##############ECHO OF PROBLEM################# ##############temp/sing6postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ! // BEGIN FIRST INPUT BLOCK Digits=30; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=2.0; x_end=3.0; 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]=6.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=3.0; array_given_ord_poles[1][2]=0.0; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 5e-15 est_needed_step_err = 5e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 1000000 step_error = 1e-14 est_needed_step_err = 1e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.728484426316951e-107 estimated_step_error = 2.728484426316951e-107 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 500000 step_error = 1.414213562373095e-14 est_needed_step_err = 1.414213562373095e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.788139764000486e-102 estimated_step_error = 1.788139764000486e-102 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 250000 step_error = 2e-14 est_needed_step_err = 2e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.171875551470848e-97 estimated_step_error = 1.171875551470848e-97 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 125000 step_error = 2.82842712474619e-14 est_needed_step_err = 2.82842712474619e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.680007228242115e-93 estimated_step_error = 7.680007228242115e-93 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 62500 step_error = 4e-14 est_needed_step_err = 4e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.033174274210456e-88 estimated_step_error = 5.033174274210456e-88 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 31250 step_error = 5.65685424949238e-14 est_needed_step_err = 5.65685424949238e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.298547301388589e-83 estimated_step_error = 3.298547301388589e-83 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 15625 step_error = 8e-14 est_needed_step_err = 8e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.161744097799704e-78 estimated_step_error = 2.161744097799704e-78 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 7812.5 step_error = 1.131370849898476e-13 est_needed_step_err = 1.131370849898476e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.41673127916833e-73 estimated_step_error = 1.41673127916833e-73 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 3906.25 step_error = 1.6e-13 est_needed_step_err = 1.6e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.284829931900477e-69 estimated_step_error = 9.284829931900477e-69 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 1953.125 step_error = 2.262741699796952e-13 est_needed_step_err = 2.262741699796952e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.085089418323007e-64 estimated_step_error = 6.085089418323007e-64 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 976.5625 step_error = 3.2e-13 est_needed_step_err = 3.2e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.988164444072296e-59 estimated_step_error = 3.988164444072296e-59 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 488.28125 step_error = 4.525483399593904e-13 est_needed_step_err = 4.525483399593904e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.613998398329204e-54 estimated_step_error = 2.613998398329204e-54 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 244.140625 step_error = 6.4e-13 est_needed_step_err = 6.4e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.713522949099779e-49 estimated_step_error = 1.713522949099779e-49 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 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 min_size = 2 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 2 desired_abs_gbl_error = 2e-10 range = 1 estimated_steps = 122.0703125 step_error = 9.050966799187808e-13 est_needed_step_err = 9.050966799187808e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.123516066226922e-44 estimated_step_error = 1.123516066226922e-44 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.441 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 2 y[1] (numeric) = 2 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 6.584e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 2.01 y[1] (numeric) = 2.000313675793494 absolute error = 0.009686324206505947 relative error = 0.4819066769405945 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.99 Order of pole (three term test) = 6.107e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 2.02 y[1] (numeric) = 2.000629718946491 absolute error = 0.01937028105350835 relative error = 0.9589248046291267 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.98 Order of pole (three term test) = 2.832e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.029999999999999 y[1] (analytic) = 2.029999999999999 y[1] (numeric) = 2.000948153341497 absolute error = 0.02905184665850236 relative error = 1.431125451157752 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.97 Order of pole (three term test) = 5.253e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.039999999999999 y[1] (analytic) = 2.039999999999999 y[1] (numeric) = 2.001269003162943 absolute error = 0.03873099683705661 relative error = 1.898578276326305 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.96 Order of pole (three term test) = 2.435e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.049999999999999 y[1] (analytic) = 2.049999999999999 y[1] (numeric) = 2.001592292901778 absolute error = 0.04840770709822051 relative error = 2.361351565766855 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.95 Order of pole (three term test) = 9.028e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.059999999999999 y[1] (analytic) = 2.059999999999999 y[1] (numeric) = 2.001918047360148 absolute error = 0.05808195263985061 relative error = 2.81951226407042 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.94 Order of pole (three term test) = 1.255e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.069999999999999 y[1] (analytic) = 2.069999999999999 y[1] (numeric) = 2.002246291656145 absolute error = 0.06775370834385352 