##############ECHO OF PROBLEM################# ##############temp/div_sin_lin_newpostode.ode################# diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ 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; glob_max_h=0.001; /* 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 */ double exact_soln_y (double x) { return(sin(x)/(2*x+1)); } /* 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 = 4.504046601192704e-152 estimated_step_error = 4.504046601192704e-152 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 = 3.022612082540083e-144 estimated_step_error = 3.022612082540083e-144 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 = 2.028437376207862e-136 estimated_step_error = 2.028437376207862e-136 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 = 1.361256910671959e-128 estimated_step_error = 1.361256910671959e-128 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 = 9.135181843500686e-121 estimated_step_error = 9.135181843500686e-121 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 = 6.130438048725262e-113 estimated_step_error = 6.130438048725262e-113 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 = 4.113961692974579e-105 estimated_step_error = 4.113961692974579e-105 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 = 2.760691181218541e-97 estimated_step_error = 2.760691181218541e-97 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 = 1.852478230655872e-89 estimated_step_error = 1.852478230655872e-89 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 = 1.242921813138977e-81 estimated_step_error = 1.242921813138977e-81 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 = 8.337682853441596e-74 estimated_step_error = 8.337682853441596e-74 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.0831945138723568 y[1] (numeric) = 0.0831945138723568 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6273 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] = 0.11 y[1] (analytic) = 0.08998221380096297 y[1] (numeric) = 0.08998221380096298 absolute error = 1.387778780781446e-17 relative error = 1.542281215542392e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6377 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] = 0.12 y[1] (analytic) = 0.09654210265235434 y[1] (numeric) = 0.09654210265235436 absolute error = 1.387778780781446e-17 relative error = 1.43748555568424e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6482 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] = 0.13 y[1] (analytic) = 0.102884240174361 y[1] (numeric) = 0.102884240174361 absolute error = 2.775557561562891e-17 relative error = 2.697748029104429e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6586 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] = 0.14 y[1] (analytic) = 0.1090180583158098 y[1] (numeric) = 0.1090180583158098 absolute error = 1.387778780781446e-17 relative error = 1.272980643960149e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6691 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] = 0.15 y[1] (analytic) = 0.1149524095950764 y[1] (numeric) = 0.1149524095950764 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.6795 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] = 0.1600000000000001 y[1] (analytic) = 0.1206956110713985 y[1] (numeric) = 0.1206956110713985 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.69 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] = 0.1700000000000001 y[1] (analytic) = 0.1262554843783553 y[1] (numeric) = 0.1262554843783553 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7005 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] = 0.1800000000000001 y[1] (analytic) = 0.1316393922248708 y[1] (numeric) = 0.1316393922248708 absolute error = 2.775557561562891e-17 relative error = 2.108455162738516e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7109 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] = 0.1900000000000001 y[1] (analytic) = 0.1368542717221019 y[1] (numeric) = 0.1368542717221019 absolute error = 2.775557561562891e-17 relative error = 2.028111747362169e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7214 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] = 0.2000000000000001 y[1] (analytic) = 0.1419066648536152 y[1] (numeric) = 0.1419066648536153 absolute error = 8.326672684688674e-17 relative error = 5.867710789537695e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7318 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.8634 Order of pole (six term test) = -5.429e-11 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (analytic) = 0.1468027463704927 y[1] (numeric) = 0.1468027463704928 absolute error = 1.110223024625157e-16 relative error = 7.56268565864045e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7423 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] = 0.2200000000000001 y[1] (analytic) = 0.1515483493617149 y[1] (numeric) = 0.151548349361715 absolute error = 1.387778780781446e-16 relative error = 9.157333528385071e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7527 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.218 Order of pole (six term test) = -6.334e-11 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 0.1561489887227318 y[1] (numeric) = 0.156148988722732 absolute error = 1.387778780781446e-16 relative error = 8.887529737676847e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7632 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] = 0.2400000000000001 y[1] (analytic) = 0.1606098827210369 y[1] (numeric) = 0.1606098827210371 absolute error = 1.387778780781446e-16 relative error = 8.640681116689914e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7736 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] = 0.2500000000000001 y[1] (analytic) = 0.1649359728363487 y[1] (numeric) = 0.1649359728363488 absolute error = 1.387778780781446e-16 relative error = 8.41404550454506e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7841 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] = 0.2600000000000001 y[1] (analytic) = 0.1691319420343126 y[1] (numeric) = 0.1691319420343127 absolute error = 1.110223024625157e-16 relative error = 6.564242160714504e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.7945 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] = 0.2700000000000001 