##############ECHO OF PROBLEM################# ##############temp/subpostode.ode################# diff ( y , x , 1 ) = sin ( x ) - cos ( x ); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.0; x_end=10.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(2.0 - cos(x) - sin(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 10 estimated_steps = 10000000 step_error = 1e-17 est_needed_step_err = 1e-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 = 2.479596309143244e-183 estimated_step_error = 2.479596309143244e-183 best_h = 2e-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 = 1.664028945667307e-175 estimated_step_error = 1.664028945667307e-175 best_h = 4e-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 = 1.116710963428165e-167 estimated_step_error = 1.116710963428165e-167 best_h = 8e-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 = 7.494120972320839e-160 estimated_step_error = 7.494120972320839e-160 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 = 5.029220196379388e-152 estimated_step_error = 5.029220196379388e-152 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 = 3.375053541863191e-144 estimated_step_error = 3.375053541863191e-144 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 = 2.264961433531628e-136 estimated_step_error = 2.264961433531628e-136 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 = 1.519991689542376e-128 estimated_step_error = 1.519991689542376e-128 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 = 1.02005157361828e-120 estimated_step_error = 1.02005157361828e-120 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 = 6.84548268459941e-113 estimated_step_error = 6.84548268459941e-113 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 = 4.593969220564806e-105 estimated_step_error = 4.593969220564806e-105 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 = 3.08301901418197e-97 estimated_step_error = 3.08301901418197e-97 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 = 2.069057493682755e-89 estimated_step_error = 2.069057493682755e-89 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 = 1.388626270308451e-81 estimated_step_error = 1.388626270308451e-81 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 = 9.320326031009437e-74 estimated_step_error = 9.320326031009437e-74 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 = 6.25666042189902e-66 estimated_step_error = 6.25666042189902e-66 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 = 4.201315597423391e-58 estimated_step_error = 4.201315597423391e-58 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 = 2.822860803119427e-50 estimated_step_error = 2.822860803119427e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.9051624180751461 y[1] (numeric) = 0.9051624180751461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.49 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0.8212640913636972 y[1] (numeric) = 0.8212640913636972 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4605 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0.7491433042130544 y[1] (numeric) = 0.7491433042130544 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4127 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (analytic) = 0.6895206636884643 y[1] (numeric) = 0.6895206636884644 absolute error = 1.110223024625157e-16 relative error = 1.610137423128441e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.6429918995054242 y[1] (numeric) = 0.6429918995054242 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2702 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (analytic) = 0.6100219116952864 y[1] (numeric) = 0.6100219116952863 absolute error = 1.110223024625157e-16 relative error = 1.81997237040188e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1812 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (analytic) = 0.5909401254778204 y[1] (numeric) = 0.5909401254778205 absolute error = 1.110223024625157e-16 relative error = 1.878740293236064e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08498 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 0.5859371997533118 y[1] (numeric) = 0.5859371997533118 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0146 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 0.5950631221018523 y[1] (numeric) = 0.5950631221018522 absolute error = 1.110223024625157e-16 relative error = 1.865723119765315e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1136 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 0.6182267093239638 y[1] (numeric) = 0.6182267093239638 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2081 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (analytic) = 0.6551965185129872 y[1] (numeric) = 0.6551965185129873 absolute error = 1.110223024625157e-16 relative error = 1.694488589690438e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2943 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (analytic) = 0.7056031595561001 y[1] (numeric) = 0.7056031595561001 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3687 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (analytic) = 0.7689429859582196 y[1] (numeric) = 0.7689429859582196 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4284 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (analytic) = 0.844583127111299 y[1] (numeric) = 0.8445831271112989 absolute error = 1.110223024625157e-16 relative error = 1.314521909077698e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (analytic) = 0.931767811728243 y[1] (numeric) = 0.9317678117282427 absolute error = 