##############ECHO OF PROBLEM################# ##############temp/lin_arcsinpostode.ode################# diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-0.8; x_end=0.8; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=100; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arcsin(0.1 * x + 0.2 ) + 10.0 * sqrt(1.0 - expt((0.1 * x + 0.2) , 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 = 1.6 estimated_steps = 1600000 step_error = 6.249999999999999e-17 est_needed_step_err = 6.249999999999999e-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 = 2.850926362169087e-184 estimated_step_error = 2.850926362169087e-184 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 = 1.913224393310235e-176 estimated_step_error = 1.913224393310235e-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 = 1.283943287899108e-168 estimated_step_error = 1.283943287899108e-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 = 8.616399317824539e-161 estimated_step_error = 8.616399317824539e-161 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 = 5.782370073794332e-153 estimated_step_error = 5.782370073794332e-153 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 = 3.880486054995988e-145 estimated_step_error = 3.880486054995988e-145 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 = 2.60415438563764e-137 estimated_step_error = 2.60415438563764e-137 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 = 1.747624164792156e-129 estimated_step_error = 1.747624164792156e-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 = 1.172818427866771e-121 estimated_step_error = 1.172818427866771e-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 = 7.870754639100936e-114 estimated_step_error = 7.870754639100936e-114 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 = 5.282112815692789e-106 estimated_step_error = 5.282112815692789e-106 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 = 3.544952200337044e-98 estimated_step_error = 3.544952200337044e-98 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 = 2.37922723116969e-90 estimated_step_error = 2.37922723116969e-90 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 = 1.597008125855334e-82 estimated_step_error = 1.597008125855334e-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 = 1.072184946902944e-74 estimated_step_error = 1.072184946902944e-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 = 7.201371451878794e-67 estimated_step_error = 7.201371451878794e-67 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 = 4.84091298322985e-59 estimated_step_error = 4.84091298322985e-59 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 = 3.25968198404761e-51 estimated_step_error = 3.25968198404761e-51 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (analytic) = 10.07208677566643 y[1] (numeric) = 10.07208677566643 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.624 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.7000000000000001 y[1] (analytic) = 10.08461961211218 y[1] (numeric) = 10.08461961211218 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.53 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.6000000000000001 y[1] (analytic) = 10.09816101618305 y[1] (numeric) = 10.09816101618305 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.429 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.5000000000000001 y[1] (analytic) = 10.11271237580762 y[1] (numeric) = 10.11271237580762 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.325 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.4000000000000001 y[1] (analytic) = 10.12827518812551 y[1] (numeric) = 10.12827518812551 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.218 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.3000000000000002 y[1] (analytic) = 10.14485106091358 y[1] (numeric) = 10.14485106091358 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.11 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 6.392 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.2000000000000001 y[1] (analytic) = 10.16244171413014 y[1] (numeric) = 10.16244171413014 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.001 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 6.736 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.1000000000000001 y[1] (analytic) = 10.18104898158115 y[1] (numeric) = 10.18104898158116 absolute error = 1.77635683940025e-15 relative error = 1.74476799258496e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.892 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 6.994 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.387778780781446e-16 y[1] (analytic) = 10.20067481271337 y[1] (numeric) = 10.20067481271338 absolute error = 1.77635683940025e-15 relative error = 1.741411104671555e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.782 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.176 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999987 y[1] (analytic) = 10.22132127453915 y[1] (numeric) = 10.22132127453915 absolute error = 1.77635683940025e-15 relative error = 1.737893557680332e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.673 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.292 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1999999999999999 y[1] (analytic) = 10.24299055369871 y[1] (numeric) = 10.24299055369871 absolute error = 1.77635683940025e-15 relative error = 1.734217004387273e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.563 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.356 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2999999999999999 y[1] (analytic) = 10.26568495866573 y[1] (numeric) = 10.26568495866573 absolute error = 1.77635683940025e-15 relative error = 1.730383161525668e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.454 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.378 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3999999999999999 y[1] (analytic) = 10.28940692210279 y[1] (numeric) = 10.28940692210279 absolute error = 3.552713678800501e-15 relative error = 3.452787615162617e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.344 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.368 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (analytic) = 10.31415900337374 y[1] (numeric) = 10.31415900337374 absolute error = 3.552713678800501e-15 relative error = 3.444501561046728e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.234 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.334 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5999999999999999 y[1] (analytic) = 10.33994389122067 y[1] (numeric) = 10.33994389122067 absolute error = 1.77635683940025e-15 relative error = 1.717955975475361e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.124 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.282 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6999999999999998 y[1] (analytic) = 10.3667644066138 y[1] (numeric) = 10.3667644066138 absolute error = 1.77635683940025e-15 relative error = 1.713511342330659e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.015 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.217 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999998 y[1] (analytic) = 10.39462350578332 y[1] (numeric) = 10.39462350578332 absolute error = 1.77635683940025e-15 relative error = 1.708918883316869e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.905 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 7.142 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arcsin (0.1 * x + 0.2) ; Iterations = 17 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 112.5 %