relative error = 3.273126006949448 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.93 Order of pole (three term test) = 3.876e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.079999999999998 y[1] (analytic) = 2.079999999999998 y[1] (numeric) = 2.002577051228654 absolute error = 0.07742294877134404 relative error = 3.722257152468466 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.92 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.089999999999998 y[1] (analytic) = 2.089999999999998 y[1] (numeric) = 2.002910351842282 absolute error = 0.08708964815771614 relative error = 4.166968811373982 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.91 Order of pole (three term test) = 6.653e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.099999999999998 y[1] (analytic) = 2.099999999999998 y[1] (numeric) = 2.003246219592373 absolute error = 0.09675378040762528 relative error = 4.60732287655359 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 3.08e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.109999999999998 y[1] (analytic) = 2.109999999999998 y[1] (numeric) = 2.003584680910117 absolute error = 0.1064153190898804 relative error = 5.043380051653108 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.89 Order of pole (three term test) = 8.556e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.119999999999997 y[1] (analytic) = 2.119999999999997 y[1] (numeric) = 2.003925762567753 absolute error = 0.1160742374322443 relative error = 5.475199878879455 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.88 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.129999999999997 y[1] (analytic) = 2.129999999999997 y[1] (numeric) = 2.004269491683859 absolute error = 0.1257305083161384 relative error = 5.902840766015895 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.87 Order of pole (three term test) = 4.887e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.139999999999997 y[1] (analytic) = 2.139999999999997 y[1] (numeric) = 2.004615895728743 absolute error = 0.1353841042712536 relative error = 6.326360012675409 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.86 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.149999999999997 y[1] (analytic) = 2.149999999999997 y[1] (numeric) = 2.004965002529937 absolute error = 0.1450349974700602 relative error = 6.745813835816764 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.85 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.159999999999997 y[1] (analytic) = 2.159999999999997 y[1] (numeric) = 2.005316840277777 absolute error = 0.1546831597222198 relative error = 7.161257394547224 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.84 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.169999999999996 y[1] (analytic) = 2.169999999999996 y[1] (numeric) = 2.005671437531102 absolute error = 0.1643285624688944 relative error = 7.572744814234776 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.83 Order of pole (three term test) = 3.578e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.179999999999996 y[1] (analytic) = 2.179999999999996 y[1] (numeric) = 2.006028823223046 absolute error = 0.1739711767769498 relative error = 7.980329209951843 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.82 Order of pole (three term test) = 3.308e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.189999999999996 y[1] (analytic) = 2.189999999999996 y[1] (numeric) = 2.006389026666941 absolute error = 0.1836109733330549 relative error = 8.384062709271927 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.81 Order of pole (three term test) = 3.058e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199999999999996 y[1] (analytic) = 2.199999999999996 y[1] (numeric) = 2.006752077562326 absolute error = 0.1932479224376702 relative error = 8.783996474439572 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.209999999999996 y[1] (analytic) = 2.209999999999996 y[1] (numeric) = 2.007118006001071 absolute error = 0.2028819939989246 relative error = 9.180180723933258 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.79 Order of pole (three term test) = 2.611e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.219999999999995 y[1] (analytic) = 2.219999999999995 y[1] (numeric) = 2.007486842473614 absolute error = 0.2125131575263817 relative error = 9.572664753440636 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.78 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.78 Order of pole (three term test) = 2.412e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.229999999999995 y[1] (analytic) = 2.229999999999995 y[1] (numeric) = 2.007858617875309 absolute error = 0.2221413821246858 relative error = 9.961496956263961 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 3 h = 0.01 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.77 Order of pole (three term test) = 8.912e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.239999999999995 y[1] (analytic) = 2.239999999999995 y[1] (numeric) = 2.0082333635129 absolute error = 0.2317666364870945 relative error = 10.34672484317388 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.76 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.249999999999995 y[1] (analytic) = 2.249999999999995 y[1] (numeric) = 2.00861111111111 absolute error = 0.2413888888888849 relative error = 10.72839506172824 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.75 Order of pole (three term test) = 7.598e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.259999999999994 y[1] (analytic) = 2.259999999999994 y[1] (numeric) = 2.008991892819353 absolute error = 0.2510081071806414 relative error = 11.10655341507266 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.74 Order of pole (three term test) = 3.506e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.269999999999994 y[1] (analytic) = 2.269999999999994 y[1] (numeric) = 2.00937574121858 absolute error = 0.260624258781414 relative error = 11.48124488023853 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.73 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.73 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.279999999999994 y[1] (analytic) = 