##############ECHO OF PROBLEM################# ##############temp/diff0postode.ode################# diff ( y , x , 1 ) = y ; ! /* 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=false; 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(exp(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 min_size = 0.006737946999085467 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 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.670738851013513e-185 estimated_step_error = 1.670738851013513e-185 Double H and LOOP opt_iter = 2 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 5000000 step_error = 1.49071198499986e-21 est_needed_step_err = 1.49071198499986e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.121213884085041e-177 estimated_step_error = 1.121213884085041e-177 Double H and LOOP opt_iter = 3 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 2500000 step_error = 2.108185106778919e-21 est_needed_step_err = 2.108185106778919e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.524339284876721e-170 estimated_step_error = 7.524339284876721e-170 Double H and LOOP opt_iter = 4 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 1250000 step_error = 2.981423969999719e-21 est_needed_step_err = 2.981423969999719e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.049498991623479e-162 estimated_step_error = 5.049498991623479e-162 Double H and LOOP opt_iter = 5 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 625000 step_error = 4.216370213557839e-21 est_needed_step_err = 4.216370213557839e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.388661912994025e-154 estimated_step_error = 3.388661912994025e-154 Double H and LOOP opt_iter = 6 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 312500 step_error = 5.962847939999439e-21 est_needed_step_err = 5.962847939999439e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.274093188416526e-146 estimated_step_error = 2.274093188416526e-146 Double H and LOOP opt_iter = 7 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 156250 step_error = 8.432740427115678e-21 est_needed_step_err = 8.432740427115678e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.526119009415009e-138 estimated_step_error = 1.526119009415009e-138 Double H and LOOP opt_iter = 8 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 78125 step_error = 1.192569587999888e-20 est_needed_step_err = 1.192569587999888e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.024162344329788e-130 estimated_step_error = 1.024162344329788e-130 Double H and LOOP opt_iter = 9 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 39062.5 step_error = 1.686548085423136e-20 est_needed_step_err = 1.686548085423136e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.873053439671597e-123 estimated_step_error = 6.873053439671597e-123 Double H and LOOP opt_iter = 10 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 19531.25 step_error = 2.385139175999775e-20 est_needed_step_err = 2.385139175999775e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.612449951998493e-115 estimated_step_error = 4.612449951998493e-115 Double H and LOOP opt_iter = 11 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 9765.625 step_error = 3.373096170846271e-20 est_needed_step_err = 3.373096170846271e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.095392114506204e-107 estimated_step_error = 3.095392114506204e-107 Double H and LOOP opt_iter = 12 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 4882.8125 step_error = 4.770278351999551e-20 est_needed_step_err = 4.770278351999551e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.07732187723548e-99 estimated_step_error = 2.07732187723548e-99 Double H and LOOP opt_iter = 13 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 2441.40625 step_error = 6.746192341692542e-20 est_needed_step_err = 6.746192341692542e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.394119988518088e-91 estimated_step_error = 1.394119988518088e-91 Double H and LOOP opt_iter = 14 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 1220.703125 step_error = 9.540556703999102e-20 est_needed_step_err = 9.540556703999102e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.356490626122458e-84 estimated_step_error = 9.356490626122458e-84 Double H and LOOP opt_iter = 15 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 610.3515625 step_error = 1.349238468338508e-19 est_needed_step_err = 1.349238468338508e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.279987395861066e-76 estimated_step_error = 6.279987395861066e-76 Double H and LOOP opt_iter = 16 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 305.17578125 step_error = 1.90811134079982e-19 est_needed_step_err = 1.90811134079982e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.215707624202576e-68 estimated_step_error = 4.215707624202576e-68 Double H and LOOP opt_iter = 17 min_size = 0.006737946999085467 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 10 estimated_steps = 152.587890625 step_error = 2.698476936677017e-19 est_needed_step_err = 2.698476936677017e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.83083221819058e-60 estimated_step_error = 2.83083221819058e-60 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = 0.006737946999085467 y[1] (numeric) = 