##############ECHO OF PROBLEM################# ##############temp/addpostode.ode################# diff ( y , x , 1 ) = sin ( x ) + sin ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-5.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; glob_display_interval=0.1; glob_max_minutes=10; /* 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) - cos(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 = 1.406735302120957e-183 estimated_step_error = 1.406735302120957e-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 = 9.440440216411675e-176 estimated_step_error = 9.440440216411675e-176 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 = 6.335371392617309e-168 estimated_step_error = 6.335371392617309e-168 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 = 4.251594707130322e-160 estimated_step_error = 4.251594707130322e-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 = 2.853195480908764e-152 estimated_step_error = 2.853195480908764e-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 = 1.914745157058884e-144 estimated_step_error = 1.914745157058884e-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 = 1.284961149263867e-136 estimated_step_error = 1.284961149263867e-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 = 8.623193751672551e-129 estimated_step_error = 8.623193751672551e-129 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.786880995731623e-121 estimated_step_error = 5.786880995731623e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.883447858320677e-113 estimated_step_error = 3.883447858320677e-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 = 2.606054205712248e-105 estimated_step_error = 2.606054205712248e-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 = 1.748781251594282e-97 estimated_step_error = 1.748781251594282e-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 = 1.173436742977145e-89 estimated_step_error = 1.173436742977145e-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 = 7.872780787500669e-82 estimated_step_error = 7.872780787500669e-82 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.280622522313891e-74 estimated_step_error = 5.280622522313891e-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 = 3.540126364021656e-66 estimated_step_error = 3.540126364021656e-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 = 2.370852568479251e-58 estimated_step_error = 2.370852568479251e-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 = 1.584490919082954e-50 estimated_step_error = 1.584490919082954e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = 1.432675629073548 y[1] (numeric) = 1.432675629073548 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 = 0.272 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = 1.626975261154849 y[1] (numeric) = 1.626975261154849 absolute error = 6.661338147750939e-16 relative error = 4.094308196808495e-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 = 0.1832 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.800000000000001 y[1] (analytic) = 1.825002033121105 y[1] (numeric) = 1.825002033121107 absolute error = 1.554312234475219e-15 relative error = 8.516769878974028e-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 = 0.08716 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.700000000000001 y[1] (analytic) = 2.024777326925779 y[1] (numeric) = 2.024777326925781 absolute error = 2.220446049250313e-15 relative error = 1.096637155959079e-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 = 0.01239 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.600000000000001 y[1] (analytic) = 2.224305053870106 y[1] (numeric) = 2.224305053870109 absolute error = 3.108624468950438e-15 relative error = 1.397571103631532e-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 = 0.1114 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.500000000000002 y[1] (analytic) = 2.421591598861556 y[1] (numeric) = 2.421591598861559 absolute error = 3.108624468950438e-15 relative error = 1.283711287407782e-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 = 0.2061 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.400000000000002 y[1] (analytic) = 2.614665739956835 y[1] (numeric) = 2.614665739956839 absolute error = 4.440892098500626e-15 relative error = 1.698454999671943e-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 = 0.2925 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.300000000000002 y[1] (analytic) = 2.801598344159946 y[1] (numeric) = 2.801598344159951 absolute error = 4.440892098500626e-15 relative error = 1.585128042268393e-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 = 0.3672 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.200000000000003 y[1] (analytic) = 2.980521642681394 y[1] (numeric) = 2.980521642681399 absolute error = 5.329070518200751e-15 relative error = 1.787965717774997e-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 = 0.4273 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.100000000000003 y[1] (analytic) = 3.149647893066533 y[1] (numeric) = 3.149647893066538 absolute error = 5.773159728050814e-15 relative error = 1.832954007576384e-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 = 0.4704 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.000000000000004 y[1] (analytic) = 3.307287241727218 y[1] (numeric) = 3.307287241727225 absolute error = 6.217248937900877e-15 relative error = 1.879863611318484e-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 = 0.4947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.900000000000003 y[1] (analytic) = 3.451864608400276 y[1] (numeric) = 3.451864608400281 absolute error = 5.773159728050814e-15 relative error = 1.672475714719968e-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 = 0.4993 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.800000000000003 y[1] (analytic) = 3.581935423828829 y[1] (numeric) = 3.581935423828835 absolute error = 5.329070518200751e-15 relative error = 