##############ECHO OF PROBLEM################# ##############temp/div_sin_cpostode.ode################# diff ( y , x , 1 ) = sin(x) / 2.0; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=-5.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_display_interval=0.1; glob_max_minutes=10; /* 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(-cos(x)/2.0); } /* 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 = 10 estimated_steps = 10000000 step_error = 1e-17 est_needed_step_err = 1e-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 = 3.516838255302393e-184 estimated_step_error = 3.516838255302393e-184 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 = 2.360110054102919e-176 estimated_step_error = 2.360110054102919e-176 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 = 1.583842848154327e-168 estimated_step_error = 1.583842848154327e-168 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 = 1.06289867678258e-160 estimated_step_error = 1.06289867678258e-160 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 = 7.13298870227191e-153 estimated_step_error = 7.13298870227191e-153 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 = 4.78686289264721e-145 estimated_step_error = 4.78686289264721e-145 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 = 3.212402873159669e-137 estimated_step_error = 3.212402873159669e-137 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 = 2.155798437918138e-129 estimated_step_error = 2.155798437918138e-129 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 = 1.446720248932906e-121 estimated_step_error = 1.446720248932906e-121 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 = 9.708619645801692e-114 estimated_step_error = 9.708619645801692e-114 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 = 6.515135514280619e-106 estimated_step_error = 6.515135514280619e-106 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 = 4.371953128985706e-98 estimated_step_error = 4.371953128985706e-98 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 = 2.933591857442864e-90 estimated_step_error = 2.933591857442864e-90 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 = 1.968195196875167e-82 estimated_step_error = 1.968195196875167e-82 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 = 1.320155630578473e-74 estimated_step_error = 1.320155630578473e-74 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 = 8.85031591005414e-67 estimated_step_error = 8.85031591005414e-67 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 = 5.927131421198128e-59 estimated_step_error = 5.927131421198128e-59 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 = 3.961227297707384e-51 estimated_step_error = 3.961227297707384e-51 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = -0.1418310927316131 y[1] (numeric) = -0.1418310927316131 absolute error = 0 relative error = 0 % Correct digits = 16 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 = 0.272 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = -0.09325618471128788 y[1] (numeric) = -0.09325618471128769 absolute error = 1.942890293094024e-16 relative error = 2.083390285704937e-13 % Correct digits = 15 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 = 0.1832 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.800000000000001 y[1] (analytic) = -0.04374949171972364 y[1] (numeric) = -0.04374949171972327 absolute error = 3.677613769070831e-16 relative error = 8.406071989661191e-13 % Correct digits = 15 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 = 0.08716 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.700000000000001 y[1] (analytic) = 0.006194331731444836 y[1] (numeric) = 0.006194331731445381 absolute error = 5.447031714567174e-16 relative error = 8.793574433406471e-12 % Correct digits = 14 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 = 0.01239 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.600000000000001 y[1] (analytic) = 0.05607626346752655 y[1] (numeric) = 0.05607626346752728 absolute error = 7.216449660063518e-16 relative error = 1.286899164428551e-12 % Correct digits = 14 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 = 0.1114 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.500000000000002 y[1] (analytic) = 0.105397899715389 y[1] (numeric) = 0.1053978997153899 absolute error = 8.881784197001252e-16 relative error = 8.426908146163407e-13 % Correct digits = 15 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 = 0.2061 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.400000000000002 y[1] (analytic) = 0.1536664349892088 y[1] (numeric) = 0.1536664349892099 absolute error = 1.082467449009528e-15 relative error = 7.044267338443452e-13 % Correct digits = 15 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 = 0.2925 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.300000000000002 y[1] (analytic) = 0.2003995860399865 y[1] (numeric) = 0.2003995860399878 absolute error = 1.249000902703301e-15 relative error = 6.232552309035624e-13 % Correct digits = 15 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 = 0.3672 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.200000000000003 y[1] (analytic) = 0.2451304106703485 y[1] (numeric) = 0.24513041067035 absolute error = 1.415534356397075e-15 relative error = 5.774617488405735e-13 % Correct digits = 15 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 = 0.4273 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.100000000000003 y[1] (analytic) = 0.2874119732666331 