##############ECHO OF PROBLEM################# ##############temp/arcsin_c_arccos_c_arctan_cpostode.ode################# diff ( y , x , 1 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; ! // 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((arcsin(0.1) + arccos(0.1) + arctan(0.1)) * 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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 10000000 step_error = 8.804123476816562e-21 est_needed_step_err = 8.804123476816562e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 5000000 step_error = 1.245091082572135e-20 est_needed_step_err = 1.245091082572135e-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 = 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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 2500000 step_error = 1.760824695363312e-20 est_needed_step_err = 1.760824695363312e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 1250000 step_error = 2.49018216514427e-20 est_needed_step_err = 2.49018216514427e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 625000 step_error = 3.521649390726625e-20 est_needed_step_err = 3.521649390726625e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 312500 step_error = 4.98036433028854e-20 est_needed_step_err = 4.98036433028854e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 156250 step_error = 7.04329878145325e-20 est_needed_step_err = 7.04329878145325e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 78125 step_error = 9.96072866057708e-20 est_needed_step_err = 9.96072866057708e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 39062.5 step_error = 1.40865975629065e-19 est_needed_step_err = 1.40865975629065e-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 = 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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 19531.25 step_error = 1.992145732115416e-19 est_needed_step_err = 1.992145732115416e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 9765.625 step_error = 2.8173195125813e-19 est_needed_step_err = 2.8173195125813e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 4882.8125 step_error = 3.984291464230832e-19 est_needed_step_err = 3.984291464230832e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 2441.40625 step_error = 5.6346390251626e-19 est_needed_step_err = 5.6346390251626e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 1220.703125 step_error = 7.968582928461664e-19 est_needed_step_err = 7.968582928461664e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 610.3515625 step_error = 1.12692780503252e-18 est_needed_step_err = 1.12692780503252e-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 = 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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 305.17578125 step_error = 1.593716585692333e-18 est_needed_step_err = 1.593716585692333e-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 = 8.352324896430293 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 8.352324896430293 desired_abs_gbl_error = 8.352324896430293e-16 range = 10 estimated_steps = 152.587890625 step_error = 2.25385561006504e-18 est_needed_step_err = 2.25385561006504e-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) = -8.352324896430293 y[1] (numeric) = -8.352324896430293 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) = -8.185278398501687 y[1] (numeric) = -8.185278398501687 absolute error = 0 relative error = 0 % 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) = -8.018231900573083 y[1] (numeric) = -8.018231900573081 absolute error = 1.77635683940025e-15 relative error = 2.215397186595825e-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) = -7.851185402644477 y[1] (numeric) = -7.851185402644475 absolute error = 1.77635683940025e-15 relative error = 2.262533296948928e-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) = -7.684138904715872 y[1] (numeric) = -7.684138904715869 absolute error = 2.664535259100376e-15 relative error = 3.467578205106509e-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) = -7.517092406787267 y[1] (numeric) = -7.517092406787263 absolute error = 3.552713678800501e-15 relative error = 4.726180664737759e-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) = -7.350045908858662 y[1] (numeric) = -7.350045908858657 absolute error = 4.440892098500626e-15 relative error = 6.041992327079522e-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) = -7.182999410930056 y[1] (numeric) = -7.182999410930051 absolute error = 4.440892098500626e-15 relative error = 6.182503776546487e-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) = -7.015952913001451 y[1] (numeric) = -7.015952913001446 absolute error = 5.329070518200751e-15 relative error = 7.595647496899968e-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) = -6.848906415072846 y[1] (numeric) = -6.84890641507284 absolute error = 6.217248937900877e-15 relative error = 9.077725057270693e-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] = -4.000000000000004 y[1] (closed_form) = -6.681859917144241 y[1] (numeric) = -6.681859917144234 absolute error = 7.105427357601002e-15 relative error = 1.063390649565995e-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) = -6.514813419215635 y[1] (numeric) = -6.514813419215628 absolute error = 7.105427357601002e-15 relative error = 1.090657076477944e-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) = -6.347766921287028 y[1] (numeric) = -6.347766921287022 absolute error = 6.217248937900877e-15 relative error = 9.794387561792063e-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] = -3.700000000000003 y[1] (closed_form) = -6.180720423358422 y[1] (numeric) = -6.180720423358416 absolute error = 6.217248937900877e-15 relative error = 1.005910073913779e-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) = -6.013673925429816 y[1] (numeric) = -6.01367392542981 absolute error = 6.217248937900877e-15 relative error = 1.033852020411384e-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) = -5.84662742750121 y[1] (numeric) = -5.846627427501204 absolute error = 6.217248937900877e-15 relative error = 1.063390649565995e-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) = -5.679580929572604 y[1] (numeric) = -5.679580929572598 absolute error = 6.217248937900877e-15 relative error = 1.094666845141466e-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) = -5.512534431643998 y[1] (numeric) = -5.512534431643992 absolute error = 6.217248937900877e-15 relative error = 1.12783856772151e-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) = -5.345487933715392 y[1] (numeric) = -5.345487933715386 absolute error = 6.217248937900877e-15 relative error = 1.163083522962807e-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) = -5.178441435786787 y[1] (numeric) = -5.17844143578678 absolute error = 6.217248937900877e-15 relative error = 1.200602346284188e-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) = -5.011394937858181 y[1] (numeric) = -5.011394937858174 absolute error = 6.217248937900877e-15 relative error = 1.240622424493661e-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) = -4.844348439929575 y[1] (numeric) = -4.844348439929568 absolute error = 6.217248937900877e-15 relative error = 1.283402508096891e-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) = -4.677301942000969 y[1] (numeric) = -4.677301942000962 absolute error = 6.217248937900877e-15 relative error = 1.329238311957494e-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) = -4.510255444072362 y[1] (numeric) = -4.510255444072357 absolute error = 5.329070518200751e-15 relative error = 1.181545166184439e-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) = -4.343208946143756 y[1] (numeric) = -4.343208946143751 absolute error = 5.329070518200751e-15 relative error = 1.226989211037687e-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) = -4.17616244821515 y[1] (numeric) = -4.176162448215145 absolute error = 5.329070518200751e-15 relative error = 1.276068779479194e-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) = -4.009115950286544 y[1] (numeric) = -4.009115950286539 absolute error = 5.329070518200751e-15 relative error = 1.329238311957494e-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) = -3.842069452357938 y[1] (numeric) = -3.842069452357933 absolute error = 5.329070518200751e-15 relative error = 1.387031282042603e-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) = -3.675022954429332 y[1] (numeric) = -3.675022954429327 absolute error = 5.329070518200751e-15 relative error = 1.450078158499085e-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) = -3.507976456500726 y[1] (numeric) = -3.507976456500721 absolute error = 5.329070518200751e-15 relative error = 1.519129499379993e-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) = -3.34092995857212 y[1] (numeric) = -3.340929958572115 absolute error = 5.329070518200751e-15 relative error = 1.595085974348993e-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) = -3.173883460643514 y[1] (numeric) = -3.173883460643509 absolute error = 4.884981308350689e-15 relative error = 1.539118045424467e-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) = -3.006836962714908 y[1] (numeric) = -3.006836962714903 absolute error = 4.884981308350689e-15 relative error = 1.624624603503604e-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) = -2.839790464786302 y[1] (numeric) = -2.839790464786297 absolute error = 4.884981308350689e-15 relative error = 1.720190756650875e-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) = -2.672743966857696 y[1] (numeric) = -2.672743966857691 absolute error = 4.884981308350689e-15 relative error = 1.827702678941555e-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) = -2.50569746892909 y[1] (numeric) = -2.505697468929085 absolute error = 4.884981308350689e-15 relative error = 1.949549524204325e-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) = -2.338650971000484 y[1] (numeric) = -2.338650971000479 absolute error = 4.884981308350689e-15 relative error = 2.088803061647491e-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) = -2.171604473071878 y[1] (numeric) = -2.171604473071874 absolute error = 4.440892098500626e-15 relative error = 2.044982018396145e-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) = -2.004557975143272 y[1] (numeric) = -2.004557975143268 absolute error = 4.440892098500626e-15 relative error = 2.215397186595824e-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) = -1.837511477214666 y[1] (numeric) = -1.837511477214662 absolute error = 4.440892098500626e-15 relative error = 2.416796930831808e-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) = -1.67046497928606 y[1] (numeric) = -1.670464979286056 absolute error = 4.440892098500626e-15 relative error = 2.658476623914988e-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) = -1.503418481357454 y[1] (numeric) = -1.50341848135745 absolute error = 4.440892098500626e-15 relative error = 2.953862915461098e-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) = -1.336371983428849 y[1] (numeric) = -1.336371983428844 absolute error = 4.662936703425657e-15 relative error = 3.489250568888421e-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) = -1.169325485500243 y[1] (numeric) = -1.169325485500238 absolute error = 4.662936703425657e-15 relative error = 3.987714935872481e-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) = -1.002278987571637 y[1] (numeric) = -1.002278987571632 