2.279999999999994 y[1] (numeric) = 2.009762689328245 absolute error = 0.2702373106717491 relative error = 11.85251362595394 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.72 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.289999999999994 y[1] (analytic) = 2.289999999999994 y[1] (numeric) = 2.010152770613406 absolute error = 0.2798472293865877 relative error = 12.22040302998203 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.71 Order of pole (three term test) = 5.508e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.299999999999994 y[1] (analytic) = 2.299999999999994 y[1] (numeric) = 2.010546018991964 absolute error = 0.2894539810080299 relative error = 12.58495569600134 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 5.079e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.309999999999993 y[1] (analytic) = 2.309999999999993 y[1] (numeric) = 2.010942468842031 absolute error = 0.299057531157962 relative error = 12.94621347004168 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.69 Order of pole (three term test) = 4.683e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.319999999999993 y[1] (analytic) = 2.319999999999993 y[1] (numeric) = 2.011342155009451 absolute error = 0.3086578449905426 relative error = 13.30421745648894 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.68 Order of pole (three term test) = 4.317e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.329999999999993 y[1] (analytic) = 2.329999999999993 y[1] (numeric) = 2.011745112815448 absolute error = 0.3182548871845454 relative error = 13.65900803367152 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.67 Order of pole (three term test) = 3.979e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.339999999999993 y[1] (analytic) = 2.339999999999993 y[1] (numeric) = 2.012151378064438 absolute error = 0.327848621935555 relative error = 14.01062486904085 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.66 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.66 Order of pole (three term test) = 3.666e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.349999999999993 y[1] (analytic) = 2.349999999999993 y[1] (numeric) = 2.012560987051979 absolute error = 0.337439012948014 relative error = 14.35910693395809 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.65 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.65 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.359999999999992 y[1] (analytic) = 2.359999999999992 y[1] (numeric) = 2.012973976572876 absolute error = 0.3470260234271159 relative error = 14.70449251809818 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.64 Order of pole (three term test) = 3.11e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.369999999999992 y[1] (analytic) = 2.369999999999992 y[1] (numeric) = 2.013390383929451 absolute error = 0.356609616070541 relative error = 15.04681924348279 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.63 Order of pole (three term test) = 5.728e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.379999999999992 y[1] (analytic) = 2.379999999999992 y[1] (numeric) = 2.013810246939958 absolute error = 0.3661897530600342 relative error = 15.38612407815275 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.62 Order of pole (three term test) = 5.273e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.389999999999992 y[1] (analytic) = 2.389999999999992 y[1] (numeric) = 2.014233603947175 absolute error = 0.3757663960528164 relative error = 15.72244334949028 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.61 Order of pole (three term test) = 2.426e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999991 y[1] (analytic) = 2.399999999999991 y[1] (numeric) = 2.014660493827159 absolute error = 0.3853395061728322 relative error = 16.0558127572014 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 4.465e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.409999999999991 y[1] (analytic) = 2.409999999999991 y[1] (numeric) = 2.015090955998168 absolute error = 0.3949090440018237 relative error = 16.38626738596785 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.59 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.59 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.419999999999991 y[1] (analytic) = 2.419999999999991 y[1] (numeric) = 2.015525030429761 absolute error = 0.4044749695702303 relative error = 16.71384171777818 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.58 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.58 Order of pole (three term test) = 3.778e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.429999999999991 y[1] (analytic) = 2.429999999999991 y[1] (numeric) = 2.015962757652079 absolute error = 0.4140372423479115 relative error = 17.03856964394704 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.57 Order of pole (three term test) = 3.474e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.439999999999991 y[1] (analytic) = 2.439999999999991 y[1] (numeric) = 2.016404178765306 absolute error = 0.4235958212346844 relative error = 17.3604844768314 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.56 Order of pole (three term test) = 3.194e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.44999999999999 y[1] (analytic) = 2.44999999999999 y[1] (numeric) = 2.016849335449314 absolute error = 0.4331506645506762 relative error = 17.67961896125216 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.55 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.55 Order of pole (three term test) = 2.935e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.45999999999999 y[1] (analytic) = 2.45999999999999 y[1] (numeric) = 2.017298269973506 absolute error = 0.4427017300264846 relative error = 17.99600528562953 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.54 Order of pole (three term test) = 5.394e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.46999999999999 y[1] (analytic) = 2.46999999999999 y[1] (numeric) = 2.017751025206846 absolute error = 0.4522489747931444 relative error = 18.30967509283993 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.53 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.53 