##############ECHO OF PROBLEM################# ##############temp/sing7postode.ode################# diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=64; max_terms=30; ! // 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_type_given_pole=1; array_given_rad_poles[1][1]=6.0; // 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(1.0/ ( x - 6.0 ) / ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )/ ( x - 6.0 )) ; } // 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 = 3.333333333333333e-21 est_needed_step_err = 3.333333333333333e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 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 = 3.333333333333333e-21 est_needed_step_err = 3.333333333333333e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.254211160650322e-174 estimated_step_error = 5.254211160650322e-174 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 500000 step_error = 4.714045207910316e-21 est_needed_step_err = 4.714045207910316e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.52604184650466e-166 estimated_step_error = 3.52604184650466e-166 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 250000 step_error = 6.666666666666667e-21 est_needed_step_err = 6.666666666666667e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.366287197015772e-158 estimated_step_error = 2.366287197015772e-158 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 125000 step_error = 9.428090415820633e-21 est_needed_step_err = 9.428090415820633e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.587989221482499e-150 estimated_step_error = 1.587989221482499e-150 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 62500 step_error = 1.333333333333333e-20 est_needed_step_err = 1.333333333333333e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.06568255319317e-142 estimated_step_error = 1.06568255319317e-142 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 31250 step_error = 1.885618083164127e-20 est_needed_step_err = 1.885618083164127e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.15168832658992e-135 estimated_step_error = 7.15168832658992e-135 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 15625 step_error = 2.666666666666667e-20 est_needed_step_err = 2.666666666666667e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.799435279580277e-127 estimated_step_error = 4.799435279580277e-127 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 7812.5 step_error = 3.771236166328253e-20 est_needed_step_err = 3.771236166328253e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.220871307371706e-119 estimated_step_error = 3.220871307371706e-119 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 3906.25 step_error = 5.333333333333333e-20 est_needed_step_err = 5.333333333333333e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.161523449266746e-111 estimated_step_error = 2.161523449266746e-111 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 1953.125 step_error = 7.542472332656506e-20 est_needed_step_err = 7.542472332656506e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.450618533821174e-103 estimated_step_error = 1.450618533821174e-103 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 976.5625 step_error = 1.066666666666667e-19 est_needed_step_err = 1.066666666666667e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.735536224832558e-96 estimated_step_error = 9.735536224832558e-96 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 488.28125 step_error = 1.508494466531301e-19 est_needed_step_err = 1.508494466531301e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.534213266775494e-88 estimated_step_error = 6.534213266775494e-88 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 244.140625 step_error = 2.133333333333333e-19 est_needed_step_err = 2.133333333333333e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.386117821653052e-80 estimated_step_error = 4.386117821653052e-80 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 122.0703125 step_error = 3.016988933062603e-19 est_needed_step_err = 3.016988933062603e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.944926520833646e-72 estimated_step_error = 2.944926520833646e-72 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 61.03515625 step_error = 4.266666666666667e-19 est_needed_step_err = 4.266666666666667e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.97825937741948e-64 estimated_step_error = 1.97825937741948e-64 Double H and LOOP opt_iter = 16 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 30.517578125 step_error = 6.033977866125205e-19 est_needed_step_err = 6.033977866125205e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.330215983235972e-56 estimated_step_error = 1.330215983235972e-56 Double H and LOOP opt_iter = 17 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0009765625 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 1 estimated_steps = 15.2587890625 step_error = 8.533333333333333e-19 est_needed_step_err = 8.533333333333333e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.962419322997394e-49 estimated_step_error = 8.962419322997394e-49 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.052 Order of pole (three term test) = 1.34e-13 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = -0.0009765625 y[1] (numeric) = -0.0009765625 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 = 4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 1.3e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = -0.001108350100176561 y[1] (numeric) = -0.001108350073647579 absolute error = 2.652898191922437e-11 relative error = 2.393556143947501e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 1.26e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = -0.001262065854394352 y[1] (numeric) = -0.001262065792763861 absolute error = 6.163049085829153e-11 relative error = 4.883302297079192e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 1.176e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = -0.001442086727182298 y[1] (numeric) = -0.001442086618766665 absolute error = 1.084156330249247e-10 relative error = 7.517968994608159e-06 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 8 h = 0.1 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 1.057e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = -0.001653817168792021 y[1] (numeric) = -0.001653816997536185 absolute error = 1.712558359012739e-10 relative error = 1.035518551463354e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 9.114e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = -0.001903968584518357 y[1] (numeric) = -0.00190396832816846 absolute error = 2.563498970389877e-10 relative error = 1.346397724854457e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 7.527e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (closed_form) = -0.002200925867886697 y[1] (numeric) = -0.002200925495313483 absolute error = 3.72573214467431e-10 relative error = 1.692802197037065e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 2.376e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (closed_form) = -0.002555231782136444 y[1] (numeric) = -0.002555231249372466 absolute error = 5.327639774656279e-10 relative error = 2.084992763436047e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 1.786e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (closed_form) = -0.002980232238769535 y[1] (numeric) = -0.002980231483075132 absolute error = 7.556944024537937e-10 relative error = 2.535689643991642e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (closed_form) = -0.003492943259127737 y[1] (numeric) = -0.003492942189997632 absolute error = 1.069130105193355e-09 relative error = 3.060828722022643e-05 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 7 h = 0.1 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 8.618e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 5.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; 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 %