##############ECHO OF PROBLEM################# ##############temp/mult2postode.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=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.00000000001; glob_type_given_pole=3; /* 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 - expt(cos(x),2)/2.0); } /* 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 = 9.999999999999999e-12 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 0.9 estimated_steps = 90000000000.00002 step_error = 1.111111111111111e-23 est_needed_step_err = 1.111111111111111e-23 opt_iter = 1 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 9.999999999999999e-12 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 90000000000.00002 step_error = 1.672203728377433e-23 est_needed_step_err = 1.672203728377433e-23 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.077147734516545e-306 estimated_step_error = 4.077147734516545e-306 Double H and LOOP opt_iter = 2 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 2e-11 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 45000000000.00001 step_error = 2.36485319172222e-23 est_needed_step_err = 2.36485319172222e-23 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.736127528235584e-298 estimated_step_error = 2.736127528235584e-298 Double H and LOOP opt_iter = 3 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 4e-11 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 22500000000 step_error = 3.344407456754866e-23 est_needed_step_err = 3.344407456754866e-23 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.836184101789904e-290 estimated_step_error = 1.836184101789904e-290 Double H and LOOP opt_iter = 4 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 8e-11 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 11250000000 step_error = 4.729706383444441e-23 est_needed_step_err = 4.729706383444441e-23 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.232242291659438e-282 estimated_step_error = 1.232242291659438e-282 Double H and LOOP opt_iter = 5 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 1.6e-10 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 5625000000.000001 step_error = 6.688814913509731e-23 est_needed_step_err = 6.688814913509731e-23 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.269438036597189e-275 estimated_step_error = 8.269438036597189e-275 Double H and LOOP opt_iter = 6 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 3.2e-10 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 2812500000 step_error = 9.459412766888881e-23 est_needed_step_err = 9.459412766888881e-23 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.549525925537611e-267 estimated_step_error = 5.549525925537611e-267 Double H and LOOP opt_iter = 7 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 6.4e-10 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 1406250000 step_error = 1.337762982701946e-22 est_needed_step_err = 1.337762982701946e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.724223806004829e-259 estimated_step_error = 3.724223806004829e-259 Double H and LOOP opt_iter = 8 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 1.28e-09 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 703125000.0000001 step_error = 1.891882553377776e-22 est_needed_step_err = 1.891882553377776e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.499284289015396e-251 estimated_step_error = 2.499284289015396e-251 Double H and LOOP opt_iter = 9 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 2.56e-09 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 351562500.0000001 step_error = 2.675525965403892e-22 est_needed_step_err = 2.675525965403892e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.677241294472591e-243 estimated_step_error = 1.677241294472591e-243 Double H and LOOP opt_iter = 10 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 5.12e-09 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 175781250 step_error = 3.783765106755552e-22 est_needed_step_err = 3.783765106755552e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.125577579237817e-235 estimated_step_error = 1.125577579237817e-235 Double H and LOOP opt_iter = 11 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 1.024e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 87890625.00000001 step_error = 5.351051930807785e-22 est_needed_step_err = 5.351051930807785e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.553623268361628e-228 estimated_step_error = 7.553623268361628e-228 Double H and LOOP opt_iter = 12 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 2.048e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 43945312.50000001 step_error = 7.567530213511105e-22 est_needed_step_err = 7.567530213511105e-22 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.069150765847445e-220 estimated_step_error = 5.069150765847445e-220 Double H and LOOP opt_iter = 13 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 4.096e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 21972656.25 step_error = 1.070210386161557e-21 est_needed_step_err = 1.070210386161557e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.401849492884454e-212 estimated_step_error = 3.401849492884454e-212 Double H and LOOP opt_iter = 14 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 8.192e-08 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 10986328.125 step_error = 1.513506042702221e-21 est_needed_step_err = 1.513506042702221e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.282942548962471e-204 estimated_step_error = 2.282942548962471e-204 Double H and LOOP opt_iter = 15 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 1.6384e-07 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 5493164.062500001 step_error = 2.140420772323114e-21 est_needed_step_err = 2.140420772323114e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.532056809439086e-196 estimated_step_error = 1.532056809439086e-196 Double H and LOOP opt_iter = 16 NO POLE (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 = 1.504983355539689 glob_desired_digits_correct = 16 estimated_h = 3.2768e-07 estimated_answer = 1.504983355539689 desired_abs_gbl_error = 1.50498335553969e-16 range = 0.9 estimated_steps = 2746582.03125 step_error = 3.027012085404442e-21 est_needed_step_err = 3.027012085404442e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.028145919384519e-188 estimated_step_error = 1.028145919384519e-188 Double H and LOOP opt_iter = 17 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09735 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE ACCURACY START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 1.504983355539689 y[1] (numeric) = 1.504983355539689 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 3.2768e-07 NO POLE (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] = 0.1900002611186727 y[1] (closed_form) = 1.517833889533035 y[1] (numeric) = 1.517833889533186 absolute error = 1.509903313490213e-13 relative error = 9.947750698561214e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 3.2768e-07 NO POLE (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] = 0.2800001945598865 y[1] (closed_form) = 1.538186273920425 y[1] (numeric) = 1.538186273920176 absolute error = 2.489120021209601e-13 relative error = 1.618217548428319e-11 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 13 h = 3.2768e-07 NO POLE (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] = 0.3700001280061825 y[1] (closed_form) = 1.56538290347412 y[1] (numeric) = 1.56538290347202 absolute error = 2.100097873380946e-12 relative error = 1.341587332224027e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 3.2768e-07 NO POLE (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] = 0.4600000614524785 y[1] (closed_form) = 1.598544985284981 y[1] (numeric) = 1.59854498528057 absolute error = 4.410916076835747e-12 relative error = 2.759331840792325e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 3.2768e-07 NO POLE (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] = 0.5499999948987744 y[1] (closed_form) = 1.636600967370481 y[1] (numeric) = 1.636600967363351 absolute error = 7.12963021953783e-12 relative error = 4.356364417279414e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 3.2768e-07 NO POLE (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] = 0.6400002560250704 y[1] (closed_form) = 1.67832132023006 y[1] (numeric) = 1.67832132022004 absolute error = 1.001998484184696e-11 relative error = 5.970242242095484e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 3.2768e-07 NO POLE (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] = 0.7300001894713664 y[1] (closed_form) = 1.722357649199783 y[1] (numeric) = 1.722357649186712 absolute error = 1.307087771351689e-11 relative error = 7.588945141323985e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 3.2768e-07 NO POLE (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] = 0.8200001229176623 y[1] (closed_form) = 1.767287173475237 y[1] (numeric) = 1.767287173459011 absolute error = 1.622635359410651e-11 relative error = 9.18150362750532e-10 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 12 h = 3.2768e-07 NO POLE (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] = 0.9100000563639583 y[1] (closed_form) = 1.811658104803621 y[1] (numeric) = 1.811658104784306 absolute error = 1.93149940486137e-11 relative error = 1.066150064264327e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 3.2768e-07 NO POLE (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] = 0.9999999898102543 y[1] (closed_form) = 1.854036704504031 y[1] (numeric) = 1.854036704481761 absolute error = 2.226974160635109e-11 relative error = 1.201148906720723e-09 % Desired digits = 16 Estimated correct digits = 10 Correct digits = 11 h = 3.2768e-07 NO POLE (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 ) = sin ( x ) * cos ( x ) ; Iterations = 2746583 Total Elapsed Time = 18.0 Seconds Elapsed Time(since restart) = 18.0 Seconds Time to Timeout = 2 Minutes 42.0 Seconds Percent Done = 100 %