Order of pole (three term test) = 2.478e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.47999999999999 y[1] (analytic) = 2.47999999999999 y[1] (numeric) = 2.018207644628097 absolute error = 0.4617923553718923 relative error = 18.62065949080219 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.52 Order of pole (three term test) = 4.551e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.48999999999999 y[1] (analytic) = 2.48999999999999 y[1] (numeric) = 2.018668172336262 absolute error = 0.4713318276637279 relative error = 18.9289890628004 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.51 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.51 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999989 y[1] (analytic) = 2.499999999999989 y[1] (numeric) = 2.019132653061222 absolute error = 0.480867346938767 relative error = 19.23469387755076 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 7.672e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.509999999999989 y[1] (analytic) = 2.509999999999989 y[1] (numeric) = 2.019601132174611 absolute error = 0.4903988678253786 relative error = 19.53780349901915 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.49 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.49 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.519999999999989 y[1] (analytic) = 2.519999999999989 y[1] (numeric) = 2.020073655700883 absolute error = 0.499926344299106 relative error = 19.83834699599635 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.48 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.48 Order of pole (three term test) = 3.23e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.529999999999989 y[1] (analytic) = 2.529999999999989 y[1] (numeric) = 2.020550270328628 absolute error = 0.5094497296713612 relative error = 20.13635295143729 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.47 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.47 Order of pole (three term test) = 5.926e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.539999999999988 y[1] (analytic) = 2.539999999999988 y[1] (numeric) = 2.021031023422097 absolute error = 0.518968976577892 relative error = 20.43184947157064 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.46 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.46 Order of pole (three term test) = 2.717e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.549999999999988 y[1] (analytic) = 2.549999999999988 y[1] (numeric) = 2.021515963032974 absolute error = 0.5284840369670145 relative error = 20.72486419478498 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.45 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.45 Order of pole (three term test) = 2.491e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.559999999999988 y[1] (analytic) = 2.559999999999988 y[1] (numeric) = 2.022005137912382 absolute error = 0.5379948620876056 relative error = 21.01542430029719 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.44 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.44 Order of pole (three term test) = 4.567e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.569999999999988 y[1] (analytic) = 2.569999999999988 y[1] (numeric) = 2.022498597523138 absolute error = 0.5475014024768496 relative error = 21.30355651660904 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.43 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.43 Order of pole (three term test) = 4.185e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.579999999999988 y[1] (analytic) = 2.579999999999988 y[1] (numeric) = 2.022996392052252 absolute error = 0.5570036079477352 relative error = 21.58928712975728 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.42 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.42 Order of pole (three term test) = 3.834e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.589999999999987 y[1] (analytic) = 2.589999999999987 y[1] (numeric) = 2.023498572423695 absolute error = 0.5665014275762927 relative error = 21.87264199136276 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.41 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.41 Order of pole (three term test) = 3.511e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999987 y[1] (analytic) = 2.599999999999987 y[1] (numeric) = 2.024005190311415 absolute error = 0.5759948096885719 relative error = 22.15364652648364 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 3.215e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.609999999999987 y[1] (analytic) = 2.609999999999987 y[1] (numeric) = 2.024516298152641 absolute error = 0.5854837018473464 relative error = 22.43232574127775 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.39 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.39 Order of pole (three term test) = 2.943e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.619999999999987 y[1] (analytic) = 2.619999999999987 y[1] (numeric) = 2.02503194916144 absolute error = 0.5949680508385464 relative error = 22.70870423047899 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.38 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.38 Order of pole (three term test) = 2.694e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.629999999999987 y[1] (analytic) = 2.629999999999987 y[1] (numeric) = 2.025552197342581 absolute error = 0.6044478026574054 relative error = 22.98280618469234 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.37 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.37 Order of pole (three term test) = 2.465e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.639999999999986 y[1] (analytic) = 2.639999999999986 y[1] (numeric) = 2.026077097505665 absolute error = 0.6139229024943211 relative error = 23.25465539751228 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.36 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.36 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.649999999999986 y[1] (analytic) = 2.649999999999986 y[1] (numeric) = 2.026606705279569 absolute error = 0.6233932947204175 relative error = 23.52427527246871 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.35 