##############ECHO OF PROBLEM################# ##############temp/divpostode.ode################# diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.0; x_end=1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=1.570796327; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.0; 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(2.0 - ln(float_abs(cos(x)))); } // 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 = 1.5 estimated_steps = 1500000 step_error = 2.721655269759087e-21 est_needed_step_err = 2.721655269759087e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 1500000 step_error = 5.443310539518174e-21 est_needed_step_err = 5.443310539518174e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.122655795896327e-163 estimated_step_error = 6.122655795896327e-163 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 750000 step_error = 7.698003589195011e-21 est_needed_step_err = 7.698003589195011e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.108844751257343e-155 estimated_step_error = 4.108844751257343e-155 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 375000 step_error = 1.088662107903635e-20 est_needed_step_err = 1.088662107903635e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.757399036095542e-147 estimated_step_error = 2.757399036095542e-147 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 187500 step_error = 1.539600717839002e-20 est_needed_step_err = 1.539600717839002e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.850459169079025e-139 estimated_step_error = 1.850459169079025e-139 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 93750 step_error = 2.17732421580727e-20 est_needed_step_err = 2.17732421580727e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.241822127175205e-131 estimated_step_error = 1.241822127175205e-131 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 46875 step_error = 3.079201435678005e-20 est_needed_step_err = 3.079201435678005e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.333727225081321e-124 estimated_step_error = 8.333727225081321e-124 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 23437.5 step_error = 4.354648431614539e-20 est_needed_step_err = 4.354648431614539e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.592669671227225e-116 estimated_step_error = 5.592669671227225e-116 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 11718.75 step_error = 6.158402871356009e-20 est_needed_step_err = 6.158402871356009e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.753177087972187e-108 estimated_step_error = 3.753177087972187e-108 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 5859.375 step_error = 8.709296863229079e-20 est_needed_step_err = 8.709296863229079e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.518714519293995e-100 estimated_step_error = 2.518714519293995e-100 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 2929.6875 step_error = 1.231680574271202e-19 est_needed_step_err = 1.231680574271202e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.690280732567496e-92 estimated_step_error = 1.690280732567496e-92 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 1464.84375 step_error = 1.741859372645816e-19 est_needed_step_err = 1.741859372645816e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.134328281966585e-84 estimated_step_error = 1.134328281966585e-84 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 732.421875 step_error = 2.463361148542404e-19 est_needed_step_err = 2.463361148542404e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.612350493554584e-77 estimated_step_error = 7.612350493554584e-77 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 366.2109375 step_error = 3.483718745291632e-19 est_needed_step_err = 3.483718745291632e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.108567987692266e-69 estimated_step_error = 5.108567987692266e-69 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 183.10546875 step_error = 4.926722297084807e-19 est_needed_step_err = 4.926722297084807e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.428318177565283e-61 estimated_step_error = 3.428318177565283e-61 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 91.552734375 step_error = 6.967437490583263e-19 est_needed_step_err = 6.967437490583263e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.300748962040727e-53 estimated_step_error = 2.300748962040727e-53 Double H and LOOP opt_iter = 16 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 45.7763671875 step_error = 9.853444594169615e-19 est_needed_step_err = 9.853444594169615e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.544123472790415e-45 estimated_step_error = 1.544123472790415e-45 Double H and LOOP opt_iter = 17 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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 = 2 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 2 desired_abs_gbl_error = 2e-16 range = 1.5 estimated_steps = 22.88818359375 step_error = 1.393487498116653e-18 est_needed_step_err = 1.393487498116653e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.036557739487112e-37 estimated_step_error = 1.036557739487112e-37 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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] = 0 y[1] (closed_form) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 0 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] = 0.1 y[1] (closed_form) = 2.005008355623235 y[1] (numeric) = 2.005008355623235 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 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] = 0.2 y[1] (closed_form) = 2.020134773052408 y[1] (numeric) = 2.020134773052408 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 0 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] = 0.3 y[1] (closed_form) = 2.045691655926058 y[1] (numeric) = 2.045691655926058 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 0 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] = 0.4 y[1] (closed_form) = 2.082229019075055 y[1] (numeric) = 2.082229019075056 absolute error = 4.440892098500626e-16 relative error = 2.132758720495265e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0 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] = 0.5 y[1] (closed_form) = 2.130584240443723 y[1] (numeric) = 2.130584240443723 absolute error = 4.440892098500626e-16 relative error = 2.084354147656584e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 0 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] = 0.6 y[1] (closed_form) = 2.191965169419438 y[1] (numeric) = 2.191965169419438 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 0.9708 Order of pole (given) = 0 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] = 0.7 y[1] (closed_form) = 2.268085757567931 y[1] (numeric) = 2.268085757567931 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.8708 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8708 Order of pole (three term test) = 6.735e-07 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.8654512996745437 y[1] (closed_form) = 2.433407021279573 y[1] (numeric) = 2.433407021279573 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.07837166957711042 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.7053 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7053 Order of pole (three term test) = 1.208e-09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9359858023828368 y[1] (closed_form) = 2.522518785970091 y[1] (numeric) = 2.522518785970091 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.07053450270829305 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.6348 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6348 Order of pole (three term test) = 6.006e-11 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9994668548238752 y[1] (closed_form) = 2.614796632542262 y[1] (numeric) = 2.614796632542262 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.06348105244103845 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.5713 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5713 Order of pole (three term test) = 3.463e-12 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.108019454498361 y[1] (closed_form) = 2.806462327285321 y[1] (numeric) = 2.806462327285321 absolute error = 4.440892098500626e-16 relative error = 1.582380798532323e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.05141965247739221 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.4628 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4628 Order of pole (three term test) = 1.979e-13 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.195947060234703 y[1] (closed_form) = 3.004760627500619 y[1] (numeric) = 3.00476062750062 absolute error = 8.881784197001252e-16 relative error = 2.955904079583599e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.04164991850668877 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.233431986890722 y[1] (closed_form) = 3.105633411622787 y[1] (numeric) = 3.105633411622788 absolute error = 8.881784197001252e-16 relative error = 2.859894591474095e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.03748492665601934 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.3374 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3374 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.297531211472515 y[1] (closed_form) = 3.309789600320398 y[1] (numeric) = 3.309789600320399 absolute error = 1.332267629550188e-15 relative error = 4.025233596181522e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.03036279059137533 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.2733 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2733 Order of pole (three term test) = 9.894e-14 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 1.409436008848183 y[1] (closed_form) = 3.828458712822224 y[1] (numeric) = 3.828458712822226 absolute error = 1.77635683940025e-15 relative error = 4.639874614426164e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.01792892421630143 SETTING H FOR POLE Radius of convergence (given) for eq 1 = 0.1614 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1614 Order of pole (three term test) = 2.968e-13 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE Finished! diff ( y , x , 1 ) = sin ( x ) / cos ( x ) ; Iterations = 31 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100.6 %