##############ECHO OF PROBLEM################# ##############temp/expt_c_linpostode.ode################# diff ( y , x , 1 ) = expt ( 2.0 , ( 0.2 * x + 0.3 ) ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=1.0; x_end=5.0; 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(7.2134752044448170367996234050095*expt(2.0,(0.2*x+0.3))); } // 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 = 4 estimated_steps = 4000000 step_error = 1.666666666666667e-21 est_needed_step_err = 1.666666666666667e-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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 4000000 step_error = 1.700232410994649e-20 est_needed_step_err = 1.700232410994649e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.233906891650465e-204 estimated_step_error = 1.233906891650465e-204 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 2000000 step_error = 2.404491734814939e-20 est_needed_step_err = 2.404491734814939e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.280608999301457e-197 estimated_step_error = 8.280608999301457e-197 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 1000000 step_error = 3.400464821989299e-20 est_needed_step_err = 3.400464821989299e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.557022660245085e-189 estimated_step_error = 5.557022660245085e-189 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 500000 step_error = 4.808983469629878e-20 est_needed_step_err = 4.808983469629878e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.729254817808204e-181 estimated_step_error = 3.729254817808204e-181 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 250000 step_error = 6.800929643978598e-20 est_needed_step_err = 6.800929643978598e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.502660595295234e-173 estimated_step_error = 2.502660595295234e-173 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 125000 step_error = 9.617966939259756e-20 est_needed_step_err = 9.617966939259756e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.679507164264681e-165 estimated_step_error = 1.679507164264681e-165 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 62500 step_error = 1.36018592879572e-19 est_needed_step_err = 1.36018592879572e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.127098271328647e-157 estimated_step_error = 1.127098271328647e-157 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 31250 step_error = 1.923593387851951e-19 est_needed_step_err = 1.923593387851951e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.563829703272082e-150 estimated_step_error = 7.563829703272082e-150 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 15625 step_error = 2.720371857591439e-19 est_needed_step_err = 2.720371857591439e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.07600185675094e-142 estimated_step_error = 5.07600185675094e-142 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 7812.5 step_error = 3.847186775703902e-19 est_needed_step_err = 3.847186775703902e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.406449421425509e-134 estimated_step_error = 3.406449421425509e-134 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 3906.25 step_error = 5.440743715182878e-19 est_needed_step_err = 5.440743715182878e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.286032514246314e-126 estimated_step_error = 2.286032514246314e-126 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 1953.125 step_error = 7.694373551407805e-19 est_needed_step_err = 7.694373551407805e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.534134483961679e-118 estimated_step_error = 1.534134483961679e-118 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 976.5625 step_error = 1.088148743036576e-18 est_needed_step_err = 1.088148743036576e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.029545637434693e-110 estimated_step_error = 1.029545637434693e-110 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 488.28125 step_error = 1.538874710281561e-18 est_needed_step_err = 1.538874710281561e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.909236469812383e-103 estimated_step_error = 6.909236469812383e-103 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 244.140625 step_error = 2.176297486073151e-18 est_needed_step_err = 2.176297486073151e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.636807622637179e-95 estimated_step_error = 4.636807622637179e-95 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 122.0703125 step_error = 3.077749420563122e-18 est_needed_step_err = 3.077749420563122e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.111839814042751e-87 estimated_step_error = 3.111839814042751e-87 Double H and LOOP opt_iter = 17 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 = 10.2013944659679 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 10.2013944659679 desired_abs_gbl_error = 1.02013944659679e-15 range = 4 estimated_steps = 61.03515625 step_error = 4.352594972146302e-18 est_needed_step_err = 4.352594972146302e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.088496051191528e-79 estimated_step_error = 2.088496051191528e-79 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H 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) = 10.2013944659679 y[1] (numeric) = 10.2013944659679 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 10.34380062584569 y[1] (numeric) = 10.34380062584569 absolute error = 1.77635683940025e-15 relative error = 1.717315427524512e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 10.48819470163427 y[1] (numeric) = 10.48819470163427 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 10.63460444360563 y[1] (numeric) = 10.63460444360563 absolute error = 1.77635683940025e-15 relative error = 1.670355346849161e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 10.78305798941109 y[1] (numeric) = 10.78305798941109 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 10.93358386948899 y[1] (numeric) = 