##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin(x); ! // BEGIN FIRST INPUT BLOCK // # Comment 1 Digits=32; max_terms=20; // # Comment 2 ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK // # Comment 3 x_start=0.1; x_end=1.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; // # Comment 4 // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK // # Comment 5 double exact_soln_y (double x) { // # Comment 6 return(2.0 - cos(x)); // # Comment 7 } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 900000.0000000001 step_error = 1.111111111111111e-16 est_needed_step_err = 1.111111111111111e-16 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.75559983954348e-110 estimated_step_error = 4.75559983954348e-110 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.116629901645971e-105 estimated_step_error = 3.116629901645971e-105 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.042514560287681e-100 estimated_step_error = 2.042514560287681e-100 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.338582326429351e-95 estimated_step_error = 1.338582326429351e-95 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.772532927382661e-91 estimated_step_error = 8.772532927382661e-91 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.749166907831384e-86 estimated_step_error = 5.749166907831384e-86 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.767773668906066e-81 estimated_step_error = 3.767773668906066e-81 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.469247685274195e-76 estimated_step_error = 2.469247685274195e-76 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.618245551695101e-71 estimated_step_error = 1.618245551695101e-71 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.060532603396255e-66 estimated_step_error = 1.060532603396255e-66 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.950295963764387e-62 estimated_step_error = 6.950295963764387e-62 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.554932186727369e-57 estimated_step_error = 4.554932186727369e-57 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.985102285959332e-52 estimated_step_error = 2.985102285959332e-52 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.95629290665759e-47 estimated_step_error = 1.95629290665759e-47 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.282044913797216e-42 estimated_step_error = 1.282044913797216e-42 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.401597766100562e-38 estimated_step_error = 8.401597766100562e-38 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.505524136524434e-33 estimated_step_error = 5.505524136524434e-33 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.607364371667479e-28 estimated_step_error = 3.607364371667479e-28 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.004995834721974 y[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.11 y[1] (analytic) = 1.006043902043303 y[1] (numeric) = 1.006043902043303 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 1.007191364146134 y[1] (numeric) = 1.007191364146134 absolute error = 2.220446049250313e-16 relative error = 2.204592025203413e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.13 y[1] (analytic) = 1.008438106285212 y[1] (numeric) = 1.008438106285212 absolute error = 2.220446049250313e-16 relative error = 2.201866465984492e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.14 y[1] (analytic) = 1.009784003787363 y[1] (numeric) = 1.009784003787363 absolute error = 2.220446049250313e-16 relative error = 2.198931693235544e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 1.011228922063958 y[1] (numeric) = 1.011228922063958 absolute error = 4.440892098500626e-16 relative error = 4.391579395728311e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 1.012772716624373 y[1] (numeric) = 1.012772716624373 absolute error = 4.440892098500626e-16 relative error = 4.384885202380218e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 1.014415233090439 y[1] (numeric) = 1.01441523309044 absolute error = 4.440892098500626e-16 relative error = 4.377785302938863e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 1.016156307211879 y[1] (numeric) = 1.016156307211879 absolute error = 2.220446049250313e-16 relative error = 2.185142220238493e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y[1] (analytic) = 1.01799576488273 y[1] (numeric) = 1.01799576488273 absolute error = 4.440892098500626e-16 relative error = 4.362387596978073e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y[1] (analytic) = 1.019933422158758 y[1] (numeric) = 1.019933422158759 absolute error = 4.440892098500626e-16 relative error = 4.354099985370787e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (analytic) = 1.021969085275852 y[1] (numeric) = 1.021969085275852 absolute error = 4.440892098500626e-16 relative error = 4.345427041270952e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y[1] (analytic) = 1.024102550669395 y[1] (numeric) = 1.024102550669395 absolute error = 4.440892098500626e-16 relative error = 4.336374414454764e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 1.026333604994625 y[1] (numeric) = 1.026333604994626 absolute error = 4.440892098500626e-16 relative error = 4.326947960087386e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y[1] (analytic) = 1.02866202514797 y[1] (numeric) = 1.028662025147971 absolute error = 6.661338147750939e-16 relative error = 6.475730594597116e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y[1] (analytic) = 1.031087578289355 y[1] (numeric) = 1.031087578289356 absolute error = 6.661338147750939e-16 relative error = 6.460496943239831e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y[1] (analytic) = 1.033610021865487 y[1] (numeric) = 1.033610021865487 absolute error = 4.440892098500626e-16 relative error = 4.296487073998746e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y[1] (analytic) = 1.03622910363411 y[1] (numeric) = 1.03622910363411 absolute error = 4.440892098500626e-16 relative error = 4.285627650223475e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 1.038944561689229 y[1] (numeric) = 1.03894456168923 absolute error = 6.661338147750939e-16 relative error = 6.411639651802221e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y[1] (analytic) = 1.041756124487303 y[1] (numeric) = 1.041756124487303 absolute error = 6.661338147750939e-16 relative error = 6.394335479457149e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y[1] (analytic) = 1.044663510874394 y[1] (numeric) = 1.044663510874395 absolute error = 6.661338147750939e-16 relative error = 6.376539506175851e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y[1] (analytic) = 1.047666430114287 y[1] (numeric) = 1.047666430114287 absolute error = 