##############ECHO OF PROBLEM################# ##############temp/expt_sin_sinpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; 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(0.0); } /* 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 = 4.9 estimated_steps = 4900000.000000001 step_error = 1.505846504842085e-21 est_needed_step_err = 1.505846504842085e-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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.505846504842085e-21 est_needed_step_err = 1.505846504842085e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.076192980277016e-142 estimated_step_error = 3.076192980277016e-142 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 2450000 step_error = 2.129588549999799e-21 est_needed_step_err = 2.129588549999799e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.064388990450618e-134 estimated_step_error = 2.064388990450618e-134 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 1225000 step_error = 3.01169300968417e-21 est_needed_step_err = 3.01169300968417e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.38537568832323e-126 estimated_step_error = 1.38537568832323e-126 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 4.259177099999599e-21 est_needed_step_err = 4.259177099999599e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.296933625119876e-119 estimated_step_error = 9.296933625119876e-119 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 6.023386019368341e-21 est_needed_step_err = 6.023386019368341e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.23884477243261e-111 estimated_step_error = 6.23884477243261e-111 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 153125 step_error = 8.518354199999198e-21 est_needed_step_err = 8.518354199999198e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.18652023043387e-103 estimated_step_error = 4.18652023043387e-103 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 1.204677203873668e-20 est_needed_step_err = 1.204677203873668e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.809126790410861e-95 estimated_step_error = 2.809126790410861e-95 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 1.70367083999984e-20 est_needed_step_err = 1.70367083999984e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.884637271693034e-87 estimated_step_error = 1.884637271693034e-87 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 19140.625 step_error = 2.409354407747336e-20 est_needed_step_err = 2.409354407747336e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.264040132935082e-79 estimated_step_error = 1.264040132935082e-79 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 9570.312500000002 step_error = 3.407341679999679e-20 est_needed_step_err = 3.407341679999679e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.473202273554506e-72 estimated_step_error = 8.473202273554506e-72 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4785.156250000001 step_error = 4.818708815494673e-20 est_needed_step_err = 4.818708815494673e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.673392116749606e-64 estimated_step_error = 5.673392116749606e-64 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 2392.578125 step_error = 6.814683359999358e-20 est_needed_step_err = 6.814683359999358e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.790182272602506e-56 estimated_step_error = 3.790182272602506e-56 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 1196.2890625 step_error = 9.637417630989345e-20 est_needed_step_err = 9.637417630989345e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.520817456655616e-48 estimated_step_error = 2.520817456655616e-48 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 598.1445312500001 step_error = 1.362936671999872e-19 est_needed_step_err = 1.362936671999872e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.661987661549568e-40 estimated_step_error = 1.661987661549568e-40 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 299.0722656250001 step_error = 1.927483526197869e-19 est_needed_step_err = 1.927483526197869e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.07748383230485e-32 estimated_step_error = 1.07748383230485e-32 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 149.5361328125 step_error = 2.725873343999743e-19 est_needed_step_err = 2.725873343999743e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.768788302254761e-25 estimated_step_error = 6.768788302254761e-25 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 = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 74.76806640625001 step_error = 3.854967052395738e-19 est_needed_step_err = 3.854967052395738e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.003073796656913e-17 estimated_step_error = 4.003073796656913e-17 Found H for OPTIMAL START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Desired digits = 16 Estimated correct digits = -16 Correct digits = -16 h = 0.032768 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] = 0.198304 y[1] (closed_form) = 0 y[1] (numeric) = 0.08725449375418594 absolute error = 0.08725449375418594 relative error = -1 % Desired digits = 16 Estimated correct digits = 12 Correct digits = -16 h = 0.032768 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] = 0.329376 y[1] (closed_form) = 0 y[1] (numeric) = 0.1960201501302923 absolute error = 0.1960201501302923 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 0.4276800000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.273073266634291 absolute error = 0.273073266634291 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 0.5259840000000001 y[1] (closed_form) = 0 y[1] (numeric) = 0.3469103968274749 absolute error = 0.3469103968274749 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 0.6242880000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.4179671267613324 absolute error = 0.4179671267613324 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 0.7225920000000002 y[1] (closed_form) = 0 y[1] (numeric) = 0.4865891220115807 absolute error = 0.4865891220115807 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 0.8208960000000003 y[1] (closed_form) = 0 y[1] (numeric) = 0.553059417352412 absolute error = 0.553059417352412 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 0.9192000000000004 y[1] (closed_form) = 0 y[1] (numeric) = 0.6176151169076496 absolute error = 0.6176151169076496 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.017504 y[1] (closed_form) = 0 y[1] (numeric) = 0.6804583653458116 absolute error = 0.6804583653458116 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.115808 y[1] (closed_form) = 0 y[1] (numeric) = 0.7417639377663704 absolute error = 0.7417639377663704 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.214112 y[1] (closed_form) = 0 y[1] (numeric) = 0.8016847017715958 absolute error = 0.8016847017715958 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.312416 