y[1] (numeric) = 0.2874119732666347 absolute error = 1.554312234475219e-15 relative error = 5.407959232906689e-13 % Correct digits = 15 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 = 0.4704 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.000000000000004 y[1] (analytic) = 0.3268218104318046 y[1] (numeric) = 0.3268218104318063 absolute error = 1.665334536937735e-15 relative error = 5.095542842558322e-13 % Correct digits = 15 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 = 0.4947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.900000000000003 y[1] (analytic) = 0.3629661521000689 y[1] (numeric) = 0.3629661521000705 absolute error = 1.665334536937735e-15 relative error = 4.588126268254914e-13 % Correct digits = 15 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 = 0.4993 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.800000000000003 y[1] (analytic) = 0.3954838559572073 y[1] (numeric) = 0.395483855957209 absolute error = 1.665334536937735e-15 relative error = 4.210878678997025e-13 % Correct digits = 15 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 = 0.484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.700000000000003 y[1] (analytic) = 0.4240500158552032 y[1] (numeric) = 0.4240500158552049 absolute error = 1.665334536937735e-15 relative error = 3.92721253312341e-13 % Correct digits = 15 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 = 0.4494 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.600000000000003 y[1] (analytic) = 0.4483792081670728 y[1] (numeric) = 0.4483792081670744 absolute error = 1.665334536937735e-15 relative error = 3.714120785719409e-13 % Correct digits = 15 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 = 0.3968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.500000000000003 y[1] (analytic) = 0.4682283436453976 y[1] (numeric) = 0.4682283436453992 absolute error = 1.609823385706477e-15 relative error = 3.438116055028145e-13 % Correct digits = 15 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 = 0.3285 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.400000000000003 y[1] (analytic) = 0.4833990962897301 y[1] (numeric) = 0.4833990962897317 absolute error = 1.609823385706477e-15 relative error = 3.330215960398927e-13 % Correct digits = 15 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 = 0.2471 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.300000000000003 y[1] (analytic) = 0.4937398849544322 y[1] (numeric) = 0.4937398849544338 absolute error = 1.554312234475219e-15 relative error = 3.148038637021735e-13 % Correct digits = 15 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 = 0.1558 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.200000000000003 y[1] (analytic) = 0.4991473878973764 y[1] (numeric) = 0.499147387897378 absolute error = 1.554312234475219e-15 relative error = 3.113934425306023e-13 % Correct digits = 15 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 = 0.05827 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.100000000000003 y[1] (analytic) = 0.4995675751366398 y[1] (numeric) = 0.4995675751366414 absolute error = 1.554312234475219e-15 relative error = 3.111315289127982e-13 % Correct digits = 15 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 = 0.04154 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.000000000000003 y[1] (analytic) = 0.4949962483002229 y[1] (numeric) = 0.4949962483002245 absolute error = 1.554312234475219e-15 relative error = 3.140048515140471e-13 % Correct digits = 15 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 = 0.1397 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.900000000000003 y[1] (analytic) = 0.4854790825747956 y[1] (numeric) = 0.4854790825747972 absolute error = 1.609823385706477e-15 relative error = 3.315947985170832e-13 % Correct digits = 15 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 = 0.2323 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.800000000000002 y[1] (analytic) = 0.4711111703343295 y[1] (numeric) = 0.4711111703343311 absolute error = 1.609823385706477e-15 relative error = 3.41707751179843e-13 % Correct digits = 15 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 = 0.3156 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.700000000000002 y[1] (analytic) = 0.4520360710085311 y[1] (numeric) = 0.4520360710085327 absolute error = 1.609823385706477e-15 relative error = 3.561271962467118e-13 % Correct digits = 15 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 = 0.3864 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.600000000000002 y[1] (analytic) = 0.4284443766844742 y[1] (numeric) = 0.4284443766844759 absolute error = 1.665334536937735e-15 relative error = 3.886932884555426e-13 % Correct digits = 15 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 = 0.4417 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.500000000000002 y[1] (analytic) = 0.4005718077734675 y[1] (numeric) = 0.4005718077734692 absolute error = 1.720845688168993e-15 relative error = 4.295973043470323e-13 % Correct digits = 15 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 = 0.4795 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.400000000000002 y[1] (analytic) = 0.3686968577706234 y[1] (numeric) = 0.3686968577706252 absolute error = 1.77635683940025e-15 relative error = 4.817933220644292e-13 % Correct digits = 15 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 = 0.4981 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.300000000000002 y[1] (analytic) = 0.3331380106399129 y[1] (numeric) = 0.3331380106399147 absolute error = 1.77635683940025e-15 relative error = 5.332195014276846e-13 % Correct digits = 15 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 = 0.4968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.200000000000002 y[1] (analytic) = 0.2942505586276736 y[1] (numeric) = 0.2942505586276755 absolute error = 1.831867990631508e-15 relative error = 6.225537851737574e-13 % Correct digits = 15 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 = 0.4758 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.100000000000002 y[1] (analytic) = 0.2524230522999295 y[1] (numeric) = 0.2524230522999314 absolute error = 1.887379141862766e-15 relative error = 7.477047459279507e-13 % Correct digits = 15 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 = 0.4358 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.000000000000002 y[1] (analytic) = 0.208073418273572 y[1] (numeric) = 0.2080734182735739 absolute error = 1.887379141862766e-15 relative error = 9.070736461787092e-13 % Correct digits = 15 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 = 0.3784 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000002 y[1] (analytic) = 0.1616447834317525 y[1] (numeric) = 0.1616447834317545 absolute error = 1.942890293094024e-15 relative error = 1.201950506441382e-12 % Correct digits = 14 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 = 0.3059 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.800000000000002 y[1] (analytic) = 0.1136010473465443 y[1] (numeric) = 0.1136010473465463 absolute error = 1.998401444325282e-15 relative error = 1.759139982423826e-12 % Correct digits = 14 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 = 0.2213 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.700000000000002 y[1] (analytic) = 0.0644222471477631 y[1] (numeric) = 0.06442224714776512 absolute error = 2.026157019940911e-15 relative error = 3.145120062784497e-12 % Correct digits = 14 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 = 0.1278 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.600000000000001 y[1] (analytic) = 0.01459976115064507 y[1] (numeric) = 0.01459976115064714 absolute error = 2.069525106840331e-15 relative error = 1.417506139645916e-11 % Correct digits = 13 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 = 0.02919 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.500000000000001 y[1] (analytic) = -0.03536860083385079 y[1] (numeric) = -0.03536860083384868 absolute error = 2.116362640691705e-15 relative error = 5.983733002709464e-12 % Correct digits = 14 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 = 0.07056 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.400000000000001 y[1] (analytic) = -0.08498357145011985 y[1] (numeric) = -0.0849835714501177 absolute error = 2.151057110211241e-15 relative error = 2.531144635965058e-12 % Correct digits = 14 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 = 0.1675 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.300000000000001 y[1] (analytic) = -0.1337494143122931 y[1] (numeric) = -0.133749414312291 absolute error = 2.192690473634684e-15 relative error = 1.639401925540357e-12 % Correct digits = 14 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 = 0.2578 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.200000000000001 y[1] (analytic) = -0.1811788772383363 y[1] (numeric) = -0.1811788772383341 absolute error = 2.220446049250313e-15 relative error = 1.225554591736084e-12 % Correct digits = 14 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 = 0.3377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.100000000000001 y[1] (analytic) = -0.2267980607127883 y[1] (numeric) = -0.226798060712786 absolute error = 2.275957200481571e-15 relative error = 1.003517046542911e-12 % Correct digits = 14 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 = 0.4042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.000000000000001 y[1] (analytic) = -0.2701511529340695 y[1] (numeric) = -0.2701511529340672 absolute error = 2.331468351712829e-15 relative error = 8.630236541251499e-13 % Correct digits = 15 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 = 0.4546 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000000009 y[1] (analytic) = -0.3108049841353319 y[1] (numeric) = -0.3108049841353295 absolute error = 2.331468351712829e-15 relative error = 7.501386627370339e-13 % Correct digits = 15 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 = 0.4869 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8000000000000009 y[1] (analytic) = -0.3483533546735824 y[1] (numeric) = -0.34835335467358 absolute error = 2.331468351712829e-15 relative error = 6.692825891966751e-13 % Correct digits = 15 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 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.700000000000001 y[1] (analytic) = -0.3824210936422439 y[1] (numeric) = -0.3824210936422416 absolute error = 2.331468351712829e-15 relative error = 6.096599770445519e-13 % Correct digits = 15 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 = 0.4927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.600000000000001 y[1] (analytic) = -0.4126678074548389 y[1] (numeric) = -0.4126678074548366 absolute error = 2.331468351712829e-15 relative error = 5.649746138649252e-13 % Correct digits = 15 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 = 0.466 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.500000000000001 