##############ECHO OF PROBLEM################# ##############temp/add_sub_sin_c_cos_c_tan_cpostode.ode################# diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-5.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; 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((sin(0.1) + cos(0.05) - tan(0.02)) * x) ; } // 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 = 10 estimated_steps = 10000000 step_error = 1.05409255338946e-21 est_needed_step_err = 1.05409255338946e-21 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 10000000 step_error = 5.684621054069414e-21 est_needed_step_err = 5.684621054069414e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 5000000 step_error = 8.039268191616604e-21 est_needed_step_err = 8.039268191616604e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 2500000 step_error = 1.136924210813883e-20 est_needed_step_err = 1.136924210813883e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 1250000 step_error = 1.607853638323321e-20 est_needed_step_err = 1.607853638323321e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 625000 step_error = 2.273848421627766e-20 est_needed_step_err = 2.273848421627766e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 312500 step_error = 3.215707276646642e-20 est_needed_step_err = 3.215707276646642e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 156250 step_error = 4.547696843255531e-20 est_needed_step_err = 4.547696843255531e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 78125 step_error = 6.431414553293283e-20 est_needed_step_err = 6.431414553293283e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 39062.5 step_error = 9.095393686511062e-20 est_needed_step_err = 9.095393686511062e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 19531.25 step_error = 1.286282910658657e-19 est_needed_step_err = 1.286282910658657e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 9765.625 step_error = 1.819078737302212e-19 est_needed_step_err = 1.819078737302212e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 4882.8125 step_error = 2.572565821317313e-19 est_needed_step_err = 2.572565821317313e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 2441.40625 step_error = 3.638157474604425e-19 est_needed_step_err = 3.638157474604425e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 1220.703125 step_error = 5.145131642634627e-19 est_needed_step_err = 5.145131642634627e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 610.3515625 step_error = 7.27631494920885e-19 est_needed_step_err = 7.27631494920885e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 305.17578125 step_error = 1.029026328526925e-18 est_needed_step_err = 1.029026328526925e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 17 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 = 5.392905049741961 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 5.392905049741961 desired_abs_gbl_error = 5.39290504974196e-16 range = 10 estimated_steps = 152.587890625 step_error = 1.45526298984177e-18 est_needed_step_err = 1.45526298984177e-18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 0 estimated_step_error = 0 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL 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 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -5.392905049741961 y[1] (numeric) = -5.392905049741961 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (closed_form) = -5.285046948747122 y[1] (numeric) = -5.285046948747121 absolute error = 8.881784197001252e-16 relative error = 1.680549725127187e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.800000000000001 y[1] (closed_form) = -5.177188847752283 y[1] (numeric) = -5.177188847752282 absolute error = 8.881784197001252e-16 relative error = 1.715561177734003e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.700000000000001 y[1] (closed_form) = -5.069330746757444 y[1] (numeric) = -5.069330746757442 absolute error = 1.77635683940025e-15 relative error = 3.504124958775835e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.600000000000001 y[1] (closed_form) = -4.961472645762606 y[1] (numeric) = -4.961472645762603 absolute error = 2.664535259100376e-15 relative error = 5.37045238247166e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.500000000000002 y[1] (closed_form) = -4.853614544767766 y[1] (numeric) = -4.853614544767764 absolute error = 2.664535259100376e-15 relative error = 5.489795768748808e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.400000000000002 y[1] (closed_form) = -4.745756443772928 y[1] (numeric) = -4.745756443772924 absolute error = 3.552713678800501e-15 relative error = 7.48608513920292e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.300000000000002 y[1] (closed_form) = -4.637898342778088 y[1] (numeric) = -4.637898342778085 absolute error = 3.552713678800501e-15 relative error = 7.660180142440196e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.200000000000003 y[1] (closed_form) = -4.53004024178325 y[1] (numeric) = -4.530040241783245 absolute error = 4.440892098500626e-15 relative error = 9.803206729908583e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.100000000000003 y[1] (closed_form) = -4.422182140788411 y[1] (numeric) = -4.422182140788406 absolute error = 5.329070518200751e-15 relative error = 1.20507711996925e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -4.000000000000004 y[1] (closed_form) = -4.314324039793572 y[1] (numeric) = -4.314324039793567 absolute error = 5.329070518200751e-15 relative error = 1.235204047968481e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.900000000000003 y[1] (closed_form) = -4.206465938798733 y[1] (numeric) = -4.206465938798727 absolute error = 5.329070518200751e-15 relative error = 1.26687594663434e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.800000000000003 y[1] (closed_form) = -4.098607837803893 y[1] (numeric) = -4.098607837803888 absolute error = 5.329070518200751e-15 relative error = 1.300214787335244e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.700000000000003 y[1] (closed_form) = -3.990749736809054 y[1] (numeric) = -3.990749736809049 absolute error = 5.773159728050814e-15 relative error = 1.446635371494618e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.600000000000003 y[1] (closed_form) = -3.882891635814215 y[1] (numeric) = -3.882891635814209 absolute error = 5.773159728050814e-15 relative error = 1.486819687369468e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.500000000000003 y[1] (closed_form) = -3.775033534819376 y[1] (numeric) = -3.77503353481937 absolute error = 6.217248937900877e-15 relative error = 1.646938730624642e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.400000000000003 y[1] (closed_form) = -3.667175433824537 y[1] (numeric) = -3.66717543382453 absolute error = 6.217248937900877e-15 relative error = 1.695378105054778e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.300000000000003 y[1] (closed_form) = -3.559317332829697 y[1] (numeric) = -3.559317332829691 absolute error = 6.217248937900877e-15 relative error = 1.746753199147347e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.200000000000003 y[1] (closed_form) = -3.451459231834858 y[1] (numeric) = -3.451459231834852 absolute error = 6.217248937900877e-15 relative error = 1.801339236620702e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.100000000000003 y[1] (closed_form) = -3.343601130840018 y[1] (numeric) = -3.343601130840012 absolute error = 6.217248937900877e-15 relative error = 1.859446953931047e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -3.000000000000003 y[1] (closed_form) = -3.235743029845179 y[1] (numeric) = -3.235743029845173 absolute error = 6.217248937900877e-15 relative error = 1.921428519062082e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.900000000000003 y[1] (closed_form) = -3.12788492885034 y[1] (numeric) = -3.127884928850333 absolute error = 6.661338147750939e-15 relative error = 2.129662151669795e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.800000000000002 y[1] (closed_form) = -3.020026827855501 y[1] (numeric) = -3.020026827855494 absolute error = 6.661338147750939e-15 relative error = 2.205721514229431e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.700000000000002 y[1] (closed_form) = -2.912168726860661 y[1] (numeric) = -2.912168726860655 absolute error = 6.661338147750939e-15 relative error = 2.287414903645336e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.600000000000002 y[1] (closed_form) = -2.804310625865822 y[1] (numeric) = -2.804310625865815 absolute error = 6.661338147750939e-15 relative error = 2.375392399939387e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.500000000000002 y[1] (closed_form) = -2.696452524870983 y[1] (numeric) = -2.696452524870976 absolute error = 6.661338147750939e-15 relative error = 2.470408095936963e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.400000000000002 y[1] (closed_form) = -2.588594423876144 y[1] (numeric) = -2.588594423876136 absolute error = 7.105427357601002e-15 relative error = 2.744897884374402e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.300000000000002 y[1] (closed_form) = -2.480736322881304 y[1] (numeric) = -2.480736322881297 absolute error = 7.105427357601002e-15 relative error = 2.864241270651551e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.200000000000002 y[1] (closed_form) = -2.372878221886465 y[1] (numeric) = -2.372878221886458 absolute error = 7.105427357601002e-15 relative error = 2.994434055681166e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.100000000000002 y[1] (closed_form) = -2.265020120891625 y[1] (numeric) = -2.265020120891618 absolute error = 7.105427357601002e-15 relative error = 3.137026153570746e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -2.000000000000002 y[1] (closed_form) = -2.157162019896786 y[1] (numeric) = -2.157162019896779 absolute error = 7.105427357601002e-15 relative error = 3.293877461249284e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.900000000000002 y[1] (closed_form) = -2.049303918901947 y[1] (numeric) = -2.04930391890194 absolute error = 7.105427357601002e-15 