0.006737946999085467 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) = 0.007446583070924338 y[1] (numeric) = 0.007446583070924341 absolute error = 2.602085213965211e-18 relative error = 3.494334501048164e-14 % 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] = -4.800000000000001 y[1] (closed_form) = 0.008229747049020023 y[1] (numeric) = 0.008229747049020028 absolute error = 5.204170427930421e-18 relative error = 6.323609215364792e-14 % 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] = -4.700000000000001 y[1] (closed_form) = 0.009095277101695807 y[1] (numeric) = 0.009095277101695817 absolute error = 1.040834085586084e-17 relative error = 1.144367647019816e-13 % Desired digits = 16 Estimated correct digits = 14 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] = -4.600000000000001 y[1] (closed_form) = 0.01005183574463357 y[1] (numeric) = 0.01005183574463358 absolute error = 1.561251128379126e-17 relative error = 1.553200000519946e-13 % Desired digits = 16 Estimated correct digits = 14 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] = -4.500000000000002 y[1] (closed_form) = 0.01110899653824229 y[1] (numeric) = 0.01110899653824231 absolute error = 2.081668171172169e-17 relative error = 1.873857970885225e-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] = -4.400000000000002 y[1] (closed_form) = 0.01227733990306842 y[1] (numeric) = 0.01227733990306844 absolute error = 2.775557561562891e-17 relative error = 2.260715744189187e-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] = -4.300000000000002 y[1] (closed_form) = 0.0135685590122009 y[1] (numeric) = 0.01356855901220093 absolute error = 3.642919299551295e-17 relative error = 2.684824008412071e-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] = -4.200000000000003 y[1] (closed_form) = 0.01499557682047766 y[1] (numeric) = 0.01499557682047771 absolute error = 4.510281037539698e-17 relative error = 3.007740943569805e-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] = -4.100000000000003 y[1] (closed_form) = 0.0165726754017612 y[1] (numeric) = 0.01657267540176125 absolute error = 5.551115123125783e-17 relative error = 3.349558830154762e-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) = 0.01831563888873412 y[1] (numeric) = 0.01831563888873419 absolute error = 6.938893903907228e-17 relative error = 3.788507704295981e-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) = 0.02024191144580432 y[1] (numeric) = 0.02024191144580439 absolute error = 7.632783294297951e-17 relative error = 3.770781882300968e-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) = 0.02237077185616552 y[1] (numeric) = 0.0223707718561656 absolute error = 7.979727989493313e-17 relative error = 3.567032930646982e-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) = 0.02472352647033931 y[1] (numeric) = 0.0247235264703394 absolute error = 9.020562075079397e-17 relative error = 3.648574197496186e-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) = 0.02732372244729247 y[1] (numeric) = 0.02732372244729257 absolute error = 9.71445146547012e-17 relative error = 3.555317722250078e-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) = 0.03019738342231841 y[1] (numeric) = 0.03019738342231851 absolute error = 1.040834085586084e-16 relative error = 3.446769115819552e-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) = 0.03337326996032598 y[1] (numeric) = 0.03337326996032609 absolute error = 1.179611963664229e-16 relative error = 3.534601089634151e-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) = 0.0368831674012399 y[1] (numeric) = 0.03688316740124002 absolute error = 1.249000902703301e-16 relative error = 3.386371048657046e-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) = 0.0407622039783661 y[1] (numeric) = 0.04076220397836623 absolute error = 1.318389841742373e-16 relative error = 3.234343860410708e-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) = 0.04504920239355768 y[1] (numeric) = 0.04504920239355782 absolute error = 1.387778780781446e-16 relative error = 3.080584576520509e-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) = 0.04978706836786381 y[1] (numeric) = 0.04978706836786396 absolute error = 1.457167719820518e-16 relative error = 2.926799603973227e-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) = 0.05502322005640709 y[1] (numeric) = 0.05502322005640724 absolute error = 1.595945597898663e-16 relative error = 2.900494729793309e-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) = 0.06081006262521781 y[1] (numeric) = 0.06081006262521798 absolute error = 1.665334536937735e-16 relative error = 2.738583821564959e-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) = 0.0672055127397496 y[1] (numeric) = 0.06720551273974978 absolute error = 1.804112415015879e-16 relative error = 2.684470873694879e-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) = 0.07427357821433371 y[1] (numeric) = 0.0742735782143339 absolute error = 1.942890293094024e-16 relative error = 2.615856593696565e-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) = 0.08208499862389862 y[1] (numeric) = 0.08208499862389883 absolute error = 2.081668171172169e-16 relative error = 2.535990992349364e-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) = 0.0907179532894123 y[1] (numeric) = 0.09071795328941254 absolute error = 2.359223927328458e-16 relative error = 2.600614147237163e-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) = 0.1002588437228035 y[1] (numeric) = 0.1002588437228038 absolute error = 2.498001805406602e-16 relative error = 2.491552577958208e-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) = 0.1108031583623337 y[1] (numeric) = 0.1108031583623339 absolute error = 2.636779683484747e-16 relative error = 2.379697223848352e-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) = 0.1224564282529817 y[1] (numeric) = 0.122456428252982 absolute error = 2.775557561562891e-16 relative error = 2.266567464983456e-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] = -2.000000000000002 y[1] (closed_form) = 0.1353352832366125 y[1] (numeric) = 0.1353352832366128 absolute error = 3.05311331771918e-16 relative error = 2.255962558101934e-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] = -1.900000000000002 y[1] (closed_form) = 0.1495686192226348 y[1] (numeric) = 0.1495686192226351 absolute error = 3.05311331771918e-16 relative error = 2.041279336258752e-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] = -1.800000000000002 y[1] (closed_form) = 0.1652988882215863 y[1] (numeric) = 0.1652988882215866 absolute error = 3.33066907387547e-16 relative error = 2.014937371756938e-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] = -1.700000000000002 y[1] (closed_form) = 0.1826835240527344 y[1] (numeric) = 0.1826835240527347 absolute error = 3.608224830031759e-16 relative error = 1.975123289711769e-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] = -1.600000000000001 y[1] (closed_form) = 0.2018965179946551 y[1] (numeric) = 0.2018965179946555 absolute error = 3.885780586188048e-16 relative error = 1.924639723747448e-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] = -1.500000000000001 y[1] (closed_form) = 0.2231301601484295 y[1] (numeric) = 0.22313016014843 absolute error = 4.163336342344337e-16 relative error = 1.865877898162589e-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] = -1.400000000000001 y[1] (closed_form) = 0.2465969639416062 y[1] (numeric) = 0.2465969639416066 absolute error = 4.718447854656915e-16 relative error = 1.913424958376307e-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] = -1.300000000000001 y[1] (closed_form) = 0.2725317930340123 y[1] (numeric) = 0.2725317930340128 absolute error = 4.440892098500626e-16 relative error = 1.6294950578285e-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] = -1.200000000000001 y[1] (closed_form) = 0.3011942119122017 y[1] (numeric) = 0.3011942119122022 absolute error = 4.996003610813204e-16 relative error = 1.658731613431383e-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] = -1.100000000000001 y[1] (closed_form) = 0.3328710836980792 y[1] (numeric) = 0.3328710836980797 absolute error = 4.996003610813204e-16 relative error = 1.500882430311874e-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] = -1.000000000000001 y[1] (closed_form) = 0.367879441171442 y[1] (numeric) = 0.3678794411714425 absolute error = 4.996003610813204e-16 relative error = 1.358054583018932e-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] = -0.9000000000000009 y[1] (closed_form) = 0.4065696597405987 y[1] (numeric) = 0.4065696597405993 absolute error = 6.106226635438361e-16 relative error = 1.501889402995364e-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] = -0.8000000000000009 y[1] (closed_form) = 0.4493289641172212 y[1] (numeric) = 0.4493289641172218 absolute error = 6.661338147750939e-16 relative error = 1.482508068634793e-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] = -0.700000000000001 y[1] (closed_form) = 0.496585303791409 y[1] (numeric) = 0.4965853037914098 absolute error = 7.771561172376096e-16 relative error = 1.565000235214481e-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] = -0.600000000000001 y[1] (closed_form) = 0.5488116360940259 y[1] (numeric) = 0.5488116360940267 absolute error = 7.771561172376096e-16 relative error = 1.41607077205714e-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] = -0.500000000000001 y[1] (closed_form) = 0.6065306597126329 y[1] (numeric) = 0.6065306597126338 absolute error = 8.881784197001252e-16 relative error = 1.464358652736424e-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] = -0.400000000000001 y[1] (closed_form) = 0.6703200460356387 y[1] (numeric) = 0.6703200460356397 absolute error = 9.992007221626409e-16 relative error = 1.490632315223222e-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] = -0.300000000000001 y[1] (closed_form) = 0.7408182206817171 y[1] (numeric) = 0.7408182206817182 absolute error = 1.110223024625157e-15 relative error = 1.498644328163939e-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] = -0.200000000000001 y[1] (closed_form) = 0.818730753077981 y[1] (numeric) = 0.8187307530779823 absolute error = 1.221245327087672e-15 relative error = 1.491632410895103e-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] = -0.100000000000001 y[1] (closed_form) = 0.9048374180359586 y[1] (numeric) = 0.9048374180359601 absolute error = 1.443289932012704e-15 relative error = 1.59508205921182e-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] = -1.02695629777827e-15 y[1] (closed_form) = 0.999999999999999 y[1] (numeric) = 1 absolute error = 1.443289932012704e-15 relative error = 1.443289932012705e-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] = 0.09999999999999898 y[1] (closed_form) = 1.105170918075647 y[1] (numeric) = 1.105170918075648 absolute error = 1.554312234475219e-15 relative error = 1.406399869064262e-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] = 0.199999999999999 y[1] (closed_form) = 1.221402758160169 y[1] (numeric) = 1.221402758160171 absolute error = 1.998401444325282e-15 relative error = 1.636152719464566e-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] = 0.299999999999999 y[1] (closed_form) = 1.349858807576002 y[1] (numeric) = 1.349858807576004 absolute error = 1.998401444325282e-15 relative error = 1.480452202192832e-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] = 0.399999999999999 y[1] (closed_form) = 1.491824697641269 y[1] (numeric) = 1.491824697641271 absolute error = 2.442490654175344e-15 relative error = 1.637250447748437e-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] = 0.499999999999999 y[1] (closed_form) = 1.648721270700126 y[1] (numeric) = 1.648721270700129 absolute error = 2.664535259100376e-15 relative error = 1.616122328529725e-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] = 0.599999999999999 y[1] (closed_form) = 1.822118800390507 y[1] (numeric) = 1.82211880039051 absolute error = 2.886579864025407e-15 relative error = 1.584188617891858e-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] = 0.699999999999999 y[1] (closed_form) = 2.013752707470474 y[1] (numeric) = 2.013752707470478 absolute error = 3.108624468950438e-15 relative error = 1.543697226287164e-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] = 0.7999999999999989 y[1] (closed_form) = 2.225540928492465 y[1] (numeric) = 2.225540928492469 absolute error = 3.552713678800501e-15 relative error = 1.596337157100514e-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] = 0.8999999999999989 y[1] (closed_form) = 2.459603111156947 y[1] (numeric) = 2.459603111156951 absolute error = 3.552713678800501e-15 relative error = 1.444425591545693e-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] = 0.9999999999999989 y[1] (closed_form) = 2.718281828459042 y[1] (numeric) = 2.718281828459046 absolute error = 3.996802888650564e-15 relative error = 1.470341613149177e-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] = 1.099999999999999 y[1] (closed_form) = 3.00416602394643 y[1] (numeric) = 3.004166023946434 absolute error = 4.440892098500626e-15 relative error = 1.478244565414144e-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] = 1.199999999999999 y[1] (closed_form) = 3.320116922736545 y[1] (numeric) = 3.320116922736549 absolute error = 4.440892098500626e-15 relative error = 1.337570995795023e-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] = 1.299999999999999 y[1] (closed_form) = 3.669296667619241 y[1] (numeric) = 3.669296667619246 absolute error = 4.440892098500626e-15 relative error = 1.210284286274956e-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] = 1.399999999999999 y[1] (closed_form) = 4.055199966844672 y[1] (numeric) = 4.055199966844676 absolute error = 4.440892098500626e-15 relative error = 1.095110508682525e-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] = 1.499999999999999 y[1] (closed_form) = 4.481689070338062 y[1] (numeric) = 4.481689070338067 absolute error = 5.329070518200751e-15 relative error = 1.18907635816841e-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] = 1.599999999999999 y[1] (closed_form) = 4.953032424395112 y[1] (numeric) = 4.953032424395118 absolute error = 5.329070518200751e-15 relative error = 1.075920781772706e-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] = 1.7 y[1] (closed_form) = 5.473947391727197 y[1] (numeric) = 5.473947391727203 absolute error = 5.329070518200751e-15 relative error = 9.735333821904465e-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] = 1.8 y[1] (closed_form) = 6.049647464412944 y[1] (numeric) = 6.049647464412949 absolute error = 5.329070518200751e-15 relative error = 8.808894319130186e-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] = 1.9 y[1] (closed_form) = 6.685894442279268 y[1] (numeric) = 6.685894442279273 absolute error = 5.329070518200751e-15 relative error = 7.970617191473388e-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] = 2 y[1] (closed_form) = 7.389056098930649 y[1] (numeric) = 7.389056098930654 absolute error = 5.329070518200751e-15 relative error = 7.212112679685812e-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] = 2.1 y[1] (closed_form) = 8.166169912567646 y[1] (numeric) = 8.166169912567653 absolute error = 7.105427357601002e-15 relative error = 8.701052554228423e-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] = 2.2 y[1] (closed_form) = 9.025013499434118 y[1] (numeric) = 9.025013499434124 absolute error = 5.329070518200751e-15 relative error = 5.904778445522427e-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] = 2.3 y[1] (closed_form) = 9.974182454814718 y[1] (numeric) = 9.974182454814724 absolute error = 5.329070518200751e-15 relative error = 5.3428644827209e-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] = 2.4 y[1] (closed_form) = 11.0231763806416 y[1] (numeric) = 11.0231763806416 absolute error = 3.552713678800501e-15 relative