y[1] (analytic) = -0.4387912809451861 y[1] (numeric) = -0.4387912809451838 absolute error = 2.275957200481571e-15 relative error = 5.186878817598665e-13 % Correct digits = 15 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 = 0.4207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.400000000000001 y[1] (analytic) = -0.4605304970014423 y[1] (numeric) = -0.4605304970014401 absolute error = 2.275957200481571e-15 relative error = 4.942033622747123e-13 % Correct digits = 15 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 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.300000000000001 y[1] (analytic) = -0.4776682445628029 y[1] (numeric) = -0.4776682445628005 absolute error = 2.331468351712829e-15 relative error = 4.880936462181529e-13 % Correct digits = 15 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 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.200000000000001 y[1] (analytic) = -0.4900332889206207 y[1] (numeric) = -0.4900332889206184 absolute error = 2.275957200481571e-15 relative error = 4.644495082149914e-13 % Correct digits = 15 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 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.100000000000001 y[1] (analytic) = -0.4975020826390129 y[1] (numeric) = -0.4975020826390105 absolute error = 2.331468351712829e-15 relative error = 4.686348928120046e-13 % Correct digits = 15 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 = 0.09933 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.02695629777827e-15 y[1] (analytic) = -0.5 y[1] (numeric) = -0.4999999999999977 absolute error = 2.331468351712829e-15 relative error = 4.662936703425657e-13 % Correct digits = 15 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 = 1.027e-15 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999898 y[1] (analytic) = -0.4975020826390129 y[1] (numeric) = -0.4975020826390106 absolute error = 2.331468351712829e-15 relative error = 4.686348928120046e-13 % Correct digits = 15 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 = 0.09933 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.199999999999999 y[1] (analytic) = -0.4900332889206209 y[1] (numeric) = -0.4900332889206185 absolute error = 2.386979502944087e-15 relative error = 4.871055817864542e-13 % Correct digits = 15 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 = 0.1947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.299999999999999 y[1] (analytic) = -0.4776682445628032 y[1] (numeric) = -0.4776682445628008 absolute error = 2.386979502944087e-15 relative error = 4.997149235090611e-13 % Correct digits = 15 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 = 0.2823 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.399999999999999 y[1] (analytic) = -0.4605304970014427 y[1] (numeric) = -0.4605304970014403 absolute error = 2.386979502944087e-15 relative error = 5.183108433612832e-13 % Correct digits = 15 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 = 0.3587 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.499999999999999 y[1] (analytic) = -0.4387912809451866 y[1] (numeric) = -0.4387912809451842 absolute error = 2.386979502944087e-15 relative error = 5.439897296505912e-13 % Correct digits = 15 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 = 0.4207 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.599999999999999 y[1] (analytic) = -0.4126678074548394 y[1] (numeric) = -0.4126678074548371 absolute error = 2.386979502944087e-15 relative error = 5.784263903855178e-13 % Correct digits = 15 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 = 0.466 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.699999999999999 y[1] (analytic) = -0.3824210936422445 y[1] (numeric) = -0.3824210936422421 absolute error = 2.386979502944087e-15 relative error = 6.241756907837069e-13 % Correct digits = 15 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 = 0.4927 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999989 y[1] (analytic) = -0.3483533546735831 y[1] (numeric) = -0.3483533546735807 absolute error = 2.386979502944087e-15 relative error = 6.852178889394517e-13 % Correct digits = 15 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 = 0.4998 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999989 y[1] (analytic) = -0.3108049841353326 y[1] (numeric) = -0.3108049841353303 absolute error = 2.386979502944087e-15 relative error = 7.679991070879137e-13 % Correct digits = 15 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 = 0.4869 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999989 y[1] (analytic) = -0.2701511529340703 y[1] (numeric) = -0.2701511529340679 absolute error = 2.442490654175344e-15 relative error = 9.041200186072971e-13 % Correct digits = 15 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 = 0.4546 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.099999999999999 y[1] (analytic) = -0.2267980607127892 y[1] (numeric) = -0.2267980607127867 absolute error = 2.414735078559715e-15 relative error = 1.064707110356499e-12 % Correct digits = 14 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 = 0.4042 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.199999999999999 y[1] (analytic) = -0.1811788772383372 y[1] (numeric) = -0.1811788772383349 absolute error = 2.359223927328458e-15 relative error = 1.302151753719582e-12 % Correct digits = 14 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 = 0.3377 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299999999999999 y[1] (analytic) = -0.1337494143122941 