y[1] (closed_form) = 0 y[1] (numeric) = 0.8603556727727687 absolute error = 0.8603556727727687 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.410719999999999 y[1] (closed_form) = 0 y[1] (numeric) = 0.9178971019814769 absolute error = 0.9178971019814769 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.509023999999999 y[1] (closed_form) = 0 y[1] (numeric) = 0.9744168775998059 absolute error = 0.9744168775998059 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.607327999999999 y[1] (closed_form) = 0 y[1] (numeric) = 1.030012425195265 absolute error = 1.030012425195265 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.705631999999998 y[1] (closed_form) = 0 y[1] (numeric) = 1.084772234546284 absolute error = 1.084772234546284 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.803935999999998 y[1] (closed_form) = 0 y[1] (numeric) = 1.138777102447827 absolute error = 1.138777102447827 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 1.902239999999998 y[1] (closed_form) = 0 y[1] (numeric) = 1.192101155867044 absolute error = 1.192101155867044 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.000543999999998 y[1] (closed_form) = 0 y[1] (numeric) = 1.244812702720825 absolute error = 1.244812702720825 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.098847999999998 y[1] (closed_form) = 0 y[1] (numeric) = 1.296974945598234 absolute error = 1.296974945598234 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.197151999999997 y[1] (closed_form) = 0 y[1] (numeric) = 1.3486465852378 absolute error = 1.3486465852378 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.328223999999997 y[1] (closed_form) = 0 y[1] (numeric) = 1.41687299086416 absolute error = 1.41687299086416 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.426527999999997 y[1] (closed_form) = 0 y[1] (numeric) = 1.467606585376224 absolute error = 1.467606585376224 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.524831999999996 y[1] (closed_form) = 0 y[1] (numeric) = 1.518018804493365 absolute error = 1.518018804493365 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.623135999999996 y[1] (closed_form) = 0 y[1] (numeric) = 1.568153924671435 absolute error = 1.568153924671435 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.721439999999996 y[1] (closed_form) = 0 y[1] (numeric) = 1.618053756002706 absolute error = 1.618053756002706 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.819743999999996 y[1] (closed_form) = 0 y[1] (numeric) = 1.667757881400731 absolute error = 1.667757881400731 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 2.918047999999995 y[1] (closed_form) = 0 y[1] (numeric) = 1.717303866637573 absolute error = 1.717303866637573 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.016351999999995 y[1] (closed_form) = 0 y[1] (numeric) = 1.766727445379194 absolute error = 1.766727445379194 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.114655999999995 y[1] (closed_form) = 0 y[1] (numeric) = 1.81606268266011 absolute error = 1.81606268266011 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.212959999999994 y[1] (closed_form) = 0 y[1] (numeric) = 1.865342119670819 absolute error = 1.865342119670819 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.311263999999994 y[1] (closed_form) = 0 y[1] (numeric) = 1.914596902271045 absolute error = 1.914596902271045 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.409567999999994 y[1] (closed_form) = 0 y[1] (numeric) = 1.963856895265926 absolute error = 1.963856895265926 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.507871999999994 y[1] (closed_form) = 0 y[1] (numeric) = 2.013150784173429 absolute error = 2.013150784173429 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.606175999999993 y[1] (closed_form) = 0 y[1] (numeric) = 2.062506165956155 absolute error = 2.062506165956155 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.704479999999993 y[1] (closed_form) = 0 y[1] (numeric) = 2.111949629978833 absolute error = 2.111949629978833 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.802783999999993 y[1] (closed_form) = 0 y[1] (numeric) = 2.161506830275984 absolute error = 2.161506830275984 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.901087999999993 y[1] (closed_form) = 0 y[1] (numeric) = 2.211202550066025 absolute error = 2.211202550066025 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 3.999391999999992 y[1] (closed_form) = 0 y[1] (numeric) = 2.2610607593233 absolute error = 2.2610607593233 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 4.097695999999992 y[1] (closed_form) = 0 y[1] (numeric) = 2.311104666114097 absolute error = 2.311104666114097 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 4.228767999999992 y[1] (closed_form) = 0 y[1] (numeric) = 2.378157514826762 absolute error = 2.378157514826762 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 4.327071999999991 y[1] (closed_form) = 0 y[1] (numeric) = 2.428721021913697 absolute error = 2.428721021913697 relative error = -1 % Desired digits = 16 Estimated correct digits = 13 Correct digits = -16 h = 0.032768 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] = 4.425375999999991 y[1] (closed_form) = 0 y[1] (numeric) = 2.479542633969403 absolute error = 2.479542633969403 relative error = -1 % Desired digits = 16 Estimated correct digits = 12 Correct digits = -16 h = 0.032768 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] = 4.523679999999991 y[1] (closed_form) = 0 y[1] (numeric) = 2.530642723982006 absolute error = 2.530642723982006 relative error = -1 % Desired digits = 16 Estimated correct digits = 12 Correct digits = -16 h = 0.032768 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] = 4.621983999999991 y[1] (closed_form) = 0 y[1] (numeric) = 2.58204109387103 absolute error = 2.58204109387103 relative error = -1 % Desired digits = 16 Estimated correct digits = 12 Correct digits = -16 h = 0.032768 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] = 4.72028799999999 y[1] (closed_form) = 0 y[1] (numeric) = 2.633756997956438 absolute error = 2.633756997956438 relative error = -1 % Desired digits = 16 Estimated correct digits = 12 Correct digits = -16 h = 0.032768 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] = 4.81859199999999 y[1] (closed_form) = 0 y[1] (numeric) = 2.685809163336385 absolute error = 2.685809163336385 relative error = -1 % Desired digits = 16 Estimated correct digits = 12 Correct digits = -16 h = 0.032768 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] = 4.91689599999999 y[1] (closed_form) = 0 y[1] (numeric) = 2.738215807430312 absolute error = 2.738215807430312 relative error = -1 % Desired digits = 16 Estimated correct digits = 12 Correct digits = -16 h = 0.032768 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 ( sin ( 0.1 * x ) , sin ( 0.2 * x ) ) ; Iterations = 150 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 101 %