##############ECHO OF PROBLEM################# ##############temp/sing4_backpostode.ode################# diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-1.0; x_end=-2.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.1; glob_type_given_pole=2; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=1.0; array_given_ord_poles[1][1]=1.0; 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(1.0 / (x * x + 1.0)); } /* 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 min_size = 0.5 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 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.907347679138423e-222 estimated_step_error = 1.907347679138423e-222 Double H and LOOP opt_iter = 2 min_size = 0.5 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 = 3.535533905932738e-21 est_needed_step_err = 3.535533905932738e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.310718689280656e-211 estimated_step_error = 1.310718689280656e-211 Double H and LOOP opt_iter = 3 min_size = 0.5 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 = 5e-21 est_needed_step_err = 5e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.007181240360502e-201 estimated_step_error = 9.007181240360502e-201 Double H and LOOP opt_iter = 4 min_size = 0.5 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 = 7.071067811865475e-21 est_needed_step_err = 7.071067811865475e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.189675437675637e-190 estimated_step_error = 6.189675437675637e-190 Double H and LOOP opt_iter = 5 min_size = 0.5 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 = 9.999999999999999e-21 est_needed_step_err = 9.999999999999999e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.253495558411153e-179 estimated_step_error = 4.253495558411153e-179 Double H and LOOP opt_iter = 6 min_size = 0.5 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 = 1.414213562373095e-20 est_needed_step_err = 1.414213562373095e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.922956506983557e-168 estimated_step_error = 2.922956506983557e-168 Double H and LOOP opt_iter = 7 min_size = 0.5 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 = 2e-20 est_needed_step_err = 2e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.008608278830409e-157 estimated_step_error = 2.008608278830409e-157 Double H and LOOP opt_iter = 8 min_size = 0.5 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 = 2.82842712474619e-20 est_needed_step_err = 2.82842712474619e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.38026092983183e-146 estimated_step_error = 1.38026092983183e-146 Double H and LOOP opt_iter = 9 min_size = 0.5 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 = 4e-20 est_needed_step_err = 4e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.484473859970062e-136 estimated_step_error = 9.484473859970062e-136 Double H and LOOP opt_iter = 10 min_size = 0.5 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 = 5.65685424949238e-20 est_needed_step_err = 5.65685424949238e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.516846597997249e-125 estimated_step_error = 6.516846597997249e-125 Double H and LOOP opt_iter = 11 min_size = 0.5 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 = 8e-20 est_needed_step_err = 8e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.477196572875267e-114 estimated_step_error = 4.477196572875267e-114 Double H and LOOP opt_iter = 12 min_size = 0.5 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 = 1.131370849898476e-19 est_needed_step_err = 1.131370849898476e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.075131187503782e-103 estimated_step_error = 3.075131187503782e-103 Double H and LOOP opt_iter = 13 min_size = 0.5 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 = 1.6e-19 est_needed_step_err = 1.6e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.111051240003244e-92 estimated_step_error = 2.111051240003244e-92 Double H and LOOP opt_iter = 14 min_size = 0.5 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 = 2.262741699796952e-19 est_needed_step_err = 2.262741699796952e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.44773538009206e-81 estimated_step_error = 1.44773538009206e-81 Double H and LOOP opt_iter = 15 min_size = 0.5 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 = 3.2e-19 est_needed_step_err = 3.2e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.908095791012024e-71 estimated_step_error = 9.908095791012024e-71 Double H and LOOP opt_iter = 16 min_size = 0.5 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 = 4.525483399593904e-19 est_needed_step_err = 4.525483399593904e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.753246192812156e-60 estimated_step_error = 6.753246192812156e-60 Double H and LOOP opt_iter = 17 min_size = 0.5 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 = 6.4e-19 est_needed_step_err = 6.4e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.565404193417324e-49 estimated_step_error = 4.565404193417324e-49 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = -1.1 y[1] (closed_form) = 0.4524886877828054 y[1] (numeric) = 0.4524886877828054 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 = 1.487 Order of pole (given) = 1 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 = 1.487 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.2 y[1] (closed_form) = 0.4098360655737704 y[1] (numeric) = 0.4098360655737705 absolute error = 5.551115123125783e-17 relative error = 1.354472090042691e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 1 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 = 1.562 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.3 y[1] (closed_form) = 0.3717472118959107 y[1] (numeric) = 0.3717472118959108 absolute error = 1.110223024625157e-16 relative error = 2.986499936241672e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 1 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 = 1.64 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.4 y[1] (closed_form) = 0.3378378378378377 y[1] (numeric) = 0.3378378378378379 absolute error = 1.665334536937735e-16 relative error = 4.929390229335697e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 1 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 = 1.72 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.5 y[1] (closed_form) = 0.3076923076923075 y[1] (numeric) = 0.3076923076923078 absolute error = 2.220446049250313e-16 relative error = 7.216449660063521e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.803 Order of pole (given) = 1 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 = 1.803 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.600000000000001 y[1] (closed_form) = 0.2808988764044942 y[1] (numeric) = 0.2808988764044945 absolute error = 2.220446049250313e-16 relative error = 7.904787935331118e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 1 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 = 1.887 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.700000000000001 y[1] (closed_form) = 0.2570694087403598 y[1] (numeric) = 0.25706940874036 absolute error = 2.220446049250313e-16 relative error = 8.637535131583722e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 1 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 = 1.972 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.800000000000001 y[1] (closed_form) = 0.2358490566037735 y[1] (numeric) = 0.2358490566037737 absolute error = 2.220446049250313e-16 relative error = 9.414691248821331e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = -0.1 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 1 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 = 2.059 Order of pole (six term test) = 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000001 y[1] (closed_form) = 0.2169197396963122 y[1] (numeric) = 0.2169197396963125 absolute error = 2.498001805406602e-16 relative error = 1.151578832292444e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = -0.1 Radius of convergence (given) for eq 1 = 2.147 Order of pole (given) = 1 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 = 2.147 Order of pole (six term test) = 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations = 10 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 0 %