6.661338147750939e-16 relative error = 6.358262473890926e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y[1] (analytic) = 1.050764581917559 y[1] (numeric) = 1.05076458191756 absolute error = 4.440892098500626e-16 relative error = 4.226343535862583e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (analytic) = 1.053957656471613 y[1] (numeric) = 1.053957656471614 absolute error = 4.440892098500626e-16 relative error = 4.213539387690036e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y[1] (analytic) = 1.057245334471654 y[1] (numeric) = 1.057245334471654 absolute error = 4.440892098500626e-16 relative error = 4.200436694970057e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y[1] (analytic) = 1.060627287152621 y[1] (numeric) = 1.060627287152622 absolute error = 4.440892098500626e-16 relative error = 4.187043037920252e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 1.064103176322065 y[1] (numeric) = 1.064103176322066 absolute error = 4.440892098500626e-16 relative error = 4.173366077009557e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y[1] (analytic) = 1.067672654393966 y[1] (numeric) = 1.067672654393966 absolute error = 4.440892098500626e-16 relative error = 4.159413543303096e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y[1] (analytic) = 1.07133536442349 y[1] (numeric) = 1.07133536442349 absolute error = 4.440892098500626e-16 relative error = 4.145193228910512e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y[1] (analytic) = 1.075090940142687 y[1] (numeric) = 1.075090940142687 absolute error = 2.220446049250313e-16 relative error = 2.065356488778162e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y[1] (analytic) = 1.078939005997115 y[1] (numeric) = 1.078939005997115 absolute error = 2.220446049250313e-16 relative error = 2.057990337644953e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (analytic) = 1.082879177183395 y[1] (numeric) = 1.082879177183395 absolute error = 2.220446049250313e-16 relative error = 2.050502120675889e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y[1] (analytic) = 1.086911059687692 y[1] (numeric) = 1.086911059687692 absolute error = 2.220446049250313e-16 relative error = 2.042895809605918e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (analytic) = 1.091034250325115 y[1] (numeric) = 1.091034250325115 absolute error = 2.220446049250313e-16 relative error = 2.035175383897112e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y[1] (analytic) = 1.095248336780037 y[1] (numeric) = 1.095248336780037 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (analytic) = 1.099552897647323 y[1] (numeric) = 1.099552897647323 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (analytic) = 1.103947502474475 y[1] (numeric) = 1.103947502474475 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 1.108431711804671 y[1] (numeric) = 1.108431711804671 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y[1] (analytic) = 1.113005077220716 y[1] (numeric) = 1.113005077220716 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 1.117667141389879 y[1] (numeric) = 1.117667141389878 absolute error = 2.220446049250313e-16 relative error = 1.986679188303836e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (analytic) = 1.122417438109627 y[1] (numeric) = 1.122417438109627 absolute error = 2.220446049250313e-16 relative error = 1.978271161743515e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (analytic) = 1.127255492354249 y[1] (numeric) = 1.127255492354249 absolute error = 2.220446049250313e-16 relative error = 1.969780643616967e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (analytic) = 1.13218082032235 y[1] (numeric) = 1.13218082032235 absolute error = 2.220446049250313e-16 relative error = 1.961211503846282e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (analytic) = 1.137192929485239 y[1] (numeric) = 1.137192929485239 absolute error = 2.220446049250313e-16 relative error = 1.952567582578462e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (analytic) = 1.142291318636176 y[1] (numeric) = 1.142291318636176 absolute error = 2.220446049250313e-16 relative error = 1.943852687159862e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y[1] (analytic) = 1.147475477940495 y[1] (numeric) = 1.147475477940494 absolute error = 2.220446049250313e-16 relative error = 1.935070589251808e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (analytic) = 1.152744888986584 y[1] (numeric) = 1.152744888986584 absolute error = 2.220446049250313e-16 relative error = 1.926225022088261e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y[1] (analytic) = 1.158099024837731 y[1] (numeric) = 1.158099024837731 absolute error = 2.220446049250313e-16 relative error = 1.917319677875935e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (analytic) = 1.163537350084813 y[1] (numeric) = 1.163537350084813 absolute error = 2.220446049250313e-16 relative error = 1.908358205336906e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y[1] (analytic) = 1.169059320899837 y[1] (numeric) = 1.169059320899836 absolute error = 4.440892098500626e-16 relative error = 3.798688414786708e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y[1] (analytic) = 1.174664385090322 y[1] (numeric) = 1.174664385090322 absolute error = 4.440892098500626e-16 relative error = 3.780562477987411e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y[1] (analytic) = 1.180351982154521 y[1] (numeric) = 1.18035198215452 absolute error = 4.440892098500626e-16 relative error = 3.76234561015823e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (analytic) = 1.186121543337466 y[1] (numeric) = 1.186121543337466 absolute error = 4.440892098500626e-16 relative error = 3.744044717377785e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y[1] (analytic) = 1.191972491687848 y[1] (numeric) = 1.191972491687848 absolute error = 4.440892098500626e-16 relative error = 3.725666598406366e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (analytic) = 1.197904242115708 y[1] (numeric) = 1.197904242115707 absolute error = 2.220446049250313e-16 relative error = 1.853608970720914e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.445 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (analytic) = 1.203916201450944 y[1] (numeric) = 1.203916201450944 absolute error = 2.220446049250313e-16 relative error = 1.844352660570777e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.602 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (analytic) = 1.210007768502635 y[1] (numeric) = 1.210007768502635 absolute error = 2.220446049250313e-16 relative error = 1.835067597952763e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.761 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (analytic) = 1.216178334119151 y[1] (numeric) = 1.216178334119151 absolute error = 2.220446049250313e-16 relative error = 1.82575695270754e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.923 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (analytic) = 1.222427281249072 y[1] (numeric) = 1.222427281249072 absolute error = 2.220446049250313e-16 relative error = 1.816423834210791e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.087 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (analytic) = 1.228753985002894 y[1] (numeric) = 1.228753985002893 absolute error = 2.220446049250313e-16 relative error = 1.807071290389414e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.253 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 1.235157812715512 y[1] (numeric) = 1.235157812715512 absolute error = 2.220446049250313e-16 relative error = 1.797702306856345e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.423 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (analytic) = 1.241638124009492 y[1] (numeric) = 1.241638124009492 absolute error = 4.440892098500626e-16 relative error = 3.576639612321275e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.595 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (analytic) = 1.248194270859105 y[1] (numeric) = 1.248194270859105 absolute error = 4.440892098500626e-16 relative error = 3.557853294298535e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.771 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (analytic) = 1.25482559765513 y[1] (numeric) = 1.254825597655129 absolute error = 4.440892098500626e-16 relative error = 3.53905124887414e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.949 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (analytic) = 1.261531441270412 y[1] (numeric) = 1.261531441270412 absolute error = 4.440892098500626e-16 relative error = 3.520238935962207e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.131 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (analytic) = 1.268311131126179 y[1] (numeric) = 1.268311131126179 absolute error = 4.440892098500626e-16 relative error = 3.501421685511344e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.316 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (analytic) = 1.275163989259095 y[1] (numeric) = 1.275163989259095 absolute error = 4.440892098500626e-16 relative error = 3.482604697048342e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.469 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (analytic) = 1.282089330389057 y[1] (numeric) = 1.282089330389057 absolute error = 4.440892098500626e-16 relative error = 3.463793039407803e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.282 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (analytic) = 1.289086461987723 y[1] (numeric) = 1.289086461987723 absolute error = 4.440892098500626e-16 relative error = 3.444991650639893e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 9.098 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (analytic) = 1.296154684347764 y[1] (numeric) = 1.296154684347764 absolute error = 2.220446049250313e-16 relative error = 1.713102669044212e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.918 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 1.303293290652835 y[1] (numeric) = 1.303293290652835 absolute error = 2.220446049250313e-16 relative error = 1.703719389315712e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.741 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (analytic) = 1.310501567048253 y[1] (numeric) = 1.310501567048253 absolute error = 2.220446049250313e-16 relative error = 1.694348259538216e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.568 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (analytic) = 1.317778792712387 y[1] (numeric) = 1.317778792712387 absolute error = 2.220446049250313e-16 relative error = 1.684991488351368e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.398 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (analytic) = 1.325124239928733 y[1] (numeric) = 1.325124239928733 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.231 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (analytic) = 1.332537174158692 y[1] (numeric) = 1.332537174158692 absolute error = 2.220446049250313e-16 relative error = 1.666329534597944e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 8.067 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (analytic) = 1.340016854115018 y[1] (numeric) = 1.340016854115018 absolute error = 2.220446049250313e-16 relative error = 1.657028448882274e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.906 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (analytic) = 1.347562531835949 y[1] (numeric) = 1.347562531835949 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.748 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (analytic) = 1.355173452759999 y[1] (numeric) = 1.355173452759999 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.593 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (analytic) = 1.36284885580142 y[1] (numeric) = 1.36284885580142 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (analytic) = 1.370587973426304 y[1] (numeric) = 1.370587973426304 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (analytic) = 1.378390031729336 y[1] (numeric) = 1.378390031729336 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 7.142 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (analytic) = 1.386254250511189 y[1] (numeric) = 1.386254250511189 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.996 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (analytic) = 1.394179843356538 y[1] (numeric) = 1.394179843356538 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.853 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (analytic) = 1.402166017712702 y[1] (numeric) = 1.402166017712702 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 6.712 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (analytic) = 1.410211974968902 y[1] (numeric) = 1.410211974968902 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (analytic) = 1.418316910536117 y[1] (numeric) = 1.418316910536117 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y[1] (analytic) = 1.426480013927544 y[1] (numeric) = 1.426480013927544 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (analytic) = 1.434700468839646 y[1] (numeric) = 1.434700468839646 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y[1] (analytic) = 1.442977453233783 y[1] (numeric) = 1.442977453233783 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y[1] (analytic) = 1.451310139418413 y[1] (numeric) = 1.451310139418413 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin(x); Iterations = 90 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 101.1 %