##############ECHO OF PROBLEM################# ##############temp/lin_arctanpostode.ode################# diff ( y , x , 1 ) = arctan ( 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=-0.6; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=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) * arctan(0.1 * x + 0.2) - 5.0 * ln(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 = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 400000.0000000001 step_error = 5.270462766947299e-21 est_needed_step_err = 5.270462766947299e-21 opt_iter = 1 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 400000.0000000001 step_error = 5.270462766947299e-21 est_needed_step_err = 5.270462766947299e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.471162334935134e-185 estimated_step_error = 2.471162334935134e-185 Double H and LOOP opt_iter = 2 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 200000 step_error = 7.453559924999299e-21 est_needed_step_err = 7.453559924999299e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.658368769248977e-177 estimated_step_error = 1.658368769248977e-177 Double H and LOOP opt_iter = 3 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 100000 step_error = 1.05409255338946e-20 est_needed_step_err = 1.05409255338946e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.112912171764129e-169 estimated_step_error = 1.112912171764129e-169 Double H and LOOP opt_iter = 4 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 50000.00000000001 step_error = 1.49071198499986e-20 est_needed_step_err = 1.49071198499986e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.468623531193766e-162 estimated_step_error = 7.468623531193766e-162 Double H and LOOP opt_iter = 5 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 25000 step_error = 2.108185106778919e-20 est_needed_step_err = 2.108185106778919e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.012103540555958e-154 estimated_step_error = 5.012103540555958e-154 Double H and LOOP opt_iter = 6 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 12500 step_error = 2.98142396999972e-20 est_needed_step_err = 2.98142396999972e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.363559215300437e-146 estimated_step_error = 3.363559215300437e-146 Double H and LOOP opt_iter = 7 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 6250.000000000001 step_error = 4.216370213557839e-20 est_needed_step_err = 4.216370213557839e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.257237610544898e-138 estimated_step_error = 2.257237610544898e-138 Double H and LOOP opt_iter = 8 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 3125 step_error = 5.962847939999439e-20 est_needed_step_err = 5.962847939999439e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.514794748910067e-130 estimated_step_error = 1.514794748910067e-130 Double H and LOOP opt_iter = 9 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 1562.5 step_error = 8.432740427115678e-20 est_needed_step_err = 8.432740427115678e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.016545751403892e-122 estimated_step_error = 1.016545751403892e-122 Double H and LOOP opt_iter = 10 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 781.2500000000001 step_error = 1.192569587999888e-19 est_needed_step_err = 1.192569587999888e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.821711040100051e-115 estimated_step_error = 6.821711040100051e-115 Double H and LOOP opt_iter = 11 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 390.6250000000001 step_error = 1.686548085423136e-19 est_needed_step_err = 1.686548085423136e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.577688216910538e-107 estimated_step_error = 4.577688216910538e-107 Double H and LOOP opt_iter = 12 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 195.3125 step_error = 2.385139175999776e-19 est_needed_step_err = 2.385139175999776e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.071652615137071e-99 estimated_step_error = 3.071652615137071e-99 Double H and LOOP opt_iter = 13 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 97.65625000000001 step_error = 3.373096170846271e-19 est_needed_step_err = 3.373096170846271e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.060838525925138e-91 estimated_step_error = 2.060838525925138e-91 Double H and LOOP opt_iter = 14 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 48.82812500000001 step_error = 4.770278351999551e-19 est_needed_step_err = 4.770278351999551e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.38231722244458e-83 estimated_step_error = 1.38231722244458e-83 Double H and LOOP opt_iter = 15 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 24.4140625 step_error = 6.746192341692542e-19 est_needed_step_err = 6.746192341692542e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.267337406320531e-76 estimated_step_error = 9.267337406320531e-76 Double H and LOOP opt_iter = 16 NO INFO (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 = 0.04991699822532158 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.4 estimated_steps = 12.20703125 step_error = 9.540556703999103e-19 est_needed_step_err = 9.540556703999103e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.206805504858393e-68 estimated_step_error = 6.206805504858393e-68 Double H and LOOP opt_iter = 17 SETTING H FOR DISPLAY INTERVAL NO INFO (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 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = 0.04991699822532158 y[1] (numeric) = 0.04991699822532158 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.04 NO INFO (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] = -0.96 y[1] (closed_form) = 0.05398293113212667 y[1] (numeric) = 0.05398297314421072 absolute error = 4.201208405468781e-08 relative error = 7.782475529507754e-05 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 7 h = 0.04 NO INFO (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] = -0.9199999999999999 y[1] (closed_form) = 0.05820715159667454 y[1] (numeric) = 0.05820723722154577 absolute error = 8.562487122804052e-08 relative error = 0.0001471036958161897 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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] = -0.8799999999999999 y[1] (closed_form) = 0.06258952694041534 y[1] (numeric) = 0.06258965777063388 absolute error = 1.308302185476506e-07 relative error = 0.0002090289301470513 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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] = -0.8399999999999999 y[1] (closed_form) = 0.06712991971303305 y[1] (numeric) = 0.06713009733273774 absolute error = 1.776197046943206e-07 relative error = 0.0002645909684587875 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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] = -0.7999999999999998 y[1] (closed_form) = 0.07182818771788424 y[1] (numeric) = 0.07182841370252901 absolute error = 2.25984644774968e-07 relative error = 0.0003146183301499349 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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] = -0.7599999999999998 y[1] (closed_form) = 0.07668418403826716 y[1] (numeric) = 0.07668445995435043 absolute error = 2.759160832727092e-07 relative error = 0.000359808331708949 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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] = -0.7199999999999998 y[1] (closed_form) = 0.08169775706447183 y[1] (numeric) = 0.08169808446927437 absolute error = 3.274048025470044e-07 relative error = 0.000400751274344818 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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] = -0.6799999999999997 y[1] (closed_form) = 0.08686875052161584 y[1] (numeric) = 0.08686913096294598 absolute error = 3.804413301333742e-07 relative error = 0.0004379495823860247 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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] = -0.6399999999999997 y[1] (closed_form) = 0.09219700349826254 y[1] (numeric) = 0.09219743851419807 absolute error = 4.350159355237526e-07 relative error = 0.0004718330520708848 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 6 h = 0.04 NO INFO (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 ) = arctan ( 0.1 * x + 0.2 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 110 %