##############ECHO OF PROBLEM################# ##############temp/div_sin_cpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / 2.0 ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* 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_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(-cos(x)/2.0); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 opt_iter = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 10000000 step_error = 7.905694150420948e-22 est_needed_step_err = 7.905694150420948e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.812732004531356e-259 estimated_step_error = 3.812732004531356e-259 Double H and LOOP opt_iter = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 5000000 step_error = 1.118033988749895e-21 est_needed_step_err = 1.118033988749895e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.620089363167353e-248 estimated_step_error = 2.620089363167353e-248 Double H and LOOP opt_iter = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 2500000 step_error = 1.58113883008419e-21 est_needed_step_err = 1.58113883008419e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.800511535879942e-237 estimated_step_error = 1.800511535879942e-237 Double H and LOOP opt_iter = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 1250000 step_error = 2.236067977499789e-21 est_needed_step_err = 2.236067977499789e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.237301879935078e-226 estimated_step_error = 1.237301879935078e-226 Double H and LOOP opt_iter = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 625000 step_error = 3.162277660168379e-21 est_needed_step_err = 3.162277660168379e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.502670667962986e-216 estimated_step_error = 8.502670667962986e-216 Double H and LOOP opt_iter = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 312500 step_error = 4.472135954999579e-21 est_needed_step_err = 4.472135954999579e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.842986520834129e-205 estimated_step_error = 5.842986520834129e-205 Double H and LOOP opt_iter = 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 156250 step_error = 6.324555320336758e-21 est_needed_step_err = 6.324555320336758e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.015263893162127e-194 estimated_step_error = 4.015263893162127e-194 Double H and LOOP opt_iter = 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.1418310927316131 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 78125 step_error = 8.944271909999158e-21 est_needed_step_err = 8.944271909999158e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.759260269679411e-183 estimated_step_error = 2.759260269679411e-183 Double H and LOOP opt_iter = 9 NO POLE (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) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -0.1418310927316131 y[1] (numeric) = -0.1418310927316131 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.8999039999999 y[1] (closed_form) = -0.09320902655618049 y[1] (numeric) = -0.09320902655622937 absolute error = 4.887756865912252e-14 relative error = 5.243866443521135e-11 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.7999359999998 y[1] (closed_form) = -0.04371761436256368 y[1] (numeric) = -0.04371761436266189 absolute error = 9.8206165421999e-14 relative error = 2.246375216349752e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.6999679999997 y[1] (closed_form) = 0.006210330500542183 y[1] (numeric) = 0.006210330500394013 absolute error = 1.48170538338821e-13 relative error = 2.385872029288702e-09 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.5999999999996 y[1] (closed_form) = 0.05607626346772601 y[1] (numeric) = 0.05607626346752801 absolute error = 1.980013375479928e-13 relative error = 3.530929582388277e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.4999039999995 y[1] (closed_form) = 0.1054448206755366 y[1] (numeric) = 0.1054448206752892 absolute error = 2.474825899767552e-13 relative error = 2.347034101734421e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.3999359999994 y[1] (closed_form) = 0.1536968859411302 y[1] (numeric) = 0.1536968859408343 absolute error = 2.959021916382198e-13 relative error = 1.925232185586102e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.2999679999993 y[1] (closed_form) = 0.2004142445926893 y[1] (numeric) = 0.2004142445923464 absolute error = 3.42864625579864e-13 relative error = 1.710779721654431e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.1999999999992 y[1] (closed_form) = 0.2451304106706985 y[1] (numeric) = 0.2451304106703109 absolute error = 3.875233467454109e-13 relative error = 1.580886458294231e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.0999039999991 y[1] (closed_form) = 0.2874512492438791 y[1] (numeric) = 0.2874512492434496 absolute error = 4.295452882274731e-13 relative error = 1.494323957044412e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.999935999999 y[1] (closed_form) = 0.3268460274426866 y[1] (numeric) = 