1.487762867736002e-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 = 0.484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.700000000000003 y[1] (analytic) = 3.696200063420813 y[1] (numeric) = 3.696200063420818 absolute error = 5.329070518200751e-15 relative error = 1.441770041329615e-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 = 0.4494 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.600000000000003 y[1] (analytic) = 3.793516832668291 y[1] (numeric) = 3.793516832668296 absolute error = 5.329070518200751e-15 relative error = 1.40478367521896e-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 = 0.3968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.500000000000003 y[1] (analytic) = 3.87291337458159 y[1] (numeric) = 3.872913374581596 absolute error = 5.329070518200751e-15 relative error = 1.375984950548107e-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 = 0.3285 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.400000000000003 y[1] (analytic) = 3.93359638515892 y[1] (numeric) = 3.933596385158926 absolute error = 5.329070518200751e-15 relative error = 1.354757833901521e-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 = 0.2471 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.300000000000003 y[1] (analytic) = 3.974959539817728 y[1] (numeric) = 3.974959539817734 absolute error = 5.773159728050814e-15 relative error = 1.452382010488475e-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 = 0.1558 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.200000000000003 y[1] (analytic) = 3.996589551589506 y[1] (numeric) = 3.996589551589511 absolute error = 5.329070518200751e-15 relative error = 1.333404506370012e-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 = 0.05827 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.100000000000003 y[1] (analytic) = 3.998270300546559 y[1] (numeric) = 3.998270300546564 absolute error = 5.329070518200751e-15 relative error = 1.332843984428035e-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 = 0.04154 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.000000000000003 y[1] (analytic) = 3.979984993200892 y[1] (numeric) = 3.979984993200897 absolute error = 4.440892098500626e-15 relative error = 1.115806242005212e-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 = 0.1397 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.900000000000003 y[1] (analytic) = 3.941916330299183 y[1] (numeric) = 3.941916330299187 absolute error = 4.440892098500626e-15 relative error = 1.126582029244536e-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 = 0.2323 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.800000000000002 y[1] (analytic) = 3.884444681337317 y[1] (numeric) = 3.884444681337323 absolute error = 5.329070518200751e-15 relative error = 1.371900221363453e-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 = 0.3156 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.700000000000002 y[1] (analytic) = 3.808144284034125 y[1] (numeric) = 3.808144284034129 absolute error = 4.440892098500626e-15 relative error = 1.166156470782721e-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 = 0.3864 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.600000000000002 y[1] (analytic) = 3.713777506737896 y[1] (numeric) = 3.713777506737902 absolute error = 5.329070518200751e-15 relative error = 1.434946091555629e-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 = 0.4417 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.500000000000002 y[1] (analytic) = 3.60228723109387 y[1] (numeric) = 3.602287231093875 absolute error = 5.329070518200751e-15 relative error = 1.479357468277877e-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 = 0.4795 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.400000000000002 y[1] (analytic) = 3.474787431082493 y[1] (numeric) = 3.474787431082499 absolute error = 5.773159728050814e-15 relative error = 1.661442560891362e-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 = 0.4981 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.300000000000002 y[1] (analytic) = 3.332552042559652 y[1] (numeric) = 3.332552042559657 absolute error = 5.329070518200751e-15 relative error = 1.599095963136895e-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 = 0.4968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.200000000000002 y[1] (analytic) = 3.177002234510694 y[1] (numeric) = 3.1770022345107 absolute error = 5.773159728050814e-15 relative error = 1.817172070368395e-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 = 0.4758 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.100000000000002 y[1] (analytic) = 3.009692209199718 y[1] (numeric) = 3.009692209199724 absolute error = 5.329070518200751e-15 relative error = 1.770636379996398e-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 = 0.4358 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.000000000000002 y[1] (analytic) = 2.832293673094288 y[1] (numeric) = 2.832293673094294 absolute error = 5.773159728050814e-15 relative error = 2.038333730323813e-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 = 0.3784 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000002 y[1] (analytic) = 2.64657913372701 y[1] (numeric) = 2.646579133727016 absolute error = 5.773159728050814e-15 relative error = 2.181366751698385e-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 = 0.3059 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.800000000000002 y[1] (analytic) = 2.454404189386177 y[1] (numeric) = 2.454404189386183 absolute error = 5.773159728050814e-15 relative error = 2.35216341017354e-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 = 0.2213 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.700000000000002 y[1] (analytic) = 2.257688988591052 y[1] (numeric) = 2.257688988591058 absolute error = 5.773159728050814e-15 relative error = 2.557110282782416e-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 = 0.1278 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.600000000000001 