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.35 Order of pole (three term test) = 8.246e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.659999999999986 y[1] (analytic) = 2.659999999999986 y[1] (numeric) = 2.027141077127179 absolute error = 0.6328589228728068 relative error = 23.79168882980489 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.34 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.34 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.669999999999986 y[1] (analytic) = 2.669999999999986 y[1] (numeric) = 2.027680270360447 absolute error = 0.6423197296395391 relative error = 24.05691871309148 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.33 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.33 Order of pole (three term test) = 3.445e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.679999999999986 y[1] (analytic) = 2.679999999999986 y[1] (numeric) = 2.028224343155752 absolute error = 0.6517756568442339 relative error = 24.3199871956805 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.32 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.32 Order of pole (three term test) = 3.148e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.689999999999985 y[1] (analytic) = 2.689999999999985 y[1] (numeric) = 2.028773354569597 absolute error = 0.6612266454303888 relative error = 24.58091618700344 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.31 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.31 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999985 y[1] (analytic) = 2.699999999999985 y[1] (numeric) = 2.029327364554633 absolute error = 0.670672635445352 relative error = 24.83972723871688 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 2.626e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.709999999999985 y[1] (analytic) = 2.709999999999985 y[1] (numeric) = 2.029886433976031 absolute error = 0.6801135660239543 relative error = 25.09644155069956 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.29 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.29 Order of pole (three term test) = 2.397e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.719999999999985 y[1] (analytic) = 2.719999999999985 y[1] (numeric) = 2.030450624628193 absolute error = 0.6895493753717918 relative error = 25.35107997690425 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.28 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.28 Order of pole (three term test) = 4.376e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.729999999999984 y[1] (analytic) = 2.729999999999984 y[1] (numeric) = 2.031019999251835 absolute error = 0.6989800007481493 relative error = 25.60366303106789 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.27 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.27 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.739999999999984 y[1] (analytic) = 2.739999999999984 y[1] (numeric) = 2.031594621551427 absolute error = 0.7084053784485569 relative error = 25.85421089228325 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.26 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.26 Order of pole (three term test) = 3.643e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.749999999999984 y[1] (analytic) = 2.749999999999984 y[1] (numeric) = 2.032174556213013 absolute error = 0.7178254437869711 relative error = 26.10274341043547 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.25 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.25 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.759999999999984 y[1] (analytic) = 2.759999999999984 y[1] (numeric) = 2.032759868922415 absolute error = 0.7272401310775685 relative error = 26.34928011150626 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.24 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.24 Order of pole (three term test) = 3.029e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.769999999999984 y[1] (analytic) = 2.769999999999984 y[1] (numeric) = 2.033350626383838 absolute error = 0.7366493736161455 relative error = 26.59384020274909 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.23 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.23 Order of pole (three term test) = 2.76e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.779999999999983 y[1] (analytic) = 2.779999999999983 y[1] (numeric) = 2.03394689633887 absolute error = 0.7460531036611129 relative error = 26.83644257773803 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.22 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.22 Order of pole (three term test) = 2.515e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.789999999999983 y[1] (analytic) = 2.789999999999983 y[1] (numeric) = 2.034548747585907 absolute error = 0.7554512524140762 relative error = 27.07710582129322 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.21 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.21 Order of pole (three term test) = 9.165e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999983 y[1] (analytic) = 2.799999999999983 y[1] (numeric) = 2.035156249999994 absolute error = 0.7648437499999887 relative error = 27.31584821428548 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 4.173e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.809999999999983 y[1] (analytic) = 2.809999999999983 y[1] (numeric) = 2.035769474553113 absolute error = 0.7742305254468693 relative error = 27.55268773832292 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.19 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.19 Order of pole (three term test) = 3.799e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.819999999999983 y[1] (analytic) = 2.819999999999983 y[1] (numeric) = 2.036388493334909 absolute error = 0.7836115066650735 relative error = 27.78764208032193 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.18 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.18 Order of pole (three term test) = 6.915e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.829999999999982 y[1] (analytic) = 2.829999999999982 y[1] (numeric) = 2.037013379573877 absolute error = 0.7929866204261051 relative error = 28.02072863696502 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.17 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.17 Order of pole (three term test) = 6.291e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.839999999999982 y[1] (analytic) = 2.839999999999982 y[1] (numeric) = 2.037644207659022 absolute error = 0.8023557923409599 relative error = 28.25196451904806 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.16 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.16 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.849999999999982 y[1] (analytic) = 2.849999999999982 y[1] (numeric) = 2.038281053161998 absolute error = 0.8117189468379835 relative error = 28.4813665557189 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.15 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.15 Order of pole (three term test) = 5.203e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.859999999999982 y[1] (analytic) = 2.859999999999982 y[1] (numeric) = 2.038923992859743 absolute error = 0.8210760071402383 relative error = 28.70895129860991 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.14 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.14 Order of pole (three term test) = 4.73e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.869999999999981 y[1] (analytic) = 2.869999999999981 y[1] (numeric) = 2.03957310475762 absolute error = 0.8304268952423617 relative error = 28.93473502586645 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.13 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.13 Order of pole (three term test) = 4.298e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.879999999999981 y[1] (analytic) = 2.879999999999981 y[1] (numeric) = 2.040228468113076 absolute error = 0.8397715318869055 relative error = 29.1587337460733 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.12 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.12 Order of pole (three term test) = 3.905e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.889999999999981 y[1] (analytic) = 2.889999999999981 y[1] (numeric) = 2.04089016345984 absolute error = 0.8491098365401406 relative error = 29.38096320208118 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.11 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.11 Order of pole (three term test) = 7.093e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999981 y[1] (analytic) = 2.899999999999981 y[1] (numeric) = 2.041558272632666 absolute error = 0.8584417273673148 relative error = 29.60143887473519 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.909999999999981 y[1] (analytic) = 2.909999999999981 y[1] (numeric) = 2.042232878792631 absolute error = 0.8677671212073497 relative error = 29.82017598650706 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.09 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.09 Order of pole (three term test) = 2.922e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.91999999999998 y[1] (analytic) = 2.91999999999998 y[1] (numeric) = 2.042914066453019 absolute error = 0.8770859335469616 relative error = 30.03718950503313 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.08 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.08 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.92999999999998 y[1] (analytic) = 2.92999999999998 y[1] (numeric) = 2.04360192150579 absolute error = 0.8863980784941905 relative error = 30.25249414655961 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.07 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.07 Order of pole (three term test) = 2.405e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.93999999999998 y[1] (analytic) = 2.93999999999998 y[1] (numeric) = 2.044296531248656 absolute error = 0.8957034687513241 relative error = 30.46610437929695 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.06 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.06 Order of pole (three term test) = 4.362e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.94999999999998 y[1] (analytic) = 2.94999999999998 y[1] (numeric) = 2.044997984412783 absolute error = 0.905002015587197 relative error = 30.67803442668485 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.05 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.05 Order of pole (three term test) = 3.954e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95999999999998 y[1] (analytic) = 2.95999999999998 y[1] (numeric) = 2.045706371191126 absolute error = 0.9142936288088537 relative error = 30.88829827056959 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.04 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.04 Order of pole (three term test) = 7.165e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.969999999999979 y[1] (analytic) = 2.969999999999979 y[1] (numeric) = 2.046421783267426 absolute error = 0.9235782167325537 relative error = 31.09690965429495 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.03 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.03 Order of pole (three term test) = 3.245e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.979999999999979 y[1] (analytic) = 2.979999999999979 y[1] (numeric) = 2.047144313845874 absolute error = 0.9328556861541055 relative error = 31.30388208570846 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.02 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.02 Order of pole (three term test) = 2.939e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.989999999999979 y[1] (analytic) = 2.989999999999979 y[1] (numeric) = 2.047874057681472 absolute error = 0.9421259423185071 relative error = 31.50922884008407 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3.01 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.01 Order of pole (three term test) = 2.661e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999979 y[1] (analytic) = 2.999999999999979 y[1] (numeric) = 2.0486111111111 absolute error = 0.9513888888888786 relative error = 31.71296296296284 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 2 h = 0.01 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 3 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 7.224e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %