##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=2.0; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0001; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; 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(sin(sqrt(2.0*x+3.0))-sqrt(2.0*x+3.0)*cos(sqrt(2.0*x+3.0))); } // 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 = 1 estimated_steps = 1000000 step_error = 2.5e-21 est_needed_step_err = 2.5e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-16 range = 1 estimated_steps = 1000000 step_error = 7.007229923977551e-21 est_needed_step_err = 7.007229923977551e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.791154658409449e-240 estimated_step_error = 1.791154658409449e-240 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-16 range = 1 estimated_steps = 500000 step_error = 9.909719593155644e-21 est_needed_step_err = 9.909719593155644e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.230871943468012e-229 estimated_step_error = 1.230871943468012e-229 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-16 range = 1 estimated_steps = 250000 step_error = 1.40144598479551e-20 est_needed_step_err = 1.40144598479551e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.45848531622724e-219 estimated_step_error = 8.45848531622724e-219 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-16 range = 1 estimated_steps = 125000 step_error = 1.981943918631129e-20 est_needed_step_err = 1.981943918631129e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.812623726234864e-208 estimated_step_error = 5.812623726234864e-208 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-16 range = 1 estimated_steps = 62500 step_error = 2.80289196959102e-20 est_needed_step_err = 2.80289196959102e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.994400317271163e-197 estimated_step_error = 3.994400317271163e-197 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-16 range = 1 estimated_steps = 31250 step_error = 3.963887837262257e-20 est_needed_step_err = 3.963887837262257e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.744925097867764e-186 estimated_step_error = 2.744925097867764e-186 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-16 range = 1 estimated_steps = 15625 step_error = 5.60578393918204e-20 est_needed_step_err = 5.60578393918204e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.886290056712885e-175 estimated_step_error = 1.886290056712885e-175 Double H and LOOP opt_iter = 8 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.125 Order of pole (six term test) = -1.313 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 2.80289196959102 y[1] (numeric) = 2.80289196959102 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.0001 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 TOP MAIN SOLVE Loop x[1] = 2.100000000000211 y[1] (closed_form) = 2.848803743596383 y[1] (numeric) = 2.848805410488842 absolute error = 1.666892459173397e-06 relative error = 5.851201448749435e-05 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 7 h = 0.0001 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.07 Order of pole (six term test) = -1.33 TOP MAIN SOLVE Loop x[1] = 2.200000000000422 y[1] (closed_form) = 2.891373776647514 y[1] (numeric) = 2.891377117962087 absolute error = 3.341314572580245e-06 relative error = 0.0001155614884373209 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.139 Order of pole (six term test) = -1.347 TOP MAIN SOLVE Loop x[1] = 2.300000000000633 y[1] (closed_form) = 2.93058958868788 y[1] (numeric) = 2.930594609403171 absolute error = 5.020715290626754e-06 relative error = 0.0001713209966351751 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.206 Order of pole (six term test) = -1.363 TOP MAIN SOLVE Loop x[1] = 2.400000000000844 y[1] (closed_form) = 2.966443639457465 y[1] (numeric) = 2.966450342161306 absolute error = 6.702703840844038e-06 relative error = 0.0002259508237975457 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.271 Order of pole (six term test) = -1.379 TOP MAIN SOLVE Loop x[1] = 2.500000000001055 y[1] (closed_form) = 2.998933019437902 y[1] (numeric) = 2.998941404476334 absolute error = 8.385038431146796e-06 relative error = 0.0002796007238840708 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.336 Order of pole (six term test) = -1.394 TOP MAIN SOLVE Loop x[1] = 2.600000000001266 y[1] (closed_form) = 3.02805916219416 y[1] (numeric) = 3.028069227810266 absolute error = 1.006561610594758e-05 relative error = 0.000332411474373372 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.399 Order of pole (six term test) = -1.408 TOP MAIN SOLVE Loop x[1] = 2.700000000001477 y[1] (closed_form) = 3.053827576101776 y[1] (numeric) = 3.053839318565277 absolute error = 1.174246350155173e-05 relative error = 0.0003845162573500967 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.462 Order of pole (six term test) = -1.421 TOP MAIN SOLVE Loop x[1] = 2.800000000001688 y[1] (closed_form) = 3.076247593690546 y[1] (numeric) = 3.076261007419004 absolute error = 1.341372845864441e-05 relative error = 0.0004360419000784033 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.525 Order of pole (six term test) = -1.434 TOP MAIN SOLVE Loop x[1] = 2.900000000001899 y[1] (closed_form) = 3.095332137042667 y[1] (numeric) = 3.095347214714997 absolute error = 1.507767233066559e-05 relative error = 0.0004871099986404386 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 6 h = 0.0001 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.588 Order of pole (six term test) = -1.446 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 10000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %