##############ECHO OF PROBLEM################# ##############temp/div_lin_linpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=1.0; array_given_ord_poles[1][2]=0.0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=16; glob_max_minutes=3.0; glob_subiter_method=3; glob_max_iter=100000000; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(0.5 * x + 0.25 * ln(2.0 * x + 3.0)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.505846504842085e-21 est_needed_step_err = 1.505846504842085e-21 opt_iter = 1 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4900000.000000001 step_error = 1.505846504842085e-21 est_needed_step_err = 1.505846504842085e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.74074920572346e-164 estimated_step_error = 4.74074920572346e-164 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 2450000 step_error = 2.129588549999799e-21 est_needed_step_err = 2.129588549999799e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.181461979665935e-156 estimated_step_error = 3.181461979665935e-156 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 1225000 step_error = 3.01169300968417e-21 est_needed_step_err = 3.01169300968417e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.13504170816769e-148 estimated_step_error = 2.13504170816769e-148 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 612500.0000000001 step_error = 4.259177099999599e-21 est_needed_step_err = 4.259177099999599e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.432800511612334e-140 estimated_step_error = 1.432800511612334e-140 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 306250.0000000001 step_error = 6.023386019368341e-21 est_needed_step_err = 6.023386019368341e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.615338319311518e-133 estimated_step_error = 9.615338319311518e-133 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 153125 step_error = 8.518354199999198e-21 est_needed_step_err = 8.518354199999198e-21 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.452713247377518e-125 estimated_step_error = 6.452713247377518e-125 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 76562.50000000001 step_error = 1.204677203873668e-20 est_needed_step_err = 1.204677203873668e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.330300858702307e-117 estimated_step_error = 4.330300858702307e-117 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 38281.25000000001 step_error = 1.70367083999984e-20 est_needed_step_err = 1.70367083999984e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.905959748507466e-109 estimated_step_error = 2.905959748507466e-109 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 19140.625 step_error = 2.409354407747336e-20 est_needed_step_err = 2.409354407747336e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.950081464176726e-101 estimated_step_error = 1.950081464176726e-101 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 9570.312500000002 step_error = 3.407341679999679e-20 est_needed_step_err = 3.407341679999679e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.308576716607997e-93 estimated_step_error = 1.308576716607997e-93 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 4785.156250000001 step_error = 4.818708815494673e-20 est_needed_step_err = 4.818708815494673e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.780357074716542e-86 estimated_step_error = 8.780357074716542e-86 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 2392.578125 step_error = 6.814683359999358e-20 est_needed_step_err = 6.814683359999358e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.890583277128911e-78 estimated_step_error = 5.890583277128911e-78 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 1196.2890625 step_error = 9.637417630989345e-20 est_needed_step_err = 9.637417630989345e-20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.950670242602175e-70 estimated_step_error = 3.950670242602175e-70 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 598.1445312500001 step_error = 1.362936671999872e-19 est_needed_step_err = 1.362936671999872e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.647990061772977e-62 estimated_step_error = 2.647990061772977e-62 Double H and LOOP opt_iter = 15 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.016384 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 299.0722656250001 step_error = 1.927483526197869e-19 est_needed_step_err = 1.927483526197869e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.772676861880176e-54 estimated_step_error = 1.772676861880176e-54 Double H and LOOP opt_iter = 16 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.032768 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 149.5361328125 step_error = 2.725873343999743e-19 est_needed_step_err = 2.725873343999743e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.183815397621867e-46 estimated_step_error = 1.183815397621867e-46 Double H and LOOP opt_iter = 17 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.3407877024514202 min_size = 1 glob_desired_digits_correct = 16 estimated_h = 0.065536 estimated_answer = 1 desired_abs_gbl_error = 1e-16 range = 4.9 estimated_steps = 74.76806640625001 step_error = 3.854967052395738e-19 est_needed_step_err = 3.854967052395738e-19 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.867629441166437e-39 estimated_step_error = 7.867629441166437e-39 Double H and LOOP opt_iter = 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.221 Order of pole (three term test) = 2.316e-13 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.3407877024514202 y[1] (numeric) = 0.3407877024514202 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 14 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 1.124e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0.4059438579055289 y[1] (numeric) = 0.4059438579055289 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 2.284e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0.4702334613655161 y[1] (numeric) = 0.4702334613655161 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0.533750266683085 y[1] (numeric) = 0.533750266683085 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (closed_form) = 0.5965735902799727 y[1] (numeric) = 0.5965735902799727 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 1.968e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0.6587711313223307 y[1] (numeric) = 0.6587711313223307 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.16e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7 y[1] (closed_form) = 0.7204011352310539 y[1] (numeric) = 0.7204011352310539 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (closed_form) = 0.7815140758737622 y[1] (numeric) = 0.7815140758737623 absolute error = 1.110223024625157e-16 relative error = 1.420605282616165e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.3 Order of pole (three term test) = 2.382e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (closed_form) = 0.8421539794784613 y[1] (numeric) = 0.8421539794784613 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 1.054e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (closed_form) = 0.902359478108525 y[1] (numeric) = 0.902359478108525 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 8.618e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 0.9621646563968453 y[1] (numeric) = 0.9621646563968453 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.6 Order of pole (three term test) = 1.309e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.021599738392557 y[1] (numeric) = 1.021599738392557 absolute error = 2.220446049250313e-16 relative error = 2.173499038619654e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.7 Order of pole (three term test) = 1.857e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 1.080691649435276 y[1] (numeric) = 1.080691649435276 absolute error = 2.220446049250313e-16 relative error = 2.05465273134166e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.8 Order of pole (three term test) = 3.71e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.4 y[1] (closed_form) = 1.139464479388093 y[1] (numeric) = 1.139464479388093 absolute error = 2.220446049250313e-16 relative error = 1.948675092042114e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.5 y[1] (closed_form) = 1.197939867307014 y[1] (numeric) = 1.197939867307014 absolute error = 2.220446049250313e-16 relative error = 1.853553846773551e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.6 y[1] (closed_form) = 1.256137323012762 y[1] (numeric) = 1.256137323012761 absolute error = 4.440892098500626e-16 relative error = 3.535355583455989e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 1.043e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (closed_form) = 1.314074497591407 y[1] (numeric) = 1.314074497591406 absolute error = 4.440892098500626e-16 relative error = 3.379482751275081e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 1.124e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (closed_form) = 1.371767412258095 y[1] (numeric) = 1.371767412258095 absolute error = 6.661338147750939e-16 relative error = 4.85602594742032e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (closed_form) = 1.429230653045515 y[1] (numeric) = 1.429230653045515 absolute error = 4.440892098500626e-16 relative error = 3.107190633672479e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (closed_form) = 1.486477537263829 y[1] (numeric) = 1.486477537263828 absolute error = 4.440892098500626e-16 relative error = 2.9875272159679e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 2.166e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (closed_form) = 1.543520256505503 y[1] (numeric) = 1.543520256505502 absolute error = 4.440892098500626e-16 relative error = 2.877119415688597e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 9.894e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (closed_form) = 1.600370000052531 y[1] (numeric) = 1.600370000052531 absolute error = 6.661338147750939e-16 relative error = 4.162373793267984e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 8.723e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (closed_form) = 1.657037061823072 y[1] (numeric) = 1.657037061823071 absolute error = 8.881784197001252e-16 relative error = 5.360039555922494e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 1.487e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (closed_form) = 1.713530933423887 y[1] (numeric) = 1.713530933423886 absolute error = 8.881784197001252e-16 relative error = 5.183322940808626e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (closed_form) = 1.769860385419959 y[1] (numeric) = 1.769860385419959 absolute error = 8.881784197001252e-16 relative error = 5.018353012570394e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (closed_form) = 1.826033538567553 y[1] (numeric) = 1.826033538567551 absolute error = 1.110223024625157e-15 relative error = 6.079970609390232e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.1 Order of pole (three term test) = 1.532e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (closed_form) = 1.882057926462318 y[1] (numeric) = 1.882057926462317 absolute error = 1.110223024625157e-15 relative error = 5.898984345885834e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.2 Order of pole (three term test) = 1.16e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (closed_form) = 1.937940550814866 y[1] (numeric) = 1.937940550814865 absolute error = 1.110223024625157e-15 relative error = 5.728880713901824e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.3 Order of pole (three term test) = 8.563e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (closed_form) = 1.993687930371041 y[1] (numeric) = 1.99368793037104 absolute error = 1.110223024625157e-15 relative error = 5.568690102961778e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.4 Order of pole (three term test) = 1.233e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y[1] (closed_form) = 2.049306144334055 y[1] (numeric) = 2.049306144334055 absolute error = 8.881784197001252e-16 relative error = 4.334044584581815e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.5 Order of pole (three term test) = 8.665e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (closed_form) = 2.10480087101375 y[1] (numeric) = 2.104800871013748 absolute error = 1.332267629550188e-15 relative error = 6.329661147035342e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.6 Order of pole (three term test) = 2.382e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (closed_form) = 2.16017742231899 y[1] (numeric) = 2.160177422318989 absolute error = 1.332267629550188e-15 relative error = 6.167399102431012e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.7 Order of pole (three term test) = 2.402e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000002 y[1] (closed_form) = 2.215440774618449 y[1] (numeric) = 2.215440774618447 absolute error = 1.332267629550188e-15 relative error = 6.013555608497978e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.8 Order of pole (three term test) = 1.054e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000000002 y[1] (closed_form) = 2.270595596419132 y[1] (numeric) = 2.270595596419131 absolute error = 1.332267629550188e-15 relative error = 5.867480900831725e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.9 Order of pole (three term test) = 1.361e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500000000000002 y[1] (closed_form) = 2.325646273248513 y[1] (numeric) = 2.325646273248511 absolute error = 1.77635683940025e-15 relative error = 7.638121324955395e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5 Order of pole (three term test) = 1.724e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600000000000002 y[1] (closed_form) = 2.380596930072557 y[1] (numeric) = 2.380596930072556 absolute error = 1.77635683940025e-15 relative error = 7.461812694793778e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.1 Order of pole (three term test) = 2.143e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000000002 y[1] (closed_form) = 2.435451451536833 y[1] (numeric) = 2.435451451536831 absolute error = 1.77635683940025e-15 relative error = 7.293747688049061e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.2 Order of pole (three term test) = 1.309e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000000002 y[1] (closed_form) = 2.490213500279506 y[1] (numeric) = 2.490213500279505 absolute error = 1.77635683940025e-15 relative error = 7.133351574878494e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.3 Order of pole (three term test) = 2.358e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (closed_form) = 2.544886533532545 y[1] (numeric) = 2.544886533532543 absolute error = 1.77635683940025e-15 relative error = 6.980102318882162e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.4 Order of pole (three term test) = 9.284e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (closed_form) = 2.599473818199594 y[1] (numeric) = 2.599473818199592 absolute error = 1.332267629550188e-15 relative error = 5.125143481817878e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.5 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (closed_form) = 2.653978444575263 y[1] (numeric) = 2.653978444575262 absolute error = 1.332267629550188e-15 relative error = 5.019888659131144e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.6 Order of pole (three term test) = 1.237e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.200000000000001 y[1] (closed_form) = 2.708403338850113 y[1] (numeric) = 2.708403338850112 absolute error = 8.881784197001252e-16 relative error = 3.279343246110503e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.7 Order of pole (three term test) = 2.791e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.300000000000001 y[1] (closed_form) = 2.76275127452808 y[1] (numeric) = 2.76275127452808 absolute error = 4.440892098500626e-16 relative error = 1.607416541418191e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.4 y[1] (closed_form) = 2.817024882867905 y[1] (numeric) = 2.817024882867905 absolute error = 4.440892098500626e-16 relative error = 1.576447593881217e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 5.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.9 Order of pole (three term test) = 8.524e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.5 y[1] (closed_form) = 2.871226662447 y[1] (numeric) = 2.871226662447 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6 Order of pole (three term test) = 1.847e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.6 y[1] (closed_form) = 2.925358987934803 y[1] (numeric) = 2.925358987934803 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 6.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.1 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999999 y[1] (closed_form) = 2.979424118152747 y[1] (numeric) = 2.979424118152747 absolute error = 0 relative error = 0 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 6.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.2 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999999 y[1] (closed_form) = 3.033424203489357 y[1] (numeric) = 3.033424203489358 absolute error = 4.440892098500626e-16 relative error = 1.463986505214883e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 6.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (closed_form) = 3.087361292731392 y[1] (numeric) = 3.087361292731393 absolute error = 8.881784197001252e-16 relative error = 2.876820480295498e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 6.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (closed_form) = 3.141237339365383 y[1] (numeric) = 3.141237339365384 absolute error = 8.881784197001252e-16 relative error = 2.827479504874222e-14 % Desired digits = 16 Estimated correct digits = 13 Correct digits = 16 h = 0.1 Radius of convergence (given) for eq 1 = 6.5 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.5 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; Iterations = 50 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 104.1 %