relative error = 3.467239432893983e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.800000000000002 y[1] (closed_form) = -1.941445817907107 y[1] (numeric) = -1.9414458179071 absolute error = 7.105427357601002e-15 relative error = 3.659863845832537e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.700000000000002 y[1] (closed_form) = -1.833587716912268 y[1] (numeric) = -1.833587716912261 absolute error = 7.105427357601002e-15 relative error = 3.875149954410921e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.600000000000001 y[1] (closed_form) = -1.725729615917429 y[1] (numeric) = -1.725729615917422 absolute error = 6.883382752675971e-15 relative error = 3.988679738231554e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.500000000000001 y[1] (closed_form) = -1.61787151492259 y[1] (numeric) = -1.617871514922583 absolute error = 6.661338147750939e-15 relative error = 4.117346826561604e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.400000000000001 y[1] (closed_form) = -1.51001341392775 y[1] (numeric) = -1.510013413927744 absolute error = 6.661338147750939e-15 relative error = 4.411443028458862e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.300000000000001 y[1] (closed_form) = -1.402155312932911 y[1] (numeric) = -1.402155312932905 absolute error = 6.439293542825908e-15 relative error = 4.592425306549482e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.200000000000001 y[1] (closed_form) = -1.294297211938072 y[1] (numeric) = -1.294297211938065 absolute error = 6.439293542825908e-15 relative error = 4.975127415428604e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.100000000000001 y[1] (closed_form) = -1.186439110943232 y[1] (numeric) = -1.186439110943226 absolute error = 6.217248937900877e-15 relative error = 5.240259597442041e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.000000000000001 y[1] (closed_form) = -1.078581009948393 y[1] (numeric) = -1.078581009948387 absolute error = 5.995204332975845e-15 relative error = 5.558418215858166e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.9000000000000009 y[1] (closed_form) = -0.9707229089535538 y[1] (numeric) = -0.9707229089535478 absolute error = 5.995204332975845e-15 relative error = 6.176020239842406e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.8000000000000009 y[1] (closed_form) = -0.8628648079587147 y[1] (numeric) = -0.8628648079587087 absolute error = 5.995204332975845e-15 relative error = 6.948022769822705e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.700000000000001 y[1] (closed_form) = -0.7550067069638755 y[1] (numeric) = -0.7550067069638695 absolute error = 5.995204332975845e-15 relative error = 7.940597451225947e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.600000000000001 y[1] (closed_form) = -0.6471486059690363 y[1] (numeric) = -0.6471486059690303 absolute error = 5.995204332975845e-15 relative error = 9.264030359763603e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.500000000000001 y[1] (closed_form) = -0.5392905049741972 y[1] (numeric) = -0.5392905049741912 absolute error = 5.995204332975845e-15 relative error = 1.111683643171632e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.400000000000001 y[1] (closed_form) = -0.4314324039793579 y[1] (numeric) = -0.431432403979352 absolute error = 5.995204332975845e-15 relative error = 1.389604553964539e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.300000000000001 y[1] (closed_form) = -0.3235743029845188 y[1] (numeric) = -0.3235743029845127 absolute error = 6.050715484207103e-15 relative error = 1.869961683730057e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.200000000000001 y[1] (closed_form) = -0.2157162019896796 y[1] (numeric) = -0.2157162019896735 absolute error = 6.050715484207103e-15 relative error = 2.804942525595081e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -0.100000000000001 y[1] (closed_form) = -0.1078581009948403 y[1] (numeric) = -0.1078581009948343 absolute error = 6.036837696399289e-15 relative error = 5.597018342357128e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = -1.02695629777827e-15 y[1] (closed_form) = -1.107655560830548e-15 y[1] (numeric) = 4.940492459581947e-15 absolute error = 6.048148020412494e-15 relative error = 546.0314771387453 % Desired digits = 16 Estimated correct digits = -1 Correct digits = 1 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.09999999999999898 y[1] (closed_form) = 0.1078581009948381 y[1] (numeric) = 0.1078581009948442 absolute error = 6.050715484207103e-15 relative error = 5.609885051190248e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.199999999999999 y[1] (closed_form) = 0.2157162019896773 y[1] (numeric) = 0.2157162019896834 absolute error = 6.050715484207103e-15 relative error = 2.804942525595109e-12 % Desired digits = 16 Estimated correct digits = 11 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.299999999999999 y[1] (closed_form) = 0.3235743029845166 y[1] (numeric) = 0.3235743029845226 absolute error = 6.050715484207103e-15 relative error = 