##############ECHO OF PROBLEM################# ##############temp/arctan_sqrtpostode.ode################# diff ( y , x , 1 ) = arctan(sqrt(0.1 * x + 0.2)); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; 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(10.0 * (0.1 * x + 0.2) * arctan(sqrt ( 0.1 * x + 0.2)) - 10.0 * sqrt( 0.1 * x + 0.2) + 10.0 * arctan(sqrt( 0.1 * x + 0.2))); } /* 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 = 1.5 estimated_steps = 1500000 step_error = 6.666666666666667e-17 est_needed_step_err = 6.666666666666667e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.792822763189861e-161 estimated_step_error = 2.792822763189861e-161 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.874230779639759e-153 estimated_step_error = 1.874230779639759e-153 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.257773843742575e-145 estimated_step_error = 1.257773843742575e-145 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 = 8.440762065201303e-138 estimated_step_error = 8.440762065201303e-138 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.664478976820091e-130 estimated_step_error = 5.664478976820091e-130 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.801339900577164e-122 estimated_step_error = 3.801339900577164e-122 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.550998991126603e-114 estimated_step_error = 2.550998991126603e-114 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.711896741012717e-106 estimated_step_error = 1.711896741012717e-106 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.148767751900283e-98 estimated_step_error = 1.148767751900283e-98 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 = 7.708354755676755e-91 estimated_step_error = 7.708354755676755e-91 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 = 5.171788310353771e-83 estimated_step_error = 5.171788310353771e-83 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.469117557772959e-75 estimated_step_error = 3.469117557772959e-75 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.325926398407866e-67 estimated_step_error = 2.325926398407866e-67 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.558013171381974e-59 estimated_step_error = 1.558013171381974e-59 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 = 1.041708390108846e-51 estimated_step_error = 1.041708390108846e-51 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.939610693763538e-44 estimated_step_error = 6.939610693763538e-44 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.589979076596559e-36 estimated_step_error = 4.589979076596559e-36 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.994423710885246e-28 estimated_step_error = 2.994423710885246e-28 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.2067734006979847 y[1] (numeric) = 0.2067734006979847 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 = 0.9997 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 3.989 Order of pole (six term test) = -0.5993 TOP MAIN SOLVE Loop x[1] = -0.9 y[1] (analytic) = 0.2381061705301097 y[1] (numeric) = 0.2381061705301101 absolute error = 3.33066907387547e-16 relative error = 1.398816782639528e-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 = 1.1 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.193 Order of pole (six term test) = -0.5994 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 0.270797914082765 y[1] (numeric) = 0.2707979140827651 absolute error = 1.110223024625157e-16 relative error = 4.099821183577636e-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 = 1.2 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.388 Order of pole (six term test) = -0.5996 TOP MAIN SOLVE Loop x[1] = -0.7000000000000001 y[1] (analytic) = 0.3047790435843121 y[1] (numeric) = 0.3047790435843118 absolute error = 2.775557561562891e-16 relative error = 9.10678611272392e-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 = 1.3 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.577 Order of pole (six term test) = -0.5997 TOP MAIN SOLVE Loop x[1] = -0.6000000000000001 y[1] (analytic) = 0.3399879263011445 y[1] (numeric) = 0.3399879263011442 absolute error = 3.33066907387547e-16 relative error = 9.796433391359102e-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 = 1.399 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.759 Order of pole (six term test) = -0.5999 TOP MAIN SOLVE Loop x[1] = -0.5000000000000001 y[1] (analytic) = 0.3763694581226096 y[1] (numeric) = 0.3763694581226096 absolute error = 5.551115123125783e-17 relative error = 1.474911155335404e-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 = 1.499 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 4.936 Order of pole (six term test) = -0.6 TOP MAIN SOLVE Loop x[1] = -0.4000000000000001 y[1] (analytic) = 0.4138739745034328 y[1] (numeric) = 0.4138739745034327 absolute error = 1.110223024625157e-16 relative error = 2.682514709839403e-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 = 1.599 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.108 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = -0.3000000000000002 y[1] (analytic) = 0.4524564022610109 y[1] (numeric) = 0.4524564022610099 absolute error = 9.992007221626409e-16 relative error = 2.208391166904578e-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 = 1.699 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.275 Order of pole (six term test) = -0.6004 TOP MAIN SOLVE Loop x[1] = -0.2000000000000001 y[1] (analytic) = 0.4920755875173732 y[1] (numeric) = 0.4920755875173731 absolute error = 1.110223024625157e-16 relative error = 2.256204235260826e-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 = 1.799 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.438 Order of pole (six term test) = -0.6005 TOP MAIN SOLVE Loop x[1] = -0.1000000000000001 y[1] (analytic) = 0.5326937551733573 y[1] (numeric) = 0.532693755173357 absolute error = 2.220446049250313e-16 relative error = 4.168335047456492e-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 = 1.899 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.598 Order of pole (six term test) = -0.6007 TOP MAIN SOLVE Loop x[1] = -1.387778780781446e-16 y[1] (analytic) = 0.5742760684080013 y[1] (numeric) = 0.5742760684080022 absolute error = 8.881784197001252e-16 relative error = 1.546605315040062e-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 = 1.999 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.753 Order of pole (six term test) = -0.6008 TOP MAIN SOLVE Loop x[1] = 0.09999999999999987 y[1] (analytic) = 0.6167902654763968 y[1] (numeric) = 0.6167902654763967 absolute error = 1.110223024625157e-16 relative error = 1.800000886472555e-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 = 2.099 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 5.906 Order of pole (six term test) = -0.601 TOP MAIN SOLVE Loop x[1] = 0.1999999999999999 y[1] (analytic) = 0.6602063571030987 y[1] (numeric) = 0.6602063571030989 absolute error = 2.220446049250313e-16 relative error = 3.363260631105321e-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 = 2.199 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.055 Order of pole (six term test) = -0.6012 TOP MAIN SOLVE Loop x[1] = 0.2999999999999999 y[1] (analytic) = 0.704496371989249 y[1] (numeric) = 0.7044963719892492 absolute error = 2.220446049250313e-16 relative error = 3.151820417443113e-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 = 2.299 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.202 Order of pole (six term test) = -0.6013 TOP MAIN SOLVE Loop x[1] = 0.3999999999999999 y[1] (analytic) = 0.749634140965318 y[1] (numeric) = 0.7496341409653187 absolute error = 6.661338147750939e-16 relative error = 8.886118952870808e-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 = 2.398 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.346 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (analytic) = 0.7955951125100755 y[1] (numeric) = 0.7955951125100765 absolute error = 9.992007221626409e-16 relative error = 1.255916114177972e-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 = 2.498 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 6.488 Order of pole (six term test) = -0.6017 Finished! diff ( y , x , 1 ) = arctan(sqrt(0.1 * x + 0.2)); Iterations = 16 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 113.3 %