y[1] (numeric) = -0.1337494143122918 absolute error = 2.331468351712829e-15 relative error = 1.743161541080874e-12 % Correct digits = 14 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 = 0.2578 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399999999999999 y[1] (analytic) = -0.08498357145012084 y[1] (numeric) = -0.08498357145011856 absolute error = 2.275957200481571e-15 relative error = 2.678114324504933e-12 % Correct digits = 14 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 = 0.1675 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499999999999999 y[1] (analytic) = -0.03536860083385179 y[1] (numeric) = -0.03536860083384955 absolute error = 2.241262730962035e-15 relative error = 6.336871343852795e-12 % Correct digits = 14 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 = 0.07056 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599999999999999 y[1] (analytic) = 0.01459976115064407 y[1] (numeric) = 0.01459976115064628 absolute error = 2.201364091014568e-15 relative error = 1.507808291040059e-11 % Correct digits = 13 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 = 0.02919 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 0.0644222471477621 y[1] (numeric) = 0.06442224714776426 absolute error = 2.164934898019055e-15 relative error = 3.360539245167049e-12 % Correct digits = 14 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 = 0.1278 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 0.1136010473465433 y[1] (numeric) = 0.1136010473465455 absolute error = 2.123301534595612e-15 relative error = 1.869086231325331e-12 % Correct digits = 14 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 = 0.2213 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 0.1616447834317516 y[1] (numeric) = 0.1616447834317536 absolute error = 2.081668171172169e-15 relative error = 1.287804114044345e-12 % Correct digits = 14 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 = 0.3059 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 0.2080734182735711 y[1] (numeric) = 0.2080734182735731 absolute error = 2.026157019940911e-15 relative error = 9.737702378095008e-13 % Correct digits = 15 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 = 0.3784 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 0.2524230522999286 y[1] (numeric) = 0.2524230522999307 absolute error = 2.109423746787797e-15 relative error = 8.356700101547716e-13 % Correct digits = 15 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 = 0.4358 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 0.2942505586276727 y[1] (numeric) = 0.2942505586276748 absolute error = 2.05391259555654e-15 relative error = 6.980148500433059e-13 % Correct digits = 15 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 = 0.4758 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 0.3331380106399121 y[1] (numeric) = 0.3331380106399141 absolute error = 1.998401444325282e-15 relative error = 5.998719391061467e-13 % Correct digits = 15 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 = 0.4968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 0.3686968577706227 y[1] (numeric) = 0.3686968577706247 absolute error = 1.998401444325282e-15 relative error = 5.420174873224839e-13 % Correct digits = 15 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 = 0.4981 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 0.4005718077734668 y[1] (numeric) = 0.4005718077734688 absolute error = 1.998401444325282e-15 relative error = 4.988871921449417e-13 % Correct digits = 15 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 = 0.4795 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 0.4284443766844737 y[1] (numeric) = 0.4284443766844756 absolute error = 1.942890293094024e-15 relative error = 4.534755031981336e-13 % Correct digits = 15 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 = 0.4417 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 0.4520360710085306 y[1] (numeric) = 0.4520360710085325 absolute error = 1.942890293094024e-15 relative error = 4.298086851253423e-13 % Correct digits = 15 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 = 0.3864 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 0.4711111703343291 y[1] (numeric) = 0.471111170334331 absolute error = 1.887379141862766e-15 relative error = 4.006228806936093e-13 % Correct digits = 15 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 = 0.3156 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 0.4854790825747953 y[1] (numeric) = 0.4854790825747972 absolute error = 1.887379141862766e-15 relative error = 3.887663155027873e-13 % Correct digits = 15 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 = 0.2323 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 0.4949962483002228 y[1] (numeric) = 0.4949962483002247 absolute error = 1.887379141862766e-15 relative error = 3.812916054099145e-13 % Correct digits = 15 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 = 0.1397 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 0.4995675751366397 y[1] (numeric) = 0.4995675751366416 absolute error = 1.887379141862766e-15 relative error = 3.778025708226835e-13 % Correct digits = 15 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 = 0.04154 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000001 y[1] (analytic) = 0.4991473878973765 y[1] (numeric) = 0.4991473878973784 absolute error = 1.887379141862766e-15 relative error = 3.781206087871598e-13 % Correct digits = 15 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 = 0.05827 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000001 y[1] (analytic) = 0.4937398849544324 y[1] (numeric) = 0.4937398849544343 absolute error = 1.887379141862766e-15 relative error = 3.822618344954963e-13 % Correct digits = 15 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 = 0.1558 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000000001 y[1] (analytic) = 0.4833990962897304 y[1] (numeric) = 0.4833990962897323 absolute error = 1.942890293094024e-15 relative error = 4.019226159102151e-13 % Correct digits = 15 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 = 0.2471 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500000000000001 y[1] (analytic) = 0.468228343645398 y[1] (numeric) = 0.4682283436453999 absolute error = 1.942890293094024e-15 relative error = 4.149450411240861e-13 % Correct digits = 15 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 = 0.3285 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600000000000001 y[1] (analytic) = 0.4483792081670733 y[1] (numeric) = 0.4483792081670752 absolute error = 1.942890293094024e-15 relative error = 4.333140916672639e-13 % Correct digits = 15 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 = 0.3968 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000000001 y[1] (analytic) = 0.4240500158552038 y[1] (numeric) = 0.4240500158552057 absolute error = 1.942890293094024e-15 relative error = 4.581747955310638e-13 % Correct digits = 15 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 = 0.4494 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000000001 y[1] (analytic) = 0.395483855957208 y[1] (numeric) = 0.39548385595721 absolute error = 1.998401444325282e-15 relative error = 5.053054414796421e-13 % Correct digits = 15 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 = 0.484 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000001 y[1] (analytic) = 0.3629661521000697 y[1] (numeric) = 0.3629661521000717 absolute error = 1.998401444325282e-15 relative error = 5.505751521905886e-13 % Correct digits = 15 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 = 0.4993 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000001 y[1] (analytic) = 0.3268218104318056 y[1] (numeric) = 0.3268218104318075 absolute error = 1.887379141862766e-15 relative error = 5.774948554899414e-13 % Correct digits = 15 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 = 0.4947 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 0.2874119732666343 y[1] (numeric) = 0.287411973266636 absolute error = 1.720845688168993e-15 relative error = 5.987383436432383e-13 % Correct digits = 15 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 = 0.4704 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 0.2451304106703497 y[1] (numeric) = 0.2451304106703513 absolute error = 1.582067810090848e-15 relative error = 6.453984251747556e-13 % Correct digits = 15 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 = 0.4273 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 0.2003995860399877 y[1] (numeric) = 0.2003995860399891 absolute error = 1.415534356397075e-15 relative error = 7.063559283573665e-13 % Correct digits = 15 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 = 0.3672 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999999 y[1] (analytic) = 0.1536664349892101 y[1] (numeric) = 0.1536664349892113 absolute error = 1.249000902703301e-15 relative error = 8.128000775126991e-13 % Correct digits = 15 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 = 0.2925 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.499999999999999 y[1] (analytic) = 0.1053978997153903 y[1] (numeric) = 0.1053978997153913 absolute error = 1.054711873393899e-15 relative error = 1.000695342356892e-12 % Correct digits = 14 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 = 0.2061 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.599999999999999 y[1] (analytic) = 0.05607626346752788 y[1] (numeric) = 0.05607626346752876 absolute error = 8.81239525796218e-16 relative error = 1.571501864254058e-12 % Correct digits = 14 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 = 0.1114 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999998 y[1] (analytic) = 0.006194331731446167 y[1] (numeric) = 0.006194331731446873 absolute error = 7.051650929845721e-16 relative error = 1.138403823942344e-11 % Correct digits = 13 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 = 0.01239 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999998 y[1] (analytic) = -0.04374949171972231 y[1] (numeric) = -0.04374949171972179 absolute error = 5.204170427930421e-16 relative error = 1.189538489103035e-12 % Correct digits = 14 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 = 0.08716 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999998 y[1] (analytic) = -0.09325618471128656 y[1] (numeric) = -0.09325618471128622 absolute error = 3.469446951953614e-16 relative error = 3.720339795901725e-13 % Correct digits = 15 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 = 0.1832 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999997 y[1] (analytic) = -0.1418310927316118 y[1] (numeric) = -0.1418310927316117 absolute error = 1.665334536937735e-16 relative error = 1.174167458533977e-13 % Correct digits = 15 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 = 0.272 Order of pole (three term test) = 28 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin(x) / 2.0; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 102 %