##############ECHO OF PROBLEM################# ##############temp/tan_sqrt_linpostode.ode################# diff ( y , x , 1 ) = tan(sqrt(2.0*x + 3.0)); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(0.0); } /* 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 = 4.9 estimated_steps = 4900000.000000001 step_error = 2.040816326530612e-17 est_needed_step_err = 2.040816326530612e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.322522384818648e-146 estimated_step_error = 1.322522384818648e-146 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 = 8.875285819891103e-139 estimated_step_error = 8.875285819891103e-139 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 = 5.956087832591041e-131 estimated_step_error = 5.956087832591041e-131 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 = 3.997041867794536e-123 estimated_step_error = 3.997041867794536e-123 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 = 2.682341185000824e-115 estimated_step_error = 2.682341185000824e-115 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 = 1.800050841493786e-107 estimated_step_error = 1.800050841493786e-107 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 = 1.207942864407096e-99 estimated_step_error = 1.207942864407096e-99 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 = 8.105685510359236e-92 estimated_step_error = 8.105685510359236e-92 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 = 5.438718559519279e-84 estimated_step_error = 5.438718559519279e-84 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 = 3.648634896522908e-76 estimated_step_error = 3.648634896522908e-76 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 = 2.446911783013983e-68 estimated_step_error = 2.446911783013983e-68 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 = 1.639890424531904e-60 estimated_step_error = 1.639890424531904e-60 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 = 1.097565316877603e-52 estimated_step_error = 1.097565316877603e-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 = 7.326411095212077e-45 estimated_step_error = 7.326411095212077e-45 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 = 4.86488978740921e-37 estimated_step_error = 4.86488978740921e-37 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 = 3.197595714309029e-29 estimated_step_error = 3.197595714309029e-29 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 = 2.061944023239766e-21 estimated_step_error = 2.061944023239766e-21 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 = 1.28784500492066e-13 estimated_step_error = 1.28784500492066e-13 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0 y[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3663 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (analytic) = 0 y[1] (numeric) = -0.4004520229550599 absolute error = 0.4004520229550599 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (analytic) = 0 y[1] (numeric) = -0.7246470759807396 absolute error = 0.7246470759807396 relative error = -1 % Correct digits = -1 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5663 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 0.9276 Order of pole (six term test) = 6.151e-11 TOP MAIN SOLVE Loop x[1] = 0.4855259453769447 y[1] (analytic) = 0 y[1] (numeric) = -1.199154222275023 absolute error = 1.199154222275023 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7518 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.268 Order of pole (six term test) = 2.067e-10 TOP MAIN SOLVE Loop x[1] = 0.578288918065417 y[1] (analytic) = 0 y[1] (numeric) = -1.393825605094335 absolute error = 1.393825605094335 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8446 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.372 Order of pole (six term test) = 2.019e-10 TOP MAIN SOLVE Loop x[1] = 0.6710518907538894 y[1] (analytic) = 0 y[1] (numeric) = -1.567638080462661 absolute error = 1.567638080462661 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9374 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.48 Order of pole (six term test) = 1.999e-09 TOP MAIN SOLVE Loop x[1] = 0.7638148634423617 y[1] (analytic) = 0 y[1] (numeric) = -1.724229312667807 absolute error = 1.724229312667807 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.584 Order of pole (six term test) = 5.397e-09 TOP MAIN SOLVE Loop x[1] = 0.856577836130834 y[1] (analytic) = 0 y[1] (numeric) = -1.86629883716951 absolute error = 1.86629883716951 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.123 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.688 Order of pole (six term test) = 1.56e-08 TOP MAIN SOLVE Loop x[1] = 0.9493408088193064 y[1] (analytic) = 0 y[1] (numeric) = -1.995905892914796 absolute error = 1.995905892914796 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.216 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.791 Order of pole (six term test) = 4.007e-08 TOP MAIN SOLVE Loop x[1] = 1.042103781507779 y[1] (analytic) = 0 y[1] (numeric) = -2.114657502502721 absolute error = 2.114657502502721 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.308 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.894 Order of pole (six term test) = 9.52e-08 TOP MAIN SOLVE Loop x[1] = 1.134866754196251 y[1] (analytic) = 0 y[1] (numeric) = -2.223832035924893 absolute error = 2.223832035924893 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.401 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 1.996 Order of pole (six term test) = 2.096e-07 TOP MAIN SOLVE Loop x[1] = 1.227629726884724 y[1] (analytic) = 0 y[1] (numeric) = -2.324463129802174 absolute error = 2.324463129802174 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.494 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.098 Order of pole (six term test) = 4.274e-07 TOP MAIN SOLVE Loop x[1] = 1.320392699573196 y[1] (analytic) = 0 y[1] (numeric) = -2.417398317442493 absolute error = 2.417398317442493 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.587 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.2 Order of pole (six term test) = 8.217e-07 TOP MAIN SOLVE Loop x[1] = 1.413155672261668 y[1] (analytic) = 0 y[1] (numeric) = -2.503341002579771 absolute error = 2.503341002579771 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.679 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.301 Order of pole (six term test) = 1.489e-06 TOP MAIN SOLVE Loop x[1] = 1.505918644950141 y[1] (analytic) = 0 y[1] (numeric) = -2.582881154586358 absolute error = 2.582881154586358 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.772 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.402 Order of pole (six term test) = 2.57e-06 TOP MAIN SOLVE Loop x[1] = 1.691444590327086 y[1] (analytic) = 0 y[1] (numeric) = -2.724678244565531 absolute error = 2.724678244565531 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.958 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.545 Order of pole (six term test) = 6.758e-06 TOP MAIN SOLVE Loop x[1] = 1.784207563015558 y[1] (analytic) = 0 y[1] (numeric) = -2.787727599691923 absolute error = 2.787727599691923 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.05 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.47 Order of pole (six term test) = 1.036e-05 TOP MAIN SOLVE Loop x[1] = 1.876970535704031 y[1] (analytic) = 0 y[1] (numeric) = -2.845982952036881 