y[1] (analytic) = 2.05839904460258 y[1] (numeric) = 2.058399044602586 absolute error = 6.217248937900877e-15 relative error = 3.020429374082447e-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 = 0.02919 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.500000000000001 y[1] (analytic) = 1.858525596664597 y[1] (numeric) = 1.858525596664603 absolute error = 5.773159728050814e-15 relative error = 3.106311658236838e-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 = 0.07056 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.400000000000001 y[1] (analytic) = 1.660065714199521 y[1] (numeric) = 1.660065714199527 absolute error = 5.995204332975845e-15 relative error = 3.61142591024881e-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 = 0.1675 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.300000000000001 y[1] (analytic) = 1.465002342750827 y[1] (numeric) = 1.465002342750834 absolute error = 6.439293542825908e-15 relative error = 4.39541518461662e-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 = 0.2578 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.200000000000001 y[1] (analytic) = 1.275284491046655 y[1] (numeric) = 1.275284491046661 absolute error = 6.439293542825908e-15 relative error = 5.04929965669153e-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 = 0.3377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.100000000000001 y[1] (analytic) = 1.092807757148847 y[1] (numeric) = 1.092807757148854 absolute error = 6.883382752675971e-15 relative error = 6.298804805920145e-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 = 0.4042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.000000000000001 y[1] (analytic) = 0.9193953882637221 y[1] (numeric) = 0.9193953882637289 absolute error = 6.772360450213455e-15 relative error = 7.366102263143885e-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 = 0.4546 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000000009 y[1] (analytic) = 0.7567800634586725 y[1] (numeric) = 0.7567800634586793 absolute error = 6.772360450213455e-15 relative error = 8.948914984972104e-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 = 0.4869 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8000000000000009 y[1] (analytic) = 0.6065865813056704 y[1] (numeric) = 0.6065865813056772 absolute error = 6.772360450213455e-15 relative error = 1.116470535110755e-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 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.700000000000001 y[1] (analytic) = 0.4703156254310245 y[1] (numeric) = 0.4703156254310311 absolute error = 6.605826996519681e-15 relative error = 1.404551887993455e-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 = 0.4927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.600000000000001 y[1] (analytic) = 0.3493287701806445 y[1] (numeric) = 0.3493287701806511 absolute error = 6.661338147750939e-15 relative error = 1.906896515940052e-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 = 0.466 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.500000000000001 y[1] (analytic) = 0.2448348762192555 y[1] (numeric) = 0.2448348762192621 absolute error = 6.63358257213531e-15 relative error = 2.709410797420372e-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 = 0.4207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.400000000000001 y[1] (analytic) = 0.1578780119942307 y[1] (numeric) = 0.1578780119942372 absolute error = 6.494804694057166e-15 relative error = 4.113812057814931e-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 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.300000000000001 y[1] (analytic) = 0.08932702174878848 y[1] (numeric) = 0.08932702174879512 absolute error = 6.63358257213531e-15 relative error = 7.426176807719754e-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 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.200000000000001 y[1] (analytic) = 0.03986684431751719 y[1] (numeric) = 0.03986684431752369 absolute error = 6.501743587961073e-15 relative error = 1.630864870110689e-11 % Correct digits = 13 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 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.100000000000001 y[1] (analytic) = 0.009991669443948581 y[1] (numeric) = 0.009991669443955218 absolute error = 6.637052019087264e-15 relative error = 6.642585662305883e-11 % Correct digits = 13 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 = 0.09933 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.02695629777827e-15 y[1] (analytic) = 0 y[1] (numeric) = 6.543376951384516e-15 absolute error = 6.543376951384516e-15 relative error = -1 % Correct digits = -1 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 = 1.027e-15 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999898 y[1] (analytic) = 0.00999166944394847 y[1] (numeric) = 0.009991669443954809 absolute error = 6.338679581219253e-15 relative error = 6.343964456368522e-11 % Correct digits = 13 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 = 0.09933 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.199999999999999 y[1] (analytic) = 0.0398668443175163 y[1] (numeric) = 0.03986684431752288 absolute error = 6.578071420904053e-15 relative error = 1.650010562289186e-11 % Correct digits = 13 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 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.299999999999999 y[1] (analytic) = 0.08932702174878748 y[1] (numeric) = 0.08932702174879391 absolute error = 6.425415755018093e-15 relative error = 7.19313778655708e-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 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.399999999999999 y[1] (analytic) = 0.157878011994229 y[1] (numeric) = 0.1578780119942356 absolute error = 6.578071420904053e-15 relative error = 4.166553238043372e-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 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.499999999999999 y[1] (analytic) = 0.2448348762192536 y[1] (numeric) = 