1.86996168373007e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.399999999999999 y[1] (closed_form) = 0.4314324039793558 y[1] (numeric) = 0.4314324039793618 absolute error = 6.050715484207103e-15 relative error = 1.402471262797551e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.499999999999999 y[1] (closed_form) = 0.539290504974195 y[1] (numeric) = 0.5392905049742011 absolute error = 6.106226635438361e-15 relative error = 1.132270377304444e-12 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 14 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.599999999999999 y[1] (closed_form) = 0.6471486059690341 y[1] (numeric) = 0.6471486059690403 absolute error = 6.217248937900877e-15 relative error = 9.607142595310435e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.699999999999999 y[1] (closed_form) = 0.7550067069638734 y[1] (numeric) = 0.7550067069638795 absolute error = 6.106226635438361e-15 relative error = 8.087645552174599e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.7999999999999989 y[1] (closed_form) = 0.8628648079587126 y[1] (numeric) = 0.8628648079587187 absolute error = 6.106226635438361e-15 relative error = 7.076689858152772e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.8999999999999989 y[1] (closed_form) = 0.9707229089535517 y[1] (numeric) = 0.9707229089535578 absolute error = 6.106226635438361e-15 relative error = 6.290390985024686e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 0.9999999999999989 y[1] (closed_form) = 1.078581009948391 y[1] (numeric) = 1.078581009948397 absolute error = 5.995204332975845e-15 relative error = 5.558418215858176e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.099999999999999 y[1] (closed_form) = 1.18643911094323 y[1] (numeric) = 1.186439110943236 absolute error = 5.995204332975845e-15 relative error = 5.053107468961978e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.199999999999999 y[1] (closed_form) = 1.29429721193807 y[1] (numeric) = 1.294297211938075 absolute error = 5.773159728050814e-15 relative error = 4.460459062108412e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.299999999999999 y[1] (closed_form) = 1.402155312932909 y[1] (numeric) = 1.402155312932915 absolute error = 5.551115123125783e-15 relative error = 3.958987333232318e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.399999999999999 y[1] (closed_form) = 1.510013413927748 y[1] (numeric) = 1.510013413927754 absolute error = 5.551115123125783e-15 relative error = 3.676202523715723e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.499999999999999 y[1] (closed_form) = 1.617871514922588 y[1] (numeric) = 1.617871514922593 absolute error = 5.329070518200751e-15 relative error = 3.293877461249288e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.599999999999999 y[1] (closed_form) = 1.725729615917427 y[1] (numeric) = 1.725729615917432 absolute error = 5.329070518200751e-15 relative error = 3.088010119921207e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 1.833587716912266 y[1] (numeric) = 1.833587716912271 absolute error = 5.10702591327572e-15 relative error = 2.785264029732853e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 1.941445817907105 y[1] (numeric) = 1.94144581790711 absolute error = 4.884981308350689e-15 relative error = 2.516156394009872e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (closed_form) = 2.049303918901945 y[1] (numeric) = 2.04930391890195 absolute error = 4.884981308350689e-15 relative error = 2.383727110114615e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 2.157162019896784 y[1] (numeric) = 2.157162019896789 absolute error = 5.329070518200751e-15 relative error = 2.470408095936965e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (closed_form) = 2.265020120891623 y[1] (numeric) = 2.265020120891629 absolute error = 5.329070518200751e-15 relative error = 2.352769615178062e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 2.372878221886463 y[1] (numeric) = 2.372878221886468 absolute error = 5.329070518200751e-15 relative error = 2.245825541760877e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 2.480736322881302 y[1] (numeric) = 2.480736322881307 absolute error = 5.773159728050814e-15 relative error = 2.327196032404387e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (closed_form) = 2.588594423876141 y[1] (numeric) = 2.588594423876147 absolute error = 5.773159728050814e-15 relative error = 2.230229531054204e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (closed_form) = 2.69645252487098 y[1] (numeric) = 2.696452524870986 absolute error = 5.773159728050814e-15 relative error = 2.141020349812036e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (closed_form) = 2.80431062586582 y[1] (numeric) = 2.804310625865825 absolute error = 5.773159728050814e-15 relative error = 2.058673413280804e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (closed_form) = 2.912168726860659 y[1] (numeric) = 2.912168726860665 absolute error = 5.773159728050814e-15 relative error = 1.982426249825959e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (closed_form) = 3.020026827855498 y[1] (numeric) = 