0.3268460274422183 absolute error = 4.683475829381223e-13 relative error = 1.432930320746359e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.8999679999989 y[1] (closed_form) = 0.3629771561731548 y[1] (numeric) = 0.362977156172651 absolute error = 5.037636974236648e-13 relative error = 1.387866120101919e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.7999999999988 y[1] (closed_form) = 0.3954838559575755 y[1] (numeric) = 0.3954838559570393 absolute error = 5.361822097427194e-13 relative error = 1.355762572013147e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.6999039999987 y[1] (closed_form) = 0.4240754460362505 y[1] (numeric) = 0.4240754460356861 absolute error = 5.644373857194296e-13 relative error = 1.330983415793379e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.5999359999986 y[1] (closed_form) = 0.4483933679032784 y[1] (numeric) = 0.4483933679026902 absolute error = 5.881961584464079e-13 relative error = 1.311786035544767e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.4999679999985 y[1] (closed_form) = 0.4682339559375704 y[1] (numeric) = 0.4682339559369619 absolute error = 6.085687509482796e-13 relative error = 1.299710845894782e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.3999999999984 y[1] (closed_form) = 0.4833990962899349 y[1] (numeric) = 0.483399096289311 absolute error = 6.238898286881067e-13 relative error = 1.290630937203713e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.2999039999983 y[1] (closed_form) = 0.4937474544727203 y[1] (numeric) = 0.4937474544720863 absolute error = 6.339928582121956e-13 relative error = 1.284042788411426e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.1999359999982 y[1] (closed_form) = 0.4991492548477636 y[1] (numeric) = 0.4991492548471241 absolute error = 6.394884621840902e-13 relative error = 1.281156800242302e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.0999679999981 y[1] (closed_form) = 0.4995669095902228 y[1] (numeric) = 0.4995669095895833 absolute error = 6.394329510328589e-13 relative error = 1.279974591506398e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.999999999998 y[1] (closed_form) = 0.4949962483000816 y[1] (numeric) = 0.4949962482994466 absolute error = 6.349920589343583e-13 relative error = 1.282821963025075e-10 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.8999039999979 y[1] (closed_form) = 0.4854675963696717 y[1] (numeric) = 0.485467596369046 absolute error = 6.25666185527507e-13 relative error = 1.288790828072236e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.7999359999978 y[1] (closed_form) = 0.4711004497483272 y[1] (numeric) = 0.4711004497477159 absolute error = 6.112332862073799e-13 relative error = 1.29745850706344e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.6999679999977 y[1] (closed_form) = 0.452029232698514 y[1] (numeric) = 0.4520292326979224 absolute error = 5.915268275202834e-13 relative error = 1.308603038765878e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.5999999999976 y[1] (closed_form) = 0.4284443766838549 y[1] (numeric) = 0.4284443766832869 absolute error = 5.680456105494613e-13 relative error = 1.325832806923772e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.4999039999975 y[1] (closed_form) = 0.4005430792640108 y[1] (numeric) = 0.4005430792634714 absolute error = 5.394018565141323e-13 relative error = 1.346676261403072e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.3999359999974 y[1] (closed_form) = 0.3686752421928904 y[1] (numeric) = 0.3686752421923828 absolute error = 5.076494780098528e-13 relative error = 1.376955704946011e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.2999679999973 y[1] (closed_form) = 0.3331260791849458 y[1] (numeric) = 0.3331260791844737 absolute error = 4.720668300706166e-13 relative error = 1.41708157831898e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.1999999999972 y[1] (closed_form) = 0.2942505586265409 y[1] (numeric) = 0.2942505586261081 absolute error = 4.32764934998886e-13 relative error = 1.47073615431312e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.0999039999971 y[1] (closed_form) = 0.2523816170859759 y[1] (numeric) = 0.2523816170855846 absolute error = 3.912981050291364e-13 relative error = 1.550422370484446e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.999935999997 y[1] (closed_form) = 0.2080443203284342 y[1] (numeric) = 0.2080443203280873 absolute error = 3.469169396197458e-13 relative error = 1.667514590506854e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.899967999997073 y[1] (closed_form) = 0.1616296425462044 y[1] (numeric) = 0.1616296425458231 absolute error = 3.812783422318944e-13 relative error = 2.358962973780629e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.799999999997147 y[1] (closed_form) = 0.1136010473451542 y[1] (numeric) = 0.1136010473447376 absolute error = 4.1661118999059e-13 relative error = 3.667318213403435e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.69990399999722 y[1] (closed_form) = 0.06437464693869774 y[1] (numeric) = 