2.220446049250313e-16 relative error = 2.383046528653774e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.495 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (analytic) = 1.029625919259784 y[1] (numeric) = 1.029625919259784 absolute error = 4.440892098500626e-16 relative error = 4.313112185145126e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4991 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 1.137179683843056 y[1] (numeric) = 1.137179683843056 absolute error = 2.220446049250313e-16 relative error = 1.952590325696286e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4834 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 1.253354463814893 y[1] (numeric) = 1.253354463814892 absolute error = 6.661338147750939e-16 relative error = 5.314807853698082e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 1.37698947917609 y[1] (numeric) = 1.376989479176089 absolute error = 8.881784197001252e-16 relative error = 6.450146737733678e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3955 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 1.506849409721462 y[1] (numeric) = 1.506849409721461 absolute error = 6.661338147750939e-16 relative error = 4.420705947638309e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3268 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (analytic) = 1.641636737950984 y[1] (numeric) = 1.641636737950984 absolute error = 4.440892098500626e-16 relative error = 2.705161255128552e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2451 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (analytic) = 1.780004713435756 y[1] (numeric) = 1.780004713435756 absolute error = 6.661338147750939e-16 relative error = 3.742314892466356e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1537 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (analytic) = 1.920570809103105 y[1] (numeric) = 1.920570809103104 absolute error = 8.881784197001252e-16 relative error = 4.624554405858637e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05608 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = 2.061930534990096 y[1] (numeric) = 2.061930534990095 absolute error = 8.881784197001252e-16 relative error = 4.307508932178414e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04375 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (analytic) = 2.202671471442978 y[1] (numeric) = 2.202671471442978 absolute error = 8.881784197001252e-16 relative error = 4.032278218586434e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1418 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 2.341387381547484 y[1] (numeric) = 2.341387381547483 absolute error = 8.881784197001252e-16 relative error = 3.793385181366719e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2343 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 2.476692261783232 y[1] (numeric) = 2.476692261783231 absolute error = 8.881784197001252e-16 relative error = 3.586147675289427e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3173 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (analytic) = 2.607234190512755 y[1] (numeric) = 2.607234190512753 absolute error = 1.77635683940025e-15 relative error = 6.81318481425292e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3878 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (analytic) = 2.73170883593561 y[1] (numeric) = 2.731708835935608 absolute error = 1.77635683940025e-15 relative error = 6.502731242921241e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4428 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y[1] (analytic) = 2.84887248854058 y[1] (numeric) = 2.848872488540578 absolute error = 1.77635683940025e-15 relative error = 6.235297811837983e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4801 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 2.95755448783999 y[1] (numeric) = 2.957554487839988 absolute error = 1.77635683940025e-15 relative error = 6.006167753472527e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4983 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (analytic) = 3.056668919222334 y[1] (numeric) = 3.056668919222332 absolute error = 2.220446049250313e-15 relative error = 7.264267435987899e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4966 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (analytic) = 3.145225464052114 y[1] (numeric) = 3.145225464052112 absolute error = 2.220446049250313e-15 relative error = 7.059735699804577e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4751 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (analytic) = 3.222339294606293 y[1] (numeric) = 3.222339294606291 absolute error = 2.220446049250313e-15 relative error = 6.89078910146738e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4347 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (analytic) = 3.287239914980417 y[1] (numeric) = 3.287239914980415 absolute error = 2.220446049250313e-15 relative error = 6.754742904925881e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (analytic) = 3.339278859629 y[1] (numeric) = 3.339278859628998 absolute error = 2.220446049250313e-15 relative error = 6.649477754298748e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (analytic) = 3.377936172618902 y[1] (numeric) = 3.3779361726189 absolute error = 2.664535259100376e-15 relative error = 7.888056857612471e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2193 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (analytic) = 3.402825602857136 y[1] (numeric) = 3.402825602857134 absolute error = 2.220446049250313e-15 relative error = 