absolute error = 2.845982952036881 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.143 Order of pole (three term test) = 28 Radius of convergence (six term test) for eq 1 = 2.219 Order of pole (six term test) = 1.525e-05 TOP MAIN SOLVE Loop x[1] = 1.969733508392503 y[1] (analytic) = 0 y[1] (numeric) = -2.899719647077438 absolute error = 2.899719647077438 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.236 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.062496481080975 y[1] (analytic) = 0 y[1] (numeric) = -2.949178186908741 absolute error = 2.949178186908741 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.329 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.155259453769448 y[1] (analytic) = 0 y[1] (numeric) = -2.994569475320384 absolute error = 2.994569475320384 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.421 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.24802242645792 y[1] (analytic) = 0 y[1] (numeric) = -3.036079075589552 absolute error = 3.036079075589552 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.514 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.340785399146393 y[1] (analytic) = 0 y[1] (numeric) = -3.073870694543992 absolute error = 3.073870694543992 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.607 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.433548371834865 y[1] (analytic) = 0 y[1] (numeric) = -3.108089054179677 absolute error = 3.108089054179677 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.699 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.526311344523338 y[1] (analytic) = 0 y[1] (numeric) = -3.138862273970763 absolute error = 3.138862273970763 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.792 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.61907431721181 y[1] (analytic) = 0 y[1] (numeric) = -3.166303858827765 absolute error = 3.166303858827765 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.885 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.711837289900282 y[1] (analytic) = 0 y[1] (numeric) = -3.190514366604205 absolute error = 3.190514366604205 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.977 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.804600262588755 y[1] (analytic) = 0 y[1] (numeric) = -3.211582813154103 absolute error = 3.211582813154103 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.069 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9901262079657 y[1] (analytic) = 0 y[1] (numeric) = -3.244598826905362 absolute error = 3.244598826905362 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.251 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.082889180654172 y[1] (analytic) = 0 y[1] (numeric) = -3.256676541429572 absolute error = 3.256676541429572 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.339 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.175652153342645 y[1] (analytic) = 0 y[1] (numeric) = -3.265874077817793 absolute error = 3.265874077817793 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.423 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.268415126031117 y[1] (analytic) = 0 y[1] (numeric) = -3.272237375671291 absolute error = 3.272237375671291 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.496 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.36117809871959 y[1] (analytic) = 0 y[1] (numeric) = -3.27580577122859 absolute error = 3.27580577122859 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.552 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.453941071408062 y[1] (analytic) = 0 y[1] (numeric) = -3.276612448261528 absolute error = 3.276612448261528 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.573 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.546704044096535 y[1] (analytic) = 0 y[1] (numeric) = -3.274684819848333 absolute error = 3.274684819848333 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.531 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.639467016785007 y[1] (analytic) = 0 y[1] (numeric) = -3.270044849587978 absolute error = 3.270044849587978 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.383 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.732229989473479 y[1] (analytic) = 0 y[1] (numeric) = -3.26270931927849 absolute error = 3.26270931927849 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.081 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.824992962161952 y[1] (analytic) = 0 y[1] (numeric) = -3.252690048804743 absolute error = 3.252690048804743 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 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] = 3.917755934850424 y[1] (analytic) = 0 y[1] (numeric) = -3.239994072912687 absolute error = 3.239994072912687 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 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] = 4.010518907538897 y[1] (analytic) = 0 y[1] (numeric) = -3.224623778643101 absolute error = 3.224623778643101 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 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] = 4.103281880227369 y[1] (analytic) = 0 y[1] (numeric) = -3.206577006423742 absolute error = 3.206577006423742 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 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] = 4.288807825604314 y[1] (analytic) = 0 y[1] (numeric) = -3.162423026957638 absolute error = 3.162423026957638 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2879 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.381570798292787 y[1] (analytic) = 0 y[1] (numeric) = -3.136289210968704 absolute error = 3.136289210968704 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1395 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.474333770981259 y[1] (analytic) = 0 y[1] (numeric) = -3.107425676574425 absolute error = 3.107425676574425 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03504 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.567096743669731 y[1] (analytic) = 0 y[1] (numeric) = -3.07580790663719 absolute error = 3.07580790663719 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 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] = 4.659859716358204 y[1] (analytic) = 0 y[1] (numeric) = -3.041406772321617 absolute error = 3.041406772321617 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.107 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.752622689046676 y[1] (analytic) = 0 y[1] (numeric) = -3.004188414934831 absolute error = 3.004188414934831 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.317 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.845385661735149 y[1] (analytic) = 0 y[1] (numeric) = -2.964114095674692 absolute error = 2.964114095674692 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.159 Order of pole (ratio test) = 0 Radius of convergence (three term test) for eq 1 = 0.6302 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.938148634423621 y[1] (analytic) = 0 y[1] (numeric) = -2.921140011721345 absolute error = 2.921140011721345 relative error = -1 % Correct digits = -1 h = 0.09276297268847235 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 4.474 Order of pole (ratio test) = 0 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan(sqrt(2.0*x + 3.0)); Iterations = 53 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102.5 %