0.06437464693824511 absolute error = 4.526240493518685e-13 relative error = 7.031091755468427e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.599935999997294 y[1] (closed_form) = 0.01456777476411601 y[1] (numeric) = 0.01456777476362679 absolute error = 4.892145716306473e-13 relative error = 3.358196976217002e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.499967999997367 y[1] (closed_form) = -0.03538456073683878 y[1] (numeric) = -0.0353845607373647 absolute error = 5.259195856588406e-13 relative error = 1.486296776637125e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399999999997441 y[1] (closed_form) = -0.08498357145138154 y[1] (numeric) = -0.08498357145194385 absolute error = 5.62314084184834e-13 relative error = 6.616738677622293e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299903999997514 y[1] (closed_form) = -0.133795664490003 y[1] (numeric) = -0.1337956644906012 absolute error = 5.9821592124365e-13 relative error = 4.471115887976682e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199935999997588 y[1] (closed_form) = -0.1812087021191372 y[1] (numeric) = -0.1812087021197704 absolute error = 6.331601909437268e-13 relative error = 3.494093735782348e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099967999997661 y[1] (closed_form) = -0.2268123199154689 y[1] (numeric) = -0.2268123199161354 absolute error = 6.665501484093284e-13 relative error = 2.938773998950966e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9999999999977344 y[1] (closed_form) = -0.2701511529350231 y[1] (numeric) = -0.2701511529357216 absolute error = 6.985523270941485e-13 relative error = 2.58578325320775e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8999039999977211 y[1] (closed_form) = -0.3108425823956397 y[1] (numeric) = -0.3108425823963326 absolute error = 6.928901896685602e-13 relative error = 2.229071011855934e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7999359999977078 y[1] (closed_form) = -0.3483763093558703 y[1] (numeric) = -0.3483763093565584 absolute error = 6.88116230662672e-13 relative error = 1.975209600029816e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6999679999976945 y[1] (closed_form) = -0.3824314009301812 y[1] (numeric) = -0.3824314009308653 absolute error = 6.840084054715589e-13 relative error = 1.78857803989907e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5999999999976813 y[1] (closed_form) = -0.4126678074554938 y[1] (numeric) = -0.4126678074561751 absolute error = 6.813438702124586e-13 relative error = 1.651071050135021e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.499903999997668 y[1] (closed_form) = -0.4388142913496127 y[1] (numeric) = -0.4388142913502904 absolute error = 6.777356453824268e-13 relative error = 1.54447031179862e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3999359999976547 y[1] (closed_form) = -0.460542957445678 y[1] (numeric) = -0.4605429574463539 absolute error = 6.759037773917953e-13 relative error = 1.467623739467386e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2999679999976415 y[1] (closed_form) = -0.4776729726418911 y[1] (numeric) = -0.4776729726425653 absolute error = 6.741829317036263e-13 relative error = 1.41139015669002e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.199999999997639 y[1] (closed_form) = -0.4900332889208553 y[1] (numeric) = -0.4900332889215289 absolute error = 6.735167978888512e-13 relative error = 1.374430703212145e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.09990399999764472 y[1] (closed_form) = -0.4975068723506325 y[1] (numeric) = -0.4975068723513062 absolute error = 6.737388424937762e-13 relative error = 1.354230222610752e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 6.400000235686883e-05 y[1] (closed_form) = -0.4999999989759999 y[1] (numeric) = -0.499999998976674 absolute error = 6.740163982499325e-13 relative error = 1.348032799260636e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000320000023585 y[1] (closed_form) = -0.497500485049508 y[1] (numeric) = -0.4975004850501822 absolute error = 6.741829317036263e-13 relative error = 1.355140250037216e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000023528 y[1] (closed_form) = -0.4900332889203871 y[1] (numeric) = -0.49003328892106 absolute error = 6.728506640740761e-13 relative error = 1.37307133879917e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000960000023552 y[1] (closed_form) = -0.4776540573914617 y[1] (numeric) = -0.4776540573921347 absolute error = 6.730171975277699e-13 relative error = 1.409005507465413e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000640000023685 y[1] (closed_form) = -0.4605180346708695 y[1] (numeric) = -0.4605180346715447 absolute error = 6.752376435770202e-13 relative error = 1.466256677785942e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000320000023817 y[1] (closed_form) = -0.4387836099113379 y[1] (numeric) = -0.4387836099120156 absolute error = 6.777356453824268e-13 relative error = 1.544578307105346e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.600000000002395 