##############ECHO OF PROBLEM################# ##############temp/diffpostode.ode################# diff ( y , x , 2 ) = diff ( y , x , 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); array_y_init[1 + 1] = exact_soln_yp(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(1.0 + exp(x)); } double exact_soln_yp (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 NO POLE (given) for Equation 1 NO 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 10000000 step_error = 1.061194973146328e-21 est_needed_step_err = 1.061194973146328e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.670738851013515e-185 estimated_step_error = 1.670738851013515e-185 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 5000000 step_error = 1.50075632334569e-21 est_needed_step_err = 1.50075632334569e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.121213884085043e-177 estimated_step_error = 1.121213884085043e-177 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 2500000 step_error = 2.122389946292657e-21 est_needed_step_err = 2.122389946292657e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.524339284876733e-170 estimated_step_error = 7.524339284876733e-170 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 1250000 step_error = 3.00151264669138e-21 est_needed_step_err = 3.00151264669138e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.049498991623487e-162 estimated_step_error = 5.049498991623487e-162 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 625000 step_error = 4.244779892585314e-21 est_needed_step_err = 4.244779892585314e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.388661912994031e-154 estimated_step_error = 3.388661912994031e-154 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 312500 step_error = 6.003025293382761e-21 est_needed_step_err = 6.003025293382761e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.27409318841653e-146 estimated_step_error = 2.27409318841653e-146 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 156250 step_error = 8.489559785170627e-21 est_needed_step_err = 8.489559785170627e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.526119009415012e-138 estimated_step_error = 1.526119009415012e-138 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 78125 step_error = 1.200605058676552e-20 est_needed_step_err = 1.200605058676552e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.02416234432979e-130 estimated_step_error = 1.02416234432979e-130 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 39062.5 step_error = 1.697911957034125e-20 est_needed_step_err = 1.697911957034125e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.873053439671608e-123 estimated_step_error = 6.873053439671608e-123 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 19531.25 step_error = 2.401210117353104e-20 est_needed_step_err = 2.401210117353104e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.612449951998501e-115 estimated_step_error = 4.612449951998501e-115 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 9765.625 step_error = 3.395823914068251e-20 est_needed_step_err = 3.395823914068251e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.095392114506209e-107 estimated_step_error = 3.095392114506209e-107 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 4882.8125 step_error = 4.802420234706209e-20 est_needed_step_err = 4.802420234706209e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.077321877235483e-99 estimated_step_error = 2.077321877235483e-99 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 2441.40625 step_error = 6.791647828136502e-20 est_needed_step_err = 6.791647828136502e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.394119988518091e-91 estimated_step_error = 1.394119988518091e-91 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 1220.703125 step_error = 9.604840469412418e-20 est_needed_step_err = 9.604840469412418e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.356490626122473e-84 estimated_step_error = 9.356490626122473e-84 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 610.3515625 step_error = 1.3583295656273e-19 est_needed_step_err = 1.3583295656273e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.279987395861075e-76 estimated_step_error = 6.279987395861075e-76 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 305.17578125 step_error = 1.920968093882484e-19 est_needed_step_err = 1.920968093882484e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.215707624202583e-68 estimated_step_error = 4.215707624202583e-68 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 = 1.006737946999085 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1.006737946999085 desired_abs_gbl_error = 1.006737946999085e-16 range = 10 estimated_steps = 152.587890625 step_error = 2.716659131254601e-19 est_needed_step_err = 2.716659131254601e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.830832218190585e-60 estimated_step_error = 2.830832218190585e-60 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) = 1.006737946999085 y[1] (numeric) = 1.006737946999085 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) = 1.007446583070924 y[1] (numeric) = 1.007446583070924 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] = -4.800000000000001 y[1] (closed_form) = 1.00822974704902 y[1] (numeric) = 1.00822974704902 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] = -4.700000000000001 y[1] (closed_form) = 1.009095277101696 y[1] (numeric) = 1.009095277101696 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] = -4.600000000000001 y[1] (closed_form) = 1.010051835744634 y[1] (numeric) = 1.010051835744634 absolute error = 2.220446049250313e-16 relative error = 2.198348610112023e-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) = 1.011108996538242 y[1] (numeric) = 1.011108996538242 absolute error = 2.220446049250313e-16 relative error = 2.196050135892873e-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) = 1.012277339903068 y[1] (numeric) = 1.012277339903069 absolute error = 2.220446049250313e-16 relative error = 2.193515513705892e-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) = 1.013568559012201 y[1] (numeric) = 1.013568559012201 absolute error = 2.220446049250313e-16 relative error = 2.190721120448236e-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) = 1.014995576820478 y[1] (numeric) = 1.014995576820478 absolute error = 2.220446049250313e-16 relative error = 2.187641108945486e-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) = 1.016572675401761 y[1] (numeric) = 1.016572675401761 absolute error = 2.220446049250313e-16 relative error = 2.184247228928092e-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) = 1.018315638888734 y[1] (numeric) = 1.018315638888734 absolute error = 2.220446049250313e-16 relative error = 2.180508640399e-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] = -3.900000000000003 y[1] (closed_form) = 1.020241911445804 y[1] (numeric) = 1.020241911445805 absolute error = 2.220446049250313e-16 relative error = 2.176391720767162e-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] = -3.800000000000003 y[1] (closed_form) = 1.022370771856165 y[1] (numeric) = 1.022370771856166 absolute error = 4.440892098500626e-16 relative error = 4.343719735295214e-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) = 1.024723526470339 y[1] (numeric) = 1.02472352647034 absolute error = 2.220446049250313e-16 relative error = 2.166873299863272e-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] = -3.600000000000003 y[1] (closed_form) = 1.027323722447292 y[1] (numeric) = 1.027323722447293 absolute error = 4.440892098500626e-16 relative error = 4.322777719881251e-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] = -3.500000000000003 y[1] (closed_form) = 1.030197383422318 y[1] (numeric) = 1.030197383422319 absolute error = 4.440892098500626e-16 relative error = 4.310719644567501e-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] = -3.400000000000003 y[1] (closed_form) = 1.033373269960326 y[1] (numeric) = 1.033373269960326 absolute error = 4.440892098500626e-16 relative error = 4.297471424503872e-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] = -3.300000000000003 y[1] (closed_form) = 1.03688316740124 y[1] (numeric) = 1.03688316740124 absolute error = 4.440892098500626e-16 relative error = 4.282924285125506e-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] = -3.200000000000003 y[1] (closed_form) = 1.040762203978366 y[1] (numeric) = 1.040762203978367 absolute error = 4.440892098500626e-16 relative error = 4.26696134960041e-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] = -3.100000000000003 y[1] (closed_form) = 1.045049202393558 y[1] (numeric) = 1.045049202393558 absolute error = 6.661338147750939e-16 relative error = 6.374186145967059e-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] = -3.000000000000003 y[1] (closed_form) = 1.049787068367864 y[1] (numeric) = 1.049787068367864 absolute error = 4.440892098500626e-16 relative error = 4.230278913041877e-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] = -2.900000000000003 y[1] (closed_form) = 1.055023220056407 y[1] (numeric) = 1.055023220056408 absolute error = 4.440892098500626e-16 relative error = 4.209283752317027e-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] = -2.800000000000002 y[1] (closed_form) = 1.060810062625218 y[1] (numeric) = 1.060810062625218 absolute error = 6.661338147750939e-16 relative error = 6.279482428047421e-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] = -2.700000000000002 y[1] (closed_form) = 1.06720551273975 y[1] (numeric) = 1.06720551273975 absolute error = 6.661338147750939e-16 relative error = 6.241851328756567e-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] = -2.600000000000002 y[1] (closed_form) = 1.074273578214334 y[1] (numeric) = 1.074273578214334 absolute error = 4.440892098500626e-16 relative error = 4.133855833895042e-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] = -2.500000000000002 y[1] (closed_form) = 1.082084998623899 y[1] (numeric) = 1.082084998623899 absolute error = 4.440892098500626e-16 relative error = 4.104014106237648e-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] = -2.400000000000002 y[1] (closed_form) = 