0.2448348762192601 absolute error = 6.550315845288424e-15 relative error = 2.675401456866999e-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 = 0.4207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.599999999999999 y[1] (analytic) = 0.3493287701806422 y[1] (numeric) = 0.3493287701806488 absolute error = 6.550315845288424e-15 relative error = 1.875114907341063e-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 = 0.466 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.699999999999999 y[1] (analytic) = 0.4703156254310219 y[1] (numeric) = 0.4703156254310283 absolute error = 6.439293542825908e-15 relative error = 1.369143016867577e-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 = 0.4927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999989 y[1] (analytic) = 0.6065865813056677 y[1] (numeric) = 0.6065865813056742 absolute error = 6.550315845288424e-15 relative error = 1.079864943795653e-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 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999989 y[1] (analytic) = 0.7567800634586694 y[1] (numeric) = 0.756780063458676 absolute error = 6.550315845288424e-15 relative error = 8.65550793628453e-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 = 0.4869 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999989 y[1] (analytic) = 0.9193953882637187 y[1] (numeric) = 0.9193953882637254 absolute error = 6.661338147750939e-15 relative error = 7.245346488338275e-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 = 0.4546 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.099999999999999 y[1] (analytic) = 1.092807757148843 y[1] (numeric) = 1.09280775714885 absolute error = 6.661338147750939e-15 relative error = 6.095617554116289e-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 = 0.4042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.199999999999999 y[1] (analytic) = 1.275284491046651 y[1] (numeric) = 1.275284491046657 absolute error = 6.439293542825908e-15 relative error = 5.049299656691546e-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 = 0.3377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299999999999999 y[1] (analytic) = 1.465002342750823 y[1] (numeric) = 1.46500234275083 absolute error = 6.217248937900877e-15 relative error = 4.243849143767782e-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 = 0.2578 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399999999999999 y[1] (analytic) = 1.660065714199517 y[1] (numeric) = 1.660065714199523 absolute error = 5.773159728050814e-15 relative error = 3.477669395054418e-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 = 0.1675 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499999999999999 y[1] (analytic) = 1.858525596664593 y[1] (numeric) = 1.858525596664599 absolute error = 5.551115123125783e-15 relative error = 2.986838132920044e-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 = 0.07056 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599999999999999 y[1] (analytic) = 2.058399044602576 y[1] (numeric) = 2.058399044602582 absolute error = 5.329070518200751e-15 relative error = 2.588939463499245e-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 = 0.02919 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) = 2.257688988591048 y[1] (numeric) = 2.257688988591054 absolute error = 5.773159728050814e-15 relative error = 2.557110282782421e-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 = 0.1278 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) = 2.454404189386174 y[1] (numeric) = 2.454404189386179 absolute error = 4.884981308350689e-15 relative error = 1.990292116300691e-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 = 0.2213 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 2.646579133727006 y[1] (numeric) = 2.646579133727011 absolute error = 4.884981308350689e-15 relative error = 1.845771866821713e-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 = 0.3059 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) = 2.832293673094284 y[1] (numeric) = 2.832293673094289 absolute error = 4.884981308350689e-15 relative error = 1.724743925658613e-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 = 0.3784 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 3.009692209199715 y[1] (numeric) = 3.009692209199719 absolute error = 4.440892098500626e-15 relative error = 1.475530316663667e-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 = 0.4358 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 3.177002234510691 y[1] (numeric) = 3.177002234510696 absolute error = 4.884981308350689e-15 relative error = 1.537607136465566e-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 = 0.4758 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 3.332552042559648 y[1] (numeric) = 3.332552042559652 absolute error = 4.440892098500626e-15 relative error = 1.332579969280747e-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 = 0.4968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 3.474787431082491 y[1] (numeric) = 3.474787431082495 absolute error = 4.440892098500626e-15 relative error = 1.278032739147202e-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 = 0.4981 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 3.602287231093867 y[1] (numeric) = 3.602287231093872 absolute error = 4.440892098500626e-15 relative error = 1.232797890231565e-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 = 0.4795 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 3.713777506737895 y[1] (numeric) = 3.713777506737899 absolute error = 3.996802888650564e-15 relative error = 1.076209568666722e-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 = 0.4417 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 3.808144284034123 y[1] (numeric) = 3.808144284034126 absolute error = 3.552713678800501e-15 relative error = 9.329251766261771e-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 = 0.3864 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 3.884444681337317 