y[1] (closed_form) = -0.412667807454163 y[1] (numeric) = -0.4126678074548448 absolute error = 6.817879594223086e-13 relative error = 1.652147192261994e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000960000024082 y[1] (closed_form) = -0.3823901694303321 y[1] (numeric) = -0.3823901694310177 absolute error = 6.855627177060342e-13 relative error = 1.792835623173459e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000640000024215 y[1] (closed_form) = -0.3483303985643934 y[1] (numeric) = -0.3483303985650832 absolute error = 6.898925875020723e-13 relative error = 1.980569569424291e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000320000024348 y[1] (closed_form) = -0.3107924507446945 y[1] (numeric) = -0.31079245074539 absolute error = 6.954992137764293e-13 relative error = 2.237825314321288e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.000000000002448 y[1] (closed_form) = -0.2701511529330399 y[1] (numeric) = -0.270151152933741 absolute error = 7.011613512020176e-13 relative error = 2.595440898880075e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.100096000002375 y[1] (closed_form) = -0.2267552817134278 y[1] (numeric) = -0.2267552817140966 absolute error = 6.687150833073474e-13 relative error = 2.949060671285558e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200064000002301 y[1] (closed_form) = -0.1811490516154795 y[1] (numeric) = -0.1811490516161144 absolute error = 6.349643033587427e-13 relative error = 3.50520357515625e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.300032000002228 y[1] (closed_form) = -0.1337339973117767 y[1] (numeric) = -0.133733997312377 absolute error = 6.002698338392065e-13 relative error = 4.488535794228789e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000002154 y[1] (closed_form) = -0.08498357144905905 y[1] (numeric) = -0.08498357144962368 absolute error = 5.64631674748739e-13 relative error = 6.64400972001031e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.500096000002081 y[1] (closed_form) = -0.03532072091055177 y[1] (numeric) = -0.0353207209110798 absolute error = 5.280359482995323e-13 relative error = 1.494975002454681e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600064000002007 y[1] (closed_form) = 0.01463174747702272 y[1] (numeric) = 0.01463174747653136 absolute error = 4.913604245704306e-13 relative error = 3.358180048842757e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.700032000001934 y[1] (closed_form) = 0.0644381137527015 y[1] (numeric) = 0.0644381137522468 absolute error = 4.547057175230407e-13 relative error = 7.056471566937783e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.80000000000186 y[1] (closed_form) = 0.1136010473474494 y[1] (numeric) = 0.1136010473470309 absolute error = 4.184430579812215e-13 relative error = 3.683443663168099e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900096000001787 y[1] (closed_form) = 0.1616902050918772 y[1] (numeric) = 0.1616902050914944 absolute error = 3.82804898890754e-13 relative error = 2.367520646493292e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.000064000001713 y[1] (closed_form) = 0.2081025153658543 y[1] (numeric) = 0.2081025153655058 absolute error = 3.485267630054523e-13 relative error = 1.674783999572159e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100032000001813 y[1] (closed_form) = 0.2524368635213348 y[1] (numeric) = 0.2524368635209417 absolute error = 3.930189507173054e-13 relative error = 1.556899991684809e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000000001913 y[1] (closed_form) = 0.2942505586284463 y[1] (numeric) = 0.2942505586280114 absolute error = 4.348743587456738e-13 relative error = 1.477904955466184e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300096000002013 y[1] (closed_form) = 0.3331738029556923 y[1] (numeric) = 0.333173802955219 absolute error = 4.73232564246473e-13 relative error = 1.420377472803306e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400064000002113 y[1] (closed_form) = 0.3687184718380082 y[1] (numeric) = 0.3687184718374993 absolute error = 5.088707233369405e-13 relative error = 1.380106401505446e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500032000002213 y[1] (closed_form) = 0.4005813831233404 y[1] (numeric) = 0.4005813831227991 absolute error = 5.412892356559951e-13 relative error = 1.351259091062977e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000002313 y[1] (closed_form) = 0.4284443766850699 y[1] (numeric) = 0.4284443766845011 absolute error = 5.68822766666699e-13 relative error = 1.327646708932802e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700096000002413 y[1] (closed_form) = 0.4520565831602837 y[1] (numeric) = 0.4520565831596909 absolute error = 5.927480728473711e-13 relative error = 1.311225397279975e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800064000002513 y[1] (closed_form) = 0.471121888990712 y[1] (numeric) = 0.4711218889900995 absolute error = 6.124545315344676e-13 relative error = 