1.090717953289412 y[1] (numeric) = 1.090717953289413 absolute error = 6.661338147750939e-16 relative error = 6.107296691744665e-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] = -2.300000000000002 y[1] (closed_form) = 1.100258843722804 y[1] (numeric) = 1.100258843722804 absolute error = 6.661338147750939e-16 relative error = 6.054337291406657e-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] = -2.200000000000002 y[1] (closed_form) = 1.110803158362334 y[1] (numeric) = 1.110803158362334 absolute error = 6.661338147750939e-16 relative error = 5.996866409321166e-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] = -2.100000000000002 y[1] (closed_form) = 1.122456428252982 y[1] (numeric) = 1.122456428252982 absolute error = 6.661338147750939e-16 relative error = 5.934607330922241e-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] = -2.000000000000002 y[1] (closed_form) = 1.135335283236612 y[1] (numeric) = 1.135335283236613 absolute error = 6.661338147750939e-16 relative error = 5.867287175961629e-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] = -1.900000000000002 y[1] (closed_form) = 1.149568619222635 y[1] (numeric) = 1.149568619222635 absolute error = 4.440892098500626e-16 relative error = 3.863094402754018e-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] = -1.800000000000002 y[1] (closed_form) = 1.165298888221586 y[1] (numeric) = 1.165298888221587 absolute error = 6.661338147750939e-16 relative error = 5.716420237830227e-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] = -1.700000000000002 y[1] (closed_form) = 1.182683524052734 y[1] (numeric) = 1.182683524052735 absolute error = 4.440892098500626e-16 relative error = 3.754928523298353e-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] = -1.600000000000001 y[1] (closed_form) = 1.201896517994655 y[1] (numeric) = 1.201896517994656 absolute error = 4.440892098500626e-16 relative error = 3.694903872348497e-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] = -1.500000000000001 y[1] (closed_form) = 1.223130160148429 y[1] (numeric) = 1.22313016014843 absolute error = 6.661338147750939e-16 relative error = 5.446140046896212e-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] = -1.400000000000001 y[1] (closed_form) = 1.246596963941606 y[1] (numeric) = 1.246596963941607 absolute error = 6.661338147750939e-16 relative error = 5.34361813836647e-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] = -1.300000000000001 y[1] (closed_form) = 1.272531793034012 y[1] (numeric) = 1.272531793034013 absolute error = 6.661338147750939e-16 relative error = 5.234712550378609e-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] = -1.200000000000001 y[1] (closed_form) = 1.301194211912202 y[1] (numeric) = 1.301194211912202 absolute error = 6.661338147750939e-16 relative error = 5.119403457814039e-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] = -1.100000000000001 y[1] (closed_form) = 1.332871083698079 y[1] (numeric) = 1.33287108369808 absolute error = 6.661338147750939e-16 relative error = 4.997736262136406e-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] = -1.000000000000001 y[1] (closed_form) = 1.367879441171442 y[1] (numeric) = 1.367879441171443 absolute error = 8.881784197001252e-16 relative error = 6.493104530758177e-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] = -0.9000000000000009 y[1] (closed_form) = 1.406569659740599 y[1] (numeric) = 1.4065696597406 absolute error = 8.881784197001252e-16 relative error = 6.314500057280663e-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] = -0.8000000000000009 y[1] (closed_form) = 1.449328964117221 y[1] (numeric) = 1.449328964117222 absolute error = 1.110223024625157e-15 relative error = 7.660255553516711e-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] = -0.700000000000001 y[1] (closed_form) = 1.496585303791409 y[1] (numeric) = 1.49658530379141 absolute error = 1.110223024625157e-15 relative error = 7.418374494340867e-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] = -0.600000000000001 y[1] (closed_form) = 1.548811636094026 y[1] (numeric) = 1.548811636094027 absolute error = 8.881784197001252e-16 relative error = 5.734579977330473e-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] = -0.500000000000001 y[1] (closed_form) = 1.606530659712633 y[1] (numeric) = 1.606530659712634 absolute error = 1.332267629550188e-15 relative error = 8.292824176716904e-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] = -0.400000000000001 y[1] (closed_form) = 1.670320046035639 y[1] (numeric) = 1.67032004603564 absolute error = 1.332267629550188e-15 relative error = 7.976121897789653e-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] = -0.300000000000001 y[1] (closed_form) = 1.740818220681717 y[1] (numeric) = 1.740818220681719 absolute error = 1.554312234475219e-15 relative error = 8.928630318830988e-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] = -0.200000000000001 y[1] (closed_form) = 1.818730753077981 y[1] (numeric) = 1.818730753077983 absolute error = 1.554312234475219e-15 relative error = 8.546137089531996e-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] = -0.100000000000001 y[1] (closed_form) = 1.904837418035959 y[1] (numeric) = 1.90483741803596 absolute error = 1.77635683940025e-15 relative error = 9.325503702210019e-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] = -1.02695629777827e-15 y[1] (closed_form) = 1.999999999999999 y[1] (numeric) = 2.000000000000001 absolute error = 1.77635683940025e-15 relative error = 8.881784197001256e-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] = 0.09999999999999898 y[1] (closed_form) = 2.105170918075647 y[1] (numeric) = 2.105170918075649 absolute error = 1.77635683940025e-15 relative error = 8.438064691792494e-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] = 0.199999999999999 y[1] (closed_form) = 2.221402758160169 y[1] (numeric) = 2.221402758160171 absolute error = 2.220446049250313e-15 relative error = 9.995693221743148e-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] = 0.299999999999999 y[1] (closed_form) = 2.349858807576002 y[1] (numeric) = 2.349858807576005 absolute error = 2.664535259100376e-15 relative error = 1.133912918729351e-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) = 2.491824697641269 y[1] (numeric) = 2.491824697641272 absolute error = 3.108624468950438e-15 relative error = 1.247529359466188e-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) = 2.648721270700126 y[1] (numeric) = 2.64872127070013 absolute error = 3.108624468950438e-15 relative error = 1.173632161049829e-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) = 2.822118800390507 y[1] (numeric) = 2.82211880039051 absolute error = 3.108624468950438e-15 relative error = 1.101521476884774e-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) = 3.013752707470474 y[1] (numeric) = 3.013752707470478 absolute error = 3.552713678800501e-15 relative error = 1.178833840611425e-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) = 3.225540928492465 y[1] (numeric) = 3.225540928492469 absolute error = 3.996802888650564e-15 relative error = 1.239110889384549e-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) = 3.459603111156947 y[1] (numeric) = 3.459603111156952 absolute error = 4.440892098500626e-15 relative error = 1.283642069860297e-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) = 3.718281828459042 y[1] (numeric) = 3.718281828459047 absolute error = 4.884981308350689e-15 relative error = 1.313773816433694e-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) = 4.00416602394643 y[1] (numeric) = 4.004166023946436 absolute error = 5.329070518200751e-15 relative error = 1.330881508491629e-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) = 4.320116922736545 y[1] (numeric) = 4.320116922736551 absolute error = 6.217248937900877e-15 relative error = 1.439139043941109e-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) = 4.669296667619241 y[1] (numeric) = 4.669296667619248 absolute error = 7.105427357601002e-15 relative error = 1.521733970530487e-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) = 5.055199966844672 y[1] (numeric) = 5.055199966844679 absolute error = 7.105427357601002e-15 relative error = 1.405568010010102e-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) = 5.481689070338062 y[1] (numeric) = 5.48168907033807 absolute error = 7.993605777301127e-15 relative error = 1.458237721025675e-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) = 5.953032424395112 y[1] (numeric) = 5.95303242439512 absolute error = 7.993605777301127e-15 relative error = 1.342778807073835e-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) = 6.473947391727197 y[1] (numeric) = 6.473947391727206 absolute error = 8.881784197001252e-15 relative error = 1.371927150404548e-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] = 1.8 y[1] (closed_form) = 7.049647464412944 y[1] (numeric) = 7.049647464412953 absolute error = 8.881784197001252e-15 relative error = 1.259890546560952e-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] = 1.9 y[1] (closed_form) = 7.685894442279268 y[1] (numeric) = 7.685894442279277 absolute error = 8.881784197001252e-15 relative error = 1.155595391493217e-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 y[1] (closed_form) = 8.389056098930649 y[1] (numeric) = 8.389056098930658 absolute error = 8.881784197001252e-15 relative error = 1.058734629052416e-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] = 2.1 y[1] (closed_form) = 9.166169912567646 y[1] (numeric) = 9.166169912567659 absolute error = 1.243449787580175e-14 relative error = 1.356564191413573e-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] = 2.2 y[1] (closed_form) = 10.02501349943412 y[1] (numeric) = 10.02501349943413 absolute error = 1.243449787580175e-14 relative error = 1.240347245068911e-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] = 2.3 y[1] (closed_form) = 10.97418245481472 y[1] (numeric) = 10.97418245481473 absolute error = 1.4210854715202e-14 relative error = 1.294935160201137e-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] = 2.4 y[1] (closed_form) = 12.0231763806416 y[1] (numeric) = 12.02317638064162 absolute error = 1.4210854715202e-14 relative error = 1.181955106146722e-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] = 2.5 y[1] (closed_form) = 13.18249396070347 y[1] (numeric) = 13.18249396070349 absolute error = 1.598721155460225e-14 relative error = 1.212760772146723e-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] = 2.6 y[1] (closed_form) = 14.46373803500169 y[1] (numeric) = 14.46373803500171 absolute error = 1.598721155460225e-14 relative error = 1.105330552580102e-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] = 2.7 y[1] (closed_form) = 15.87973172487284 y[1] (numeric) = 15.87973172487285 absolute error = 1.598721155460225e-14 relative error = 1.006768365586496e-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] = 2.8 y[1] (closed_form) = 17.44464677109706 y[1] (numeric) = 17.44464677109707 absolute error = 1.4210854715202e-14 relative error = 8.146255353675077e-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) = 19.17414536944307 y[1] (numeric) = 19.17414536944308 absolute error = 1.4210854715202e-14 relative error = 7.411467077875175e-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) = 21.08553692318768 y[1] (numeric) = 21.08553692318769 absolute error = 1.77635683940025e-14 relative error = 8.424527418349961e-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) = 23.19795128144165 y[1] (numeric) = 23.19795128144166 absolute error = 1.4210854715202e-14 relative error = 6.125909371389482e-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) = 25.53253019710936 y[1] (numeric) = 25.53253019710938 absolute error = 1.77635683940025e-14 relative error = 6.957229956008663e-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) = 28.11263892065791 y[1] (numeric) = 28.11263892065792 absolute error = 1.4210854715202e-14 relative error = 5.054970028003843e-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) = 30.96410004739704 y[1] (numeric) = 30.96410004739705 absolute error = 1.77635683940025e-14 relative error = 5.736826959870187e-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) = 34.11545195869234 y[1] (numeric) = 34.11545195869236 absolute error = 2.131628207280301e-14 relative error = 6.248277788790012e-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) = 37.59823444367802 y[1] (numeric) = 37.59823444367804 absolute error = 1.4210854715202e-14 relative error = 3.779660115820012e-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) = 41.44730436006743 y[1] (numeric) = 41.44730436006745 absolute error = 1.4210854715202e-14 relative error = 3.428655960770638e-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) = 45.70118449330087 y[1] (numeric) = 45.70118449330089 absolute error = 1.4210854715202e-14 relative error = 3.10951562257322e-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) = 50.40244910553024 y[1] (numeric) = 50.40244910553024 absolute error = 7.105427357601002e-15 relative error = 1.409738511460822e-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) = 55.59815003314429 y[1] (numeric) = 55.59815003314432 absolute error = 3.552713678800501e-14 relative error = 6.389985416210046e-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) = 61.340287597362 y[1] (numeric) = 61.34028759736206 absolute error = 6.394884621840902e-14 relative error = 1.042526025279986e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (closed_form) = 67.68633104092515 y[1] (numeric) = 67.68633104092524 absolute error = 8.526512829121202e-14 relative error = 1.259709707705359e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (closed_form) = 74.69979369959579 y[1] (numeric) = 74.6997936995959 absolute error = 1.13686837721616e-13 relative error = 1.521916354666334e-13 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 15 h = 0.1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999999 y[1] (closed_form) = 82.45086866496807 y[1] (numeric) = 82.45086866496824 absolute error = 1.70530256582424e-13 relative error = 2.068265129811535e-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) = 91.01713130052174 y[1] (numeric) = 91.01713130052195 absolute error = 2.131628207280301e-13 relative error = 2.342007682314287e-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) = 100.4843156419337 y[1] (numeric) = 100.484315641934 absolute error = 2.700062395888381e-13 relative error = 2.687048599216017e-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) = 110.9471724521233 y[1] (numeric) = 110.9471724521237 absolute error = 3.410605131648481e-13 relative error = 3.074080263848318e-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) = 122.5104175187346 y[1] (numeric) = 122.5104175187351 absolute error = 4.263256414560601e-13 relative error = 3.479913382801631e-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) = 135.2897796849352 y[1] (numeric) = 135.2897796849357 absolute error = 5.115907697472721e-13 relative error = 3.78144432594001e-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) = 149.4131591025762 y[1] (numeric) = 149.4131591025769 absolute error = 6.536993168992922e-13 relative error = 4.375112077313818e-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 , 2 ) = diff ( y , x , 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 %