3.020026827855504 absolute error = 6.217248937900877e-15 relative error = 2.058673413280804e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (closed_form) = 3.127884928850337 y[1] (numeric) = 3.127884928850344 absolute error = 6.217248937900877e-15 relative error = 1.987684674891811e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3 y[1] (closed_form) = 3.235743029845177 y[1] (numeric) = 3.235743029845183 absolute error = 6.217248937900877e-15 relative error = 1.921428519062083e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (closed_form) = 3.343601130840016 y[1] (numeric) = 3.343601130840022 absolute error = 6.217248937900877e-15 relative error = 1.859446953931048e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.200000000000001 y[1] (closed_form) = 3.451459231834856 y[1] (numeric) = 3.451459231834862 absolute error = 6.217248937900877e-15 relative error = 1.801339236620703e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.300000000000001 y[1] (closed_form) = 3.559317332829695 y[1] (numeric) = 3.559317332829701 absolute error = 6.217248937900877e-15 relative error = 1.746753199147348e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.400000000000001 y[1] (closed_form) = 3.667175433824534 y[1] (numeric) = 3.667175433824541 absolute error = 6.661338147750939e-15 relative error = 1.816476541130121e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.500000000000001 y[1] (closed_form) = 3.775033534819373 y[1] (numeric) = 3.77503353481938 absolute error = 6.661338147750939e-15 relative error = 1.764577211383546e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.600000000000001 y[1] (closed_form) = 3.882891635814213 y[1] (numeric) = 3.882891635814219 absolute error = 6.661338147750939e-15 relative error = 1.715561177734003e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.700000000000001 y[1] (closed_form) = 3.990749736809052 y[1] (numeric) = 3.990749736809059 absolute error = 6.661338147750939e-15 relative error = 1.669194659416867e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.800000000000001 y[1] (closed_form) = 4.098607837803891 y[1] (numeric) = 4.098607837803898 absolute error = 6.217248937900877e-15 relative error = 1.516917251891118e-13 % Desired digits = 16 Estimated correct digits = 12 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 3.900000000000001 y[1] (closed_form) = 4.206465938798731 y[1] (numeric) = 4.206465938798737 absolute error = 6.217248937900877e-15 relative error = 1.478021937740064e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.000000000000001 y[1] (closed_form) = 4.314324039793569 y[1] (numeric) = 4.314324039793576 absolute error = 7.105427357601002e-15 relative error = 1.646938730624643e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (closed_form) = 4.422182140788408 y[1] (numeric) = 4.422182140788416 absolute error = 7.993605777301127e-15 relative error = 1.807615679953876e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 4.530040241783247 y[1] (numeric) = 4.530040241783255 absolute error = 7.993605777301127e-15 relative error = 1.764577211383546e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 4.637898342778086 y[1] (numeric) = 4.637898342778095 absolute error = 8.881784197001252e-15 relative error = 1.91504503561005e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.399999999999999 y[1] (closed_form) = 4.745756443772925 y[1] (numeric) = 4.745756443772934 absolute error = 8.881784197001252e-15 relative error = 1.871521284800731e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.499999999999999 y[1] (closed_form) = 4.853614544767764 y[1] (numeric) = 4.853614544767773 absolute error = 9.769962616701378e-15 relative error = 2.012925115207897e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.599999999999999 y[1] (closed_form) = 4.961472645762602 y[1] (numeric) = 4.961472645762613 absolute error = 1.06581410364015e-14 relative error = 2.148180952988666e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.699999999999998 y[1] (closed_form) = 5.069330746757442 y[1] (numeric) = 5.069330746757452 absolute error = 1.06581410364015e-14 relative error = 2.102474975265502e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.799999999999998 y[1] (closed_form) = 5.17718884775228 y[1] (numeric) = 5.177188847752292 absolute error = 1.154631945610163e-14 relative error = 2.230229531054205e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.899999999999998 y[1] (closed_form) = 5.285046948747119 y[1] (numeric) = 5.285046948747131 absolute error = 1.243449787580175e-14 relative error = 2.352769615178063e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 TOP MAIN SOLVE Loop x[1] = 4.999999999999997 y[1] (closed_form) = 5.392905049741958 y[1] (numeric) = 5.39290504974197 absolute error = 1.243449787580175e-14 relative error = 2.305714222874502e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 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 Finished! diff ( y , x , 1 ) = sin ( 0.1 ) + cos ( 0.05 ) - tan ( 0.02 ) ; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102 %