1.299991670619537e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900032000002613 y[1] (closed_form) = 0.4854829103158093 y[1] (numeric) = 0.485482910315182 absolute error = 6.273315200644447e-13 relative error = 1.292180438764286e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000002713 y[1] (closed_form) = 0.4949962483004142 y[1] (numeric) = 0.4949962482997777 absolute error = 6.36435348866371e-13 relative error = 1.2857377223597e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100096000002813 y[1] (closed_form) = 0.4995695687064844 y[1] (numeric) = 0.4995695687058433 absolute error = 6.410982855697966e-13 relative error = 1.283301317231486e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200064000002913 y[1] (closed_form) = 0.4991455189024492 y[1] (numeric) = 0.4991455189018094 absolute error = 6.398215290914777e-13 relative error = 1.281833663454207e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300032000003013 y[1] (closed_form) = 0.493737360770294 y[1] (numeric) = 0.4937373607696584 absolute error = 6.356026815979021e-13 relative error = 1.287329523952329e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000003113 y[1] (closed_form) = 0.4833990962893327 y[1] (numeric) = 0.4833990962887076 absolute error = 6.251110740151944e-13 relative error = 1.293157307933902e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500096000003214 y[1] (closed_form) = 0.468211503892335 y[1] (numeric) = 0.4682115038917258 absolute error = 6.091238624605921e-13 relative error = 1.300958770548833e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600064000003314 y[1] (closed_form) = 0.4483650465938839 y[1] (numeric) = 0.4483650465932947 absolute error = 5.891398480173393e-13 relative error = 1.313973630399796e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700032000003413 y[1] (closed_form) = 0.424041538258933 y[1] (numeric) = 0.4240415382583669 absolute error = 5.661027202563673e-13 relative error = 1.335017136719015e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000003513 y[1] (closed_form) = 0.3954838559561335 y[1] (numeric) = 0.3954838559555962 absolute error = 5.373479439185758e-13 relative error = 1.358710187093396e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900096000003614 y[1] (closed_form) = 0.3629331376506891 y[1] (numeric) = 0.3629331376501847 absolute error = 5.044298312384399e-13 relative error = 1.389869865572695e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000064000003714 y[1] (closed_form) = 0.3267975920812363 y[1] (numeric) = 0.3267975920807676 absolute error = 4.686806498455098e-13 relative error = 1.43416188246884e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100032000003814 y[1] (closed_form) = 0.2873988806841444 y[1] (numeric) = 0.2873988806837162 absolute error = 4.282130205979229e-13 relative error = 1.489960641386545e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200000000003913 y[1] (closed_form) = 0.2451304106686443 y[1] (numeric) = 0.2451304106682583 absolute error = 3.859967900865513e-13 relative error = 1.574658929643468e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300096000004014 y[1] (closed_form) = 0.2003556091498113 y[1] (numeric) = 0.2003556091494701 absolute error = 3.412270466185419e-13 relative error = 1.703107030876271e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.400064000004114 y[1] (closed_form) = 0.1536359834062 y[1] (numeric) = 0.1536359834059058 absolute error = 2.941813459500509e-13 relative error = 1.914794564579714e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.500032000004214 y[1] (closed_form) = 0.1053822591774867 y[1] (numeric) = 0.1053822591772409 absolute error = 2.458588888032409e-13 relative error = 2.333019720038085e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.600000000004314 y[1] (closed_form) = 0.0560762634653841 y[1] (numeric) = 0.05607626346518743 absolute error = 1.966690699184426e-13 relative error = 3.507171444114612e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.700096000004414 y[1] (closed_form) = 0.006146335384405884 y[1] (numeric) = 0.006146335384259225 absolute error = 1.466587268295072e-13 relative error = 2.38611656632993e-09 % Desired digits = 16 Estimated correct digits = 9 Correct digits = 11 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.800064000004514 y[1] (closed_form) = -0.04378136889983344 y[1] (numeric) = -0.04378136889993015 absolute error = 9.670042544485113e-14 relative error = 2.208711784825417e-10 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 12 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.900032000004614 y[1] (closed_form) = -0.09327190390760615 y[1] (numeric) = -0.09327190390765357 absolute error = 4.7420400939302e-14 relative error = 5.084103460166953e-11 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 13 h = 0.000128 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) / 2.0 ; Iterations = 78125 Total Elapsed Time = 1.0 Seconds Elapsed Time(since restart) = 1.0 Seconds Time to Timeout = 2 Minutes 59.0 Seconds Percent Done = 100 %