6.525300760009405e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1256 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (analytic) = 3.413698463384114 y[1] (numeric) = 3.413698463384112 absolute error = 2.220446049250313e-15 relative error = 6.504517235682001e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02698 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (analytic) = 3.41044611617154 y[1] (numeric) = 3.410446116171538 absolute error = 2.220446049250313e-15 relative error = 6.510720221385337e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07275 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 3.393101057597679 y[1] (numeric) = 3.393101057597677 absolute error = 2.664535259100376e-15 relative error = 7.85280253629366e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1696 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y[1] (analytic) = 3.361836593754287 y[1] (numeric) = 3.361836593754285 absolute error = 2.664535259100376e-15 relative error = 7.925832159869468e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2596 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y[1] (analytic) = 3.31696510882943 y[1] (numeric) = 3.316965108829427 absolute error = 2.664535259100376e-15 relative error = 8.033051815973732e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3394 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (analytic) = 3.258934943867935 y[1] (numeric) = 3.258934943867932 absolute error = 3.108624468950438e-15 relative error = 9.538774239110469e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4055 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (analytic) = 3.188325917095877 y[1] (numeric) = 3.188325917095873 absolute error = 3.552713678800501e-15 relative error = 1.114288115826167e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4556 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (analytic) = 3.105843530568519 y[1] (numeric) = 3.105843530568515 absolute error = 3.552713678800501e-15 relative error = 1.143880444663026e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4874 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y[1] (analytic) = 3.012311921026992 y[1] (numeric) = 3.012311921026988 absolute error = 3.996802888650564e-15 relative error = 1.326822385408191e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y[1] (analytic) = 2.908665625396395 y[1] (numeric) = 2.908665625396391 absolute error = 4.440892098500626e-15 relative error = 1.526779860746427e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4923 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (analytic) = 2.795940243201759 y[1] (numeric) = 2.795940243201754 absolute error = 4.884981308350689e-15 relative error = 1.747169425465501e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4652 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (analytic) = 2.675262089199914 y[1] (numeric) = 2.675262089199909 absolute error = 5.329070518200751e-15 relative error = 1.991980725819094e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4195 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.099999999999998 y[1] (analytic) = 2.547836939614754 y[1] (numeric) = 2.547836939614748 absolute error = 5.773159728050814e-15 relative error = 2.265906282418429e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3571 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.199999999999998 y[1] (analytic) = 2.41493798441978 y[1] (numeric) = 2.414937984419773 absolute error = 6.217248937900877e-15 relative error = 2.574496313367919e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2805 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.299999999999997 y[1] (analytic) = 2.277893106044744 y[1] (numeric) = 2.277893106044737 absolute error = 7.105427357601002e-15 relative error = 3.119297977040996e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.399999999999997 y[1] (analytic) = 2.138071611613357 y[1] (numeric) = 2.13807161161335 absolute error = 7.549516567451064e-15 relative error = 3.530993314931257e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09716 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.499999999999996 y[1] (analytic) = 1.996870551279137 y[1] (numeric) = 1.996870551279129 absolute error = 8.215650382226158e-15 relative error = 4.114262878464232e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.002213 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.599999999999996 y[1] (analytic) = 1.855700759362077 y[1] (numeric) = 1.855700759362068 absolute error = 8.659739592076221e-15 relative error = 4.666560353757212e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1015 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.699999999999996 y[1] (analytic) = 1.715972757758484 y[1] (numeric) = 1.715972757758475 absolute error = 9.325873406851315e-15 relative error = 5.43474444141723e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1967 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.799999999999995 y[1] (analytic) = 1.579082662472445 y[1] (numeric) = 1.579082662472435 absolute error = 9.769962616701378e-15 relative error = 6.187112840187912e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2841 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.899999999999995 y[1] (analytic) = 1.446398234086207 y[1] (numeric) = 1.446398234086197 absolute error = 9.992007221626409e-15 relative error = 6.908199267775706e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3602 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 5.999999999999995 y[1] (analytic) = 1.319245211548566 y[1] (numeric) = 1.319245211548556 absolute error = 1.06581410364015e-14 relative error = 8.078968900626657e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4219 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.099999999999994 y[1] (analytic) = 1.198894065829518 y[1] (numeric) = 1.198894065829506 absolute error = 1.110223024625157e-14 relative error = 9.260393026109364e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4668 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.199999999999994 y[1] (analytic) = 1.086547305794286 y[1] (numeric) = 1.086547305794274 absolute error = 1.176836406102666e-14 relative error = 1.083097256628304e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4931 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.299999999999994 y[1] (analytic) = 0.9833274631322413 y[1] (numeric) = 0.9833274631322293 absolute error = 1.199040866595169e-14 relative error = 1.219370872421081e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4997 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.399999999999993 y[1] (analytic) = 0.89026587639132 y[1] (numeric) = 0.8902658763913077 absolute error = 1.232347557333924e-14 relative error = 1.384246650370591e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4864 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.499999999999993 y[1] (analytic) = 0.8082923861841664 y[1] (numeric) = 0.8082923861841539 absolute error = 1.254552017826427e-14 relative error = 1.552101738516911e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4537 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.599999999999993 y[1] (analytic) = 0.7382260445280973 y[1] (numeric) = 0.7382260445280844 absolute error = 1.287858708565182e-14 relative error = 1.744531662234202e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4029 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.699999999999992 y[1] (analytic) = 0.6807669311480864 y[1] (numeric) = 0.6807669311480734 absolute error = 1.298960938811433e-14 relative error = 1.908084660664682e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3361 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.799999999999992 y[1] (analytic) = 0.6364891585115696 y[1] (numeric) = 0.6364891585115564 absolute error = 1.321165399303936e-14 relative error = 2.075707624609793e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2559 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.899999999999991 y[1] (analytic) = 0.6058351354864451 y[1] (numeric) = 0.6058351354864319 absolute error = 1.321165399303936e-14 relative error = 2.180734199648439e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1654 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.999999999999991 y[1] (analytic) = 0.5891111469379071 y[1] (numeric) = 0.5891111469378939 absolute error = 1.321165399303936e-14 relative error = 2.242641997475543e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06837 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.099999999999991 y[1] (analytic) = 0.5864842934313171 y[1] (numeric) = 0.5864842934313039 absolute error = 1.321165399303936e-14 relative error = 2.252686754105986e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0314 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.19999999999999 y[1] (analytic) = 0.5979808216185905 y[1] (numeric) = 0.5979808216185774 absolute error = 1.310063169057685e-14 relative error = 2.190811346610847e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1299 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.29999999999999 y[1] (analytic) = 0.6234858619903271 y[1] (numeric) = 0.6234858619903141 absolute error = 1.298960938811433e-14 relative error = 2.08338475336845e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2232 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.39999999999999 y[1] (analytic) = 0.6627445766139779 y[1] (numeric) = 0.662744576613965 absolute error = 1.287858708565182e-14 relative error = 1.943220290303948e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3077 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.499999999999989 y[1] (analytic) = 0.715364705390229 y[1] (numeric) = 0.7153647053902165 absolute error = 1.254552017826427e-14 relative error = 1.753723671818661e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3798 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.599999999999989 y[1] (analytic) = 0.7808204853862503 y[1] (numeric) = 0.7808204853862379 absolute error = 1.232347557333924e-14 relative error = 1.578272574040262e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4369 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.699999999999989 y[1] (analytic) = 0.8584579040851257 y[1] (numeric) = 0.8584579040851136 absolute error = 1.210143096841421e-14 relative error = 1.409670865726482e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.799999999999988 y[1] (analytic) = 0.9475012340627343 y[1] (numeric) = 0.9475012340627227 absolute error = 1.165734175856414e-14 relative error = 1.230324704547277e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4971 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.899999999999988 y[1] (analytic) = 1.047060783799752 y[1] (numeric) = 1.047060783799741 absolute error = 1.154631945610163e-14 relative error = 1.102736310512975e-12 % Correct digits = 14 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4979 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 7.999999999999988 y[1] (analytic) = 1.156141787185218 y[1] (numeric) = 1.156141787185207 absolute error = 1.110223024625157e-14 relative error = 9.6028275850849e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.099999999999987 y[1] (analytic) = 1.27365434289069 y[1] (numeric) = 1.273654342890679 absolute error = 1.043609643147647e-14 relative error = 8.193821573120597e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4407 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.199999999999987 y[1] (analytic) = 1.398424304304045 y[1] (numeric) = 1.398424304304035 absolute error = 9.992007221626409e-15 relative error = 7.145189904718609e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.385 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.299999999999986 y[1] (analytic) = 1.529205011214308 y[1] (numeric) = 1.529205011214299 absolute error = 9.325873406851315e-15 relative error = 6.098510885369021e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3139 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.399999999999986 y[1] (analytic) = 1.664689746028385 y[1] (numeric) = 1.664689746028376 absolute error = 8.881784197001252e-15 relative error = 5.335399114574593e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2303 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.499999999999986 y[1] (analytic) = 1.803524790061314 y[1] (numeric) = 1.803524790061305 absolute error = 8.881784197001252e-15 relative error = 4.924680961385234e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1376 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.599999999999985 y[1] (analytic) = 1.944322949445879 y[1] (numeric) = 1.944322949445871 absolute error = 8.215650382226158e-15 relative error = 4.225455644890461e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03934 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.699999999999985 y[1] (analytic) = 2.085677415515195 y[1] (numeric) = 2.085677415515188 absolute error = 7.549516567451064e-15 relative error = 3.619695218105536e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06047 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.799999999999985 y[1] (analytic) = 2.226175821169872 y[1] (numeric) = 2.226175821169865 absolute error = 7.105427357601002e-15 relative error = 3.191763781652721e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1579 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.899999999999984 y[1] (analytic) = 2.364414352783206 y[1] (numeric) = 2.364414352783199 absolute error = 6.661338147750939e-15 relative error = 2.817331124686215e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.249 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 8.999999999999984 y[1] (analytic) = 2.499011776642899 y[1] (numeric) = 2.499011776642893 absolute error = 6.217248937900877e-15 relative error = 2.487883008799963e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3302 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.099999999999984 y[1] (analytic) = 2.62862323978174 y[1] (numeric) = 2.628623239781734 absolute error = 5.773159728050814e-15 relative error = 2.196267475946904e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3982 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.199999999999983 y[1] (analytic) = 2.751953707303897 y[1] (numeric) = 2.751953707303891 absolute error = 5.329070518200751e-15 relative error = 1.936468082314389e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4503 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.299999999999983 y[1] (analytic) = 2.867770901945522 y[1] (numeric) = 2.867770901945517 absolute error = 4.884981308350689e-15 relative error = 1.703407097490484e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4845 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.399999999999983 y[1] (analytic) = 2.974917616581831 y[1] (numeric) = 2.974917616581826 absolute error = 4.440892098500626e-15 relative error = 1.492778177704025e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4994 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.499999999999982 y[1] (analytic) = 3.072323276658171 y[1] (numeric) = 3.072323276658167 absolute error = 3.996802888650564e-15 relative error = 1.300905708398619e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4944 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.599999999999982 y[1] (analytic) = 3.159014637017092 y[1] (numeric) = 3.159014637017088 absolute error = 3.552713678800501e-15 relative error = 1.124627166069468e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4696 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.699999999999982 y[1] (analytic) = 3.23412550624224 y[1] (numeric) = 3.234125506242237 absolute error = 3.552713678800501e-15 relative error = 1.098508289781379e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4261 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.799999999999981 y[1] (analytic) = 3.29690540135667 y[1] (numeric) = 3.296905401356667 absolute error = 3.108624468950438e-15 relative error = 9.428916182039209e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3657 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.899999999999981 y[1] (analytic) = 3.346727046400674 y[1] (numeric) = 3.34672704640067 absolute error = 3.552713678800501e-15 relative error = 1.061548680111622e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2907 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 9.99999999999998 y[1] (analytic) = 3.383092639965817 y[1] (numeric) = 3.383092639965813 absolute error = 3.552713678800501e-15 relative error = 1.050137864045129e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.204 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) - cos ( x ); Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102 %