error = 3.222949135640807e-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] = 2.5 y[1] (closed_form) = 12.18249396070347 y[1] (numeric) = 12.18249396070348 absolute error = 3.552713678800501e-15 relative error = 2.916244974354456e-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] = 2.6 y[1] (closed_form) = 13.46373803500169 y[1] (numeric) = 13.46373803500169 absolute error = 1.77635683940025e-15 relative error = 1.319363786477614e-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] = 2.7 y[1] (closed_form) = 14.87973172487284 y[1] (numeric) = 14.87973172487284 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] = 2.8 y[1] (closed_form) = 16.44464677109706 y[1] (numeric) = 16.44464677109705 absolute error = 3.552713678800501e-15 relative error = 2.160407412973269e-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] = 2.9 y[1] (closed_form) = 18.17414536944307 y[1] (numeric) = 18.17414536944306 absolute error = 3.552713678800501e-15 relative error = 1.95481746546048e-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 y[1] (closed_form) = 20.08553692318768 y[1] (numeric) = 20.08553692318767 absolute error = 3.552713678800501e-15 relative error = 1.768791988178859e-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] = 3.100000000000001 y[1] (closed_form) = 22.19795128144165 y[1] (numeric) = 22.19795128144164 absolute error = 7.105427357601002e-15 relative error = 3.2009383512529e-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] = 3.200000000000001 y[1] (closed_form) = 24.53253019710936 y[1] (numeric) = 24.53253019710936 absolute error = 7.105427357601002e-15 relative error = 2.896328793039955e-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] = 3.300000000000001 y[1] (closed_form) = 27.11263892065791 y[1] (numeric) = 27.1126389206579 absolute error = 1.06581410364015e-14 relative error = 3.93106000031622e-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] = 3.400000000000001 y[1] (closed_form) = 29.96410004739704 y[1] (numeric) = 29.96410004739703 absolute error = 1.06581410364015e-14 relative error = 3.556970180830567e-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] = 3.500000000000001 y[1] (closed_form) = 33.11545195869234 y[1] (numeric) = 33.11545195869233 absolute error = 1.4210854715202e-14 relative error = 4.291306285938173e-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] = 3.600000000000001 y[1] (closed_form) = 36.59823444367802 y[1] (numeric) = 36.598234443678 absolute error = 2.131628207280301e-14 relative error = 5.824401749654669e-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] = 3.700000000000001 y[1] (closed_form) = 40.44730436006743 y[1] (numeric) = 40.44730436006741 absolute error = 2.842170943040401e-14 relative error = 7.026848854348874e-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] = 3.800000000000001 y[1] (closed_form) = 44.70118449330087 y[1] (numeric) = 44.70118449330084 absolute error = 2.842170943040401e-14 relative error = 6.358155774297975e-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] = 3.900000000000001 y[1] (closed_form) = 49.40244910553024 y[1] (numeric) = 49.4024491055302 absolute error = 4.263256414560601e-14 relative error = 8.62964588142931e-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) = 54.59815003314429 y[1] (numeric) = 54.59815003314426 absolute error = 2.131628207280301e-14 relative error = 3.904213248958576e-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) = 60.340287597362 y[1] (numeric) = 60.340287597362 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] = 4.2 y[1] (closed_form) = 66.68633104092515 y[1] (numeric) = 66.68633104092518 absolute error = 2.842170943040401e-14 relative error = 4.261999271329189e-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) = 73.69979369959579 y[1] (numeric) = 73.69979369959584 absolute error = 5.684341886080801e-14 relative error = 7.712832832681291e-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) = 81.45086866496807 y[1] (numeric) = 81.45086866496817 absolute error = 9.947598300641403e-14 relative error = 1.221300455561606e-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) = 90.01713130052174 y[1] (numeric) = 90.01713130052187 absolute error = 1.27897692436818e-13 relative error = 1.420815022529792e-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) = 99.48431564193369 y[1] (numeric) = 99.48431564193388 absolute error = 1.84741111297626e-13 relative error = 1.856987306044811e-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) = 109.9471724521233 y[1] (numeric) = 109.9471724521236 absolute error = 2.415845301584341e-13 relative error = 2.197278245273951e-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) = 121.5104175187346 y[1] (numeric) = 121.510417518735 absolute error = 3.126388037344441e-13 relative error = 2.572938272442698e-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) = 134.2897796849352 y[1] (numeric) = 134.2897796849356 absolute error = 3.979039320256561e-13 relative error = 2.963024684076487e-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) = 148.4131591025762 y[1] (numeric) = 148.4131591025767 absolute error = 5.115907697472721e-13 relative error = 3.447071491778466e-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 ) = y ; 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 %