y[1] (numeric) = 3.884444681337321 absolute error = 3.996802888650564e-15 relative error = 1.02892516602259e-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 = 0.3156 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 3.941916330299181 y[1] (numeric) = 3.941916330299185 absolute error = 4.440892098500626e-15 relative error = 1.126582029244536e-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 = 0.2323 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 3.979984993200891 y[1] (numeric) = 3.979984993200895 absolute error = 3.996802888650564e-15 relative error = 1.004225617804691e-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 = 0.1397 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) = 3.998270300546559 y[1] (numeric) = 3.998270300546563 absolute error = 4.440892098500626e-15 relative error = 1.110703320356696e-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 = 0.04154 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000001 y[1] (analytic) = 3.996589551589506 y[1] (numeric) = 3.996589551589511 absolute error = 4.884981308350689e-15 relative error = 1.222287464172511e-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 = 0.05827 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000001 y[1] (analytic) = 3.974959539817729 y[1] (numeric) = 3.974959539817734 absolute error = 4.884981308350689e-15 relative error = 1.228938624259478e-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 = 0.1558 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000000001 y[1] (analytic) = 3.933596385158921 y[1] (numeric) = 3.933596385158926 absolute error = 4.884981308350689e-15 relative error = 1.241861347743061e-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 = 0.2471 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500000000000001 y[1] (analytic) = 3.872913374581592 y[1] (numeric) = 3.872913374581596 absolute error = 4.440892098500626e-15 relative error = 1.146654125456755e-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 = 0.3285 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600000000000001 y[1] (analytic) = 3.793516832668293 y[1] (numeric) = 3.793516832668298 absolute error = 4.884981308350689e-15 relative error = 1.287718368950713e-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 = 0.3968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000000001 y[1] (analytic) = 3.696200063420815 y[1] (numeric) = 3.69620006342082 absolute error = 4.440892098500626e-15 relative error = 1.201475034441345e-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 = 0.4494 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000000001 y[1] (analytic) = 3.581935423828832 y[1] (numeric) = 3.581935423828837 absolute error = 4.440892098500626e-15 relative error = 1.239802389780001e-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 = 0.484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000001 y[1] (analytic) = 3.451864608400278 y[1] (numeric) = 3.451864608400283 absolute error = 4.884981308350689e-15 relative error = 1.415171758609203e-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 = 0.4993 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000001 y[1] (analytic) = 3.307287241727223 y[1] (numeric) = 3.307287241727226 absolute error = 3.552713678800501e-15 relative error = 1.074207777896275e-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 = 0.4947 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) = 3.149647893066537 y[1] (numeric) = 3.14964789306654 absolute error = 3.108624468950438e-15 relative error = 9.869752348488206e-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 = 0.4704 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 2.980521642681399 y[1] (numeric) = 2.980521642681401 absolute error = 2.220446049250313e-15 relative error = 7.449857157395808e-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 = 0.4273 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 2.801598344159951 y[1] (numeric) = 2.801598344159953 absolute error = 2.220446049250313e-15 relative error = 7.92564021134195e-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 = 0.3672 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999999 y[1] (analytic) = 2.61466573995684 y[1] (numeric) = 2.614665739956842 absolute error = 1.332267629550188e-15 relative error = 5.095364999015818e-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 = 0.2925 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.499999999999999 y[1] (analytic) = 2.421591598861562 y[1] (numeric) = 2.421591598861562 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 = 0.2061 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.599999999999999 y[1] (analytic) = 2.224305053870111 y[1] (numeric) = 2.224305053870111 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 = 0.1114 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999998 y[1] (analytic) = 2.024777326925784 y[1] (numeric) = 2.024777326925784 absolute error = 8.881784197001252e-16 relative error = 4.386548623836305e-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 = 0.01239 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999998 y[1] (analytic) = 1.825002033121111 y[1] (numeric) = 1.825002033121109 absolute error = 1.77635683940025e-15 relative error = 9.733451290256003e-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 = 0.08716 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999998 y[1] (analytic) = 1.626975261154854 y[1] (numeric) = 1.626975261154851 absolute error = 2.220446049250313e-15 relative error = 1.364769398936161e-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 = 0.1832 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999997 y[1] (analytic) = 1.432675629073553 y[1] (numeric) = 1.43267562907355 absolute error = 2.886579864025407e-15 relative error = 2.01481745445201e-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 = 0.272 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) + sin ( 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 %