absolute error = 4.884981308350689e-15 relative error = 4.873873810510808e-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) = -0.835232489643031 y[1] (numeric) = -0.8352324896430261 absolute error = 4.884981308350689e-15 relative error = 5.848648572612968e-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] = -0.400000000000001 y[1] (closed_form) = -0.6681859917144252 y[1] (numeric) = -0.6681859917144202 absolute error = 4.996003610813204e-15 relative error = 7.476965504760893e-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] = -0.300000000000001 y[1] (closed_form) = -0.5011394937858193 y[1] (numeric) = -0.5011394937858142 absolute error = 5.10702591327572e-15 relative error = 1.019082705834076e-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) = -0.3340929958572135 y[1] (numeric) = -0.3340929958572084 absolute error = 5.10702591327572e-15 relative error = 1.528624058751112e-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) = -0.1670464979286076 y[1] (numeric) = -0.1670464979286025 absolute error = 5.10702591327572e-15 relative error = 3.057248117502208e-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) = -1.715494530695865e-15 y[1] (numeric) = 3.386180225106727e-15 absolute error = 5.101674755802592e-15 relative error = 297.3879930548757 % Desired digits = 16 Estimated correct digits = -2 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) = 0.1670464979286042 y[1] (numeric) = 0.1670464979286093 absolute error = 5.10702591327572e-15 relative error = 3.057248117502271e-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) = 0.33409299585721 y[1] (numeric) = 0.3340929958572151 absolute error = 5.10702591327572e-15 relative error = 1.528624058751128e-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) = 0.5011394937858159 y[1] (numeric) = 0.501139493785821 absolute error = 5.10702591327572e-15 relative error = 1.019082705834083e-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) = 0.6681859917144218 y[1] (numeric) = 0.6681859917144268 absolute error = 4.996003610813204e-15 relative error = 7.47696550476093e-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] = 0.499999999999999 y[1] (closed_form) = 0.8352324896430277 y[1] (numeric) = 0.8352324896430328 absolute error = 5.10702591327572e-15 relative error = 6.11449623500449e-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] = 0.599999999999999 y[1] (closed_form) = 1.002278987571634 y[1] (numeric) = 1.002278987571639 absolute error = 5.10702591327572e-15 relative error = 5.095413529170408e-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) = 1.169325485500239 y[1] (numeric) = 1.169325485500245 absolute error = 5.329070518200751e-15 relative error = 4.557388498139991e-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) = 1.336371983428845 y[1] (numeric) = 1.336371983428851 absolute error = 5.329070518200751e-15 relative error = 3.987714935872491e-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) = 1.503418481357451 y[1] (numeric) = 1.503418481357456 absolute error = 5.551115123125783e-15 relative error = 3.692328644326381e-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) = 1.670464979286057 y[1] (numeric) = 1.670464979286062 absolute error = 5.551115123125783e-15 relative error = 3.323095779893742e-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) = 1.837511477214663 y[1] (numeric) = 1.837511477214668 absolute error = 5.551115123125783e-15 relative error = 3.020996163539765e-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) = 2.004557975143269 y[1] (numeric) = 2.004557975143274 absolute error = 5.329070518200751e-15 relative error = 2.658476623914993e-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) = 2.171604473071875 y[1] (numeric) = 2.17160447307188 absolute error = 5.329070518200751e-15 relative error = 2.453978422075378e-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) = 2.338650971000481 y[1] (numeric) = 2.338650971000486 absolute error = 5.329070518200751e-15 relative error = 2.278694249069993e-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) = 2.505697468929087 y[1] (numeric) = 2.505697468929092 absolute error = 5.329070518200751e-15 relative error = 2.126781299131994e-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) = 2.672743966857693 y[1] (numeric) = 2.672743966857698 absolute error = 5.329070518200751e-15 relative error = 1.993857467936244e-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) = 2.839790464786299 y[1] (numeric) = 2.839790464786304 absolute error = 4.884981308350689e-15 relative error = 1.720190756650877e-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) = 3.006836962714905 y[1] (numeric) = 3.00683696271491 absolute error = 4.884981308350689e-15 relative error = 1.624624603503606e-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) = 3.173883460643511 y[1] (numeric) = 3.173883460643516 absolute error = 4.884981308350689e-15 relative error = 1.539118045424469e-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) = 3.340929958572117 y[1] (numeric) = 3.340929958572122 absolute error = 4.884981308350689e-15 relative error = 1.462162143153245e-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) = 3.507976456500723 y[1] (numeric) = 3.507976456500728 absolute error = 4.884981308350689e-15 relative error = 1.392535374431662e-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) = 3.675022954429329 y[1] (numeric) = 3.675022954429334 absolute error = 4.884981308350689e-15 relative error = 1.329238311957496e-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) = 3.842069452357935 y[1] (numeric) = 3.84206945235794 absolute error = 4.884981308350689e-15 relative error = 1.271445341872387e-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) = 4.009115950286541 y[1] (numeric) = 4.009115950286545 absolute error = 4.440892098500626e-15 relative error = 1.107698593297913e-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) = 4.176162448215146 y[1] (numeric) = 4.176162448215151 absolute error = 4.440892098500626e-15 relative error = 1.063390649565996e-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) = 4.343208946143752 y[1] (numeric) = 4.343208946143757 absolute error = 4.440892098500626e-15 relative error = 1.022491009198073e-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) = 4.510255444072358 y[1] (numeric) = 4.510255444072363 absolute error = 4.440892098500626e-15 relative error = 9.84620971820367e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 2.8 y[1] (closed_form) = 4.677301942000964 y[1] (numeric) = 4.677301942000969 absolute error = 4.440892098500626e-15 relative error = 9.494559371124967e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 2.9 y[1] (closed_form) = 4.84434843992957 y[1] (numeric) = 4.844348439929575 absolute error = 4.440892098500626e-15 relative error = 9.167160772120658e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3 y[1] (closed_form) = 5.011394937858177 y[1] (numeric) = 5.011394937858181 absolute error = 3.552713678800501e-15 relative error = 7.089270997106641e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.100000000000001 y[1] (closed_form) = 5.178441435786783 y[1] (numeric) = 5.178441435786787 absolute error = 3.552713678800501e-15 relative error = 6.860584835909651e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.200000000000001 y[1] (closed_form) = 5.345487933715389 y[1] (numeric) = 5.345487933715392 absolute error = 3.552713678800501e-15 relative error = 6.646191559787476e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.300000000000001 y[1] (closed_form) = 5.512534431643995 y[1] (numeric) = 5.512534431643998 absolute error = 3.552713678800501e-15 relative error = 6.444791815551492e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.400000000000001 y[1] (closed_form) = 5.679580929572601 y[1] (numeric) = 5.679580929572604 absolute error = 3.552713678800501e-15 relative error = 6.255239115094095e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.500000000000001 y[1] (closed_form) = 5.846627427501207 y[1] (numeric) = 5.84662742750121 absolute error = 3.552713678800501e-15 relative error = 6.076517997519978e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.600000000000001 y[1] (closed_form) = 6.013673925429813 y[1] (numeric) = 6.013673925429816 absolute error = 3.552713678800501e-15 relative error = 5.9077258309222e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.700000000000001 y[1] (closed_form) = 6.180720423358419 y[1] (numeric) = 6.180720423358422 absolute error = 3.552713678800501e-15 relative error = 5.7480575652216e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.800000000000001 y[1] (closed_form) = 6.347766921287024 y[1] (numeric) = 6.347766921287028 absolute error = 3.552713678800501e-15 relative error = 5.596792892452611e-14 % Desired digits = 16 Estimated correct digits = 12 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] = 3.900000000000001 y[1] (closed_form) = 6.51481341921563 y[1] (numeric) = 6.514813419215634 absolute error = 3.552713678800501e-15 relative error = 5.453285382389723e-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] = 4.000000000000001 y[1] (closed_form) = 6.681859917144236 y[1] (numeric) = 6.68185991714424 absolute error = 3.552713678800501e-15 relative error = 5.31695324782998e-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] = 4.100000000000001 y[1] (closed_form) = 6.848906415072841 y[1] (numeric) = 6.848906415072846 absolute error = 4.440892098500626e-15 relative error = 6.484089326621928e-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] = 4.2 y[1] (closed_form) = 7.015952913001446 y[1] (numeric) = 7.015952913001452 absolute error = 5.329070518200751e-15 relative error = 7.595647496899973e-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] = 4.3 y[1] (closed_form) = 7.182999410930051 y[1] (numeric) = 7.182999410930058 absolute error = 6.217248937900877e-15 relative error = 8.655505287165087e-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] = 4.399999999999999 y[1] (closed_form) = 7.350045908858657 y[1] (numeric) = 7.350045908858664 absolute error = 6.217248937900877e-15 relative error = 8.458789257911335e-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] = 4.499999999999999 y[1] (closed_form) = 7.517092406787262 y[1] (numeric) = 7.51709240678727 absolute error = 7.105427357601002e-15 relative error = 9.452361329475525e-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] = 4.599999999999999 y[1] (closed_form) = 7.684138904715867 y[1] (numeric) = 7.684138904715875 absolute error = 7.993605777301127e-15 relative error = 1.040273461531953e-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) = 7.851185402644473 y[1] (numeric) = 7.851185402644481 absolute error = 8.881784197001252e-15 relative error = 1.131266648474465e-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) = 8.018231900573078 y[1] (numeric) = 8.018231900573086 absolute error = 8.881784197001252e-15 relative error = 1.107698593297913e-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) = 8.185278398501683 y[1] (numeric) = 8.185278398501692 absolute error = 8.881784197001252e-15 relative error = 1.08509249955714e-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) = 8.352324896430289 y[1] (numeric) = 8.352324896430298 absolute error = 8.881784197001252e-15 relative error = 1.063390649565997e-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 ) = arcsin ( 0.1 ) + arccos ( 0.1 ) + arctan ( 0.1 ) ; 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 %