##############ECHO OF PROBLEM################# ##############temp/arccos_sqrtpostode.ode################# diff ( y , x , 1 ) = arccos ( 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=0.0; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; // 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(10.0 * (0.1 * x + 0.2) * arccos(sqrt ( 0.1 * x + 0.2)) - 5.0 * sqrt( 0.1 * x + 0.2) * sqrt( 0.8 - 0.1 * x) + 5.0 * arcsin(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 = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.5 estimated_steps = 500000 step_error = 4.714045207910316e-21 est_needed_step_err = 4.714045207910316e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 500000 step_error = 1.193848674614856e-20 est_needed_step_err = 1.193848674614856e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.25875997052594e-168 estimated_step_error = 1.25875997052594e-168 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 250000 step_error = 1.688356987061474e-20 est_needed_step_err = 1.688356987061474e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.44739325058823e-161 estimated_step_error = 8.44739325058823e-161 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 125000 step_error = 2.387697349229713e-20 est_needed_step_err = 2.387697349229713e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.668947075830024e-153 estimated_step_error = 5.668947075830024e-153 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 62500 step_error = 3.376713974122948e-20 est_needed_step_err = 3.376713974122948e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.804362530936719e-145 estimated_step_error = 3.804362530936719e-145 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 31250 step_error = 4.775394698459425e-20 est_needed_step_err = 4.775394698459425e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.553059843214273e-137 estimated_step_error = 2.553059843214273e-137 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 15625 step_error = 6.753427948245897e-20 est_needed_step_err = 6.753427948245897e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.713323238756048e-129 estimated_step_error = 1.713323238756048e-129 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 7812.5 step_error = 9.55078939691885e-20 est_needed_step_err = 9.55078939691885e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.14978341491193e-121 estimated_step_error = 1.14978341491193e-121 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 3906.25 step_error = 1.350685589649179e-19 est_needed_step_err = 1.350685589649179e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.71595384942909e-114 estimated_step_error = 7.71595384942909e-114 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 1953.125 step_error = 1.91015787938377e-19 est_needed_step_err = 1.91015787938377e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.177938614013485e-106 estimated_step_error = 5.177938614013485e-106 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 min_size = 2.532535480592211 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 2.532535480592211 desired_abs_gbl_error = 2.532535480592211e-16 range = 0.5 estimated_steps = 976.5625 step_error = 2.701371179298359e-19 est_needed_step_err = 2.701371179298359e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.474653988869495e-98 estimated_step_error = 3.474653988869495e-98 Double H and LOOP opt_iter = 11 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.953 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 2.532535480592211 y[1] (numeric) = 2.532535480592211 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.001 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.05000000000000004 y[1] (closed_form) = 2.587737149360984 y[1] (numeric) = 2.587737149425986 absolute error = 6.500178173496352e-11 relative error = 2.51191593207274e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.001 Radius of convergence (given) for eq 1 = 2.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.05 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1000000000000001 y[1] (closed_form) = 2.642629173205489 y[1] (numeric) = 2.642629173335314 absolute error = 1.298254836967772e-10 relative error = 4.912739366276648e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.001 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1500000000000001 y[1] (closed_form) = 2.69721429444846 y[1] (numeric) = 2.697214294642953 absolute error = 1.944937544351433e-10 relative error = 7.210912193200962e-09 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 11 h = 0.001 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.15 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (closed_form) = 2.751495138739343 y[1] (numeric) = 2.75149513899837 absolute error = 2.590265779645051e-10 relative error = 9.414030005634819e-09 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 11 h = 0.001 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 1.495 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000002 y[1] (closed_form) = 2.80547422150072 y[1] (numeric) = 2.805474221824166 absolute error = 3.234457146561454e-10 relative error = 1.152909237865411e-08 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 10 h = 0.001 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.25 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (closed_form) = 2.859153953861397 y[1] (numeric) = 2.859153954249172 absolute error = 3.877755894166057e-10 relative error = 1.356259913506581e-08 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 10 h = 0.001 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.3 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000003 y[1] (closed_form) = 2.912536648126649 y[1] (numeric) = 2.912536648578679 absolute error = 4.520299690113916e-10 relative error = 1.552014699290182e-08 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 10 h = 0.001 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.35 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000003 y[1] (closed_form) = 2.965624522830128 y[1] (numeric) = 2.965624523346361 absolute error = 5.162332783470447e-10 relative error = 1.740723663339544e-08 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 10 h = 0.001 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (closed_form) = 3.018419707406812 y[1] (numeric) = 3.018419707987211 absolute error = 5.803992841890704e-10 relative error = 1.92285811931603e-08 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 10 h = 0.001 Radius of convergence (given) for eq 1 = 2.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.45 Order of pole (three term test) = 1.494 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = arccos ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 500 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.2 %