10.93358386948899 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (closed_form) = 11.08621101254771 y[1] (numeric) = 11.08621101254771 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (closed_form) = 11.24096875112537 y[1] (numeric) = 11.24096875112537 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (closed_form) = 11.39788682722705 y[1] (numeric) = 11.39788682722705 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (closed_form) = 11.55699539804077 y[1] (numeric) = 11.55699539804077 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y[1] (closed_form) = 11.71832504173318 y[1] (numeric) = 11.71832504173318 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (closed_form) = 11.88190676332625 y[1] (numeric) = 11.88190676332625 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (closed_form) = 12.04777200065591 y[1] (numeric) = 12.04777200065591 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (closed_form) = 12.21595263041394 y[1] (numeric) = 12.21595263041394 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (closed_form) = 12.38648097427416 y[1] (numeric) = 12.38648097427416 absolute error = 1.77635683940025e-15 relative error = 1.434109367373685e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (closed_form) = 12.55938980510412 y[1] (numeric) = 12.55938980510412 absolute error = 1.77635683940025e-15 relative error = 1.41436555992421e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (closed_form) = 12.73471235326357 y[1] (numeric) = 12.73471235326357 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.700000000000002 y[1] (closed_form) = 12.91248231299079 y[1] (numeric) = 12.91248231299079 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.800000000000002 y[1] (closed_form) = 13.09273384887809 y[1] (numeric) = 13.09273384887809 absolute error = 1.77635683940025e-15 relative error = 1.356750133244681e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.900000000000002 y[1] (closed_form) = 13.27550160243774 y[1] (numeric) = 13.27550160243774 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.000000000000002 y[1] (closed_form) = 13.46082069875947 y[1] (numeric) = 13.46082069875947 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.100000000000002 y[1] (closed_form) = 13.648726753261 y[1] (numeric) = 13.64872675326101 absolute error = 1.77635683940025e-15 relative error = 1.301481721711395e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (closed_form) = 13.83925587853278 y[1] (numeric) = 13.83925587853278 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (closed_form) = 14.0324446912782 y[1] (numeric) = 14.0324446912782 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (closed_form) = 14.2283303193508 y[1] (numeric) = 14.2283303193508 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (closed_form) = 14.42695040888964 y[1] (numeric) = 14.42695040888964 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (closed_form) = 14.62834313155429 y[1] (numeric) = 14.62834313155429 absolute error = 1.77635683940025e-15 relative error = 1.214325384238857e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (closed_form) = 14.83254719186083 y[1] (numeric) = 14.83254719186083 absolute error = 1.77635683940025e-15 relative error = 1.197607407832826e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (closed_form) = 15.03960183462027 y[1] (numeric) = 15.03960183462027 absolute error = 1.77635683940025e-15 relative error = 1.181119592748249e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.900000000000003 y[1] (closed_form) = 15.24954685248073 y[1] (numeric) = 15.24954685248073 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.000000000000003 y[1] (closed_form) = 15.46242259357504 y[1] (numeric) = 15.46242259357504 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.100000000000002 y[1] (closed_form) = 15.67826996927494 y[1] (numeric) = 15.67826996927494 absolute error = 1.77635683940025e-15 relative error = 1.133005645955464e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.200000000000002 y[1] (closed_form) = 15.89713046205365 y[1] (numeric) = 15.89713046205366 absolute error = 5.329070518200751e-15 relative error = 3.352221667250708e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.300000000000002 y[1] (closed_form) = 16.11904613345815 y[1] (numeric) = 16.11904613345815 absolute error = 3.552713678800501e-15 relative error = 2.204047093969269e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.400000000000001 y[1] (closed_form) = 16.34405963219271 y[1] (numeric) = 16.34405963219271 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.500000000000001 y[1] (closed_form) = 16.57221420231533 y[1] (numeric) = 16.57221420231533 absolute error = 7.105427357601002e-15 relative error = 4.28755462055776e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.600000000000001 y[1] (closed_form) = 16.80355369154858 y[1] (numeric) = 16.80355369154859 absolute error = 3.552713678800501e-15 relative error = 2.114263294547839e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.7 y[1] (closed_form) = 17.03812255970642 y[1] (numeric) = 17.03812255970643 absolute error = 1.06581410364015e-14 relative error = 6.255466820978867e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.8 y[1] (closed_form) = 17.27596588723868 y[1] (numeric) = 17.27596588723869 absolute error = 1.06581410364015e-14 relative error = 6.169345960722464e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (closed_form) = 17.51712938389483 y[1] (numeric) = 17.51712938389483 absolute error = 7.105427357601002e-15 relative error = 4.05627383453233e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.999999999999999 y[1] (closed_form) = 17.76165939750863 y[1] (numeric) = 17.76165939750864 absolute error = 1.06581410364015e-14 relative error = 6.000644870994704e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 Finished! diff ( y , x , 1 ) = expt ( 2.0 , ( 0.2 * x + 0.3 ) ) ; Iterations = 41 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 105 %