.4751133003293413 absolute error 6.661338147750939e-16 relative error 4.5158145793029536e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.23079632699999908 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23079632679466972 Order of pole (three term test) 1.2689679497518063e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.350000000000001 y[1] (analytic) 1.5186530149603914 y[1] (numeric) 1.5186530149603907 absolute error 6.661338147750939e-16 relative error 4.3863463754587e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.22079632699999907 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22079632679477554 Order of pole (three term test) 7.070181828080386e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.360000000000001 y[1] (analytic) 1.5642797364730108 y[1] (numeric) 1.56427973647301 absolute error 6.661338147750939e-16 relative error 4.2584059567058583e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.21079632699999906 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21079632679483148 Order of pole (three term test) 3.908177995751743e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.370000000000001 y[1] (analytic) 1.612193099490702 y[1] (numeric) 1.6121930994907014 absolute error 6.661338147750939e-16 relative error 4.131848815042864e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.20079632699999905 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20079632679486276 Order of pole (three term test) 2.0849923297875292e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.380000000000001 y[1] (analytic) 1.6626233574003848 y[1] (numeric) 1.6626233574003841 absolute error 6.661338147750939e-16 relative error 4.0065226547558895e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.19079632699999904 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19079632679487918 Order of pole (three term test) 1.1048538682752259e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.390000000000001 y[1] (analytic) 1.7158379811678246 y[1] (numeric) 1.715837981167824 absolute error 6.661338147750939e-16 relative error 3.8822652376637185e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.18079632699999904 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.18079632679488833 Order of pole (three term test) 5.450599382375268e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.400000000000001 y[1] (analytic) 1.772150137669705 y[1] (numeric) 1.7721501376697042 absolute error 8.881784197001252e-16 relative error 5.0118689202487015e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.17079632699999903 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17079632679489182 Order of pole (three term test) 3.0742580972422964e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.410000000000001 y[1] (analytic) 1.8319297289558871 y[1] (numeric) 1.8319297289558865 absolute error 6.661338147750939e-16 relative error 3.6362410863584736e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.16079632699999902 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16079632679489486 Order of pole (three term test) 7.88232764689688e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.420000000000001 y[1] (analytic) 1.8956179807145515 y[1] (numeric) 1.8956179807145508 absolute error 6.661338147750939e-16 relative error 3.51407204168846e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.150796326999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15079632679489569 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.430000000000001 y[1] (analytic) 1.9637470439243763 y[1] (numeric) 1.9637470439243756 absolute error 6.661338147750939e-16 relative error 3.392156932004256e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.140796326999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14079632679489545 Order of pole (three term test) 3.989970606284383e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.440000000000001 y[1] (analytic) 2.0369668305394475 y[1] (numeric) 2.0369668305394466 absolute error 8.881784197001252e-16 relative error 4.3602988835361154e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.130796326999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13079632679489528 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.450000000000001 y[1] (analytic) 2.116082544013728 y[1] (numeric) 2.1160825440137274 absolute error 4.440892098500626e-16 relative error 2.0986384066461145e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.12079632699999898 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12079632679489619 Order of pole (three term test) 4.755236969557983e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.460000000000001 y[1] (analytic) 2.202108465746907 y[1] (numeric) 2.2021084657469068 absolute error 4.440892098500626e-16 relative error 2.0166545688267778e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.11079632699999897 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11079632679489597 Order of pole (three term test) 4.022764795181124e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.470000000000001 y[1] (analytic) 2.2963472549526465 y[1] (numeric) 2.2963472549526456 absolute error 8.881784197001252e-16 relative error 3.867787930525519e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.10079632699999896 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10079632679489568 Order of pole (three term test) 2.7511708070638142e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.480000000000001 y[1] (analytic) 2.4005108212575945 y[1] (numeric) 2.4005108212575936 absolute error 8.881784197001252e-16 relative error 3.69995590869622e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.09079632699999896 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09079632679489565 Order of pole (three term test) 2.909714951059549e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 1.490000000000001 y[1] (analytic) 2.5169120195352614 y[1] (numeric) 2.51691201953526 absolute error 1.3322676295501878e-15 relative error 5.2932626139080786e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.08079632699999895 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.08079632679489586 Order of pole (three term test) 8.962665790384782e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations 140 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 10 Minutes 0.0 Seconds Percent Done 100.71428571428581%