y[1] (analytic) = 0.1732022316161242 y[1] (numeric) = 0.1732022316161243 absolute error = 1.110223024625157e-16 relative error = 6.409981062402207e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.805 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6227 Order of pole (six term test) = -3.637e-11 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 0.1771510567718678 y[1] (numeric) = 0.177151056771868 absolute error = 1.665334536937735e-16 relative error = 9.400646924067323e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8155 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] = 0.2900000000000001 y[1] (analytic) = 0.1809824209524276 y[1] (numeric) = 0.1809824209524278 absolute error = 1.665334536937735e-16 relative error = 9.201636977634854e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8259 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] = 0.3000000000000002 y[1] (analytic) = 0.1847001291633373 y[1] (numeric) = 0.1847001291633375 absolute error = 1.942890293094024e-16 relative error = 1.051916044615135e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8364 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] = 0.3100000000000002 y[1] (analytic) = 0.1883078002737306 y[1] (numeric) = 0.1883078002737308 absolute error = 1.665334536937735e-16 relative error = 8.843683238383901e-14 % Correct digits = 16 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8468 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] = 0.3200000000000002 y[1] (analytic) = 0.1918088784244621 y[1] (numeric) = 0.1918088784244623 absolute error = 2.220446049250313e-16 relative error = 1.157634655647479e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8573 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.246 Order of pole (six term test) = -6.542e-11 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (analytic) = 0.1952066436113665 y[1] (numeric) = 0.1952066436113668 absolute error = 2.498001805406602e-16 relative error = 1.27967048620529e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8677 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] = 0.3400000000000002 y[1] (analytic) = 0.1985042215123896 y[1] (numeric) = 0.1985042215123898 absolute error = 2.498001805406602e-16 relative error = 1.258412433939441e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8782 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] = 0.3500000000000002 y[1] (analytic) = 0.2017045926208538 y[1] (numeric) = 0.2017045926208541 absolute error = 2.498001805406602e-16 relative error = 1.238445675900956e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8886 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.192 Order of pole (six term test) = -2.955e-11 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 0.2048106007413314 y[1] (numeric) = 0.2048106007413317 absolute error = 2.220446049250313e-16 relative error = 1.084146055532867e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.8991 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] = 0.3700000000000002 y[1] (analytic) = 0.2078249608994035 y[1] (numeric) = 0.2078249608994037 absolute error = 2.220446049250313e-16 relative error = 1.068421252019437e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9095 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] = 0.3800000000000002 y[1] (analytic) = 0.210750266711922 y[1] (numeric) = 0.2107502667119223 absolute error = 2.498001805406602e-16 relative error = 1.185289985336608e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.92 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] = 0.3900000000000002 y[1] (analytic) = 0.2135889972602031 y[1] (numeric) = 0.2135889972602034 absolute error = 2.775557561562891e-16 relative error = 1.29948527179122e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9305 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] = 0.4000000000000002 y[1] (analytic) = 0.2163435235048059 y[1] (numeric) = 0.2163435235048062 absolute error = 2.498001805406602e-16 relative error = 1.154645983821703e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9409 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.5845 Order of pole (six term test) = -2.709e-11 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (analytic) = 0.2190161142771555 y[1] (numeric) = 0.2190161142771558 absolute error = 2.498001805406602e-16 relative error = 1.140556170330685e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9514 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] = 0.4200000000000003 y[1] (analytic) = 0.2216089418802012 y[1] (numeric) = 0.2216089418802015 absolute error = 2.498001805406602e-16 relative error = 1.127211647784947e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9618 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] = 0.4300000000000003 y[1] (analytic) = 0.2241240873275328 y[1] (numeric) = 0.224124087327533 absolute error = 2.775557561562891e-16 relative error = 1.2384021702704e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9723 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] = 0.4400000000000003 y[1] (analytic) = 0.2265635452478722 y[1] (numeric) = 0.2265635452478725 absolute error = 2.775557561562891e-16 relative error = 1.225068030484025e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9827 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.465 Order of pole (six term test) = -1.009e-10 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (analytic) = 0.2289292284795949 y[1] (numeric) = 0.2289292284795952 absolute error = 3.33066907387547e-16 relative error = 1.454890271546231e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 0.9932 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] = 0.4600000000000003 y[1] (analytic) = 0.231222972377875 y[1] (numeric) = 0.2312229723778753 absolute error = 3.33066907387547e-16 relative error = 1.440457684469319e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.004 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.199 Order of pole (six term test) = -3.697e-11 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 0.2334465388551899 y[1] (numeric) = 0.2334465388551902 absolute error = 3.33066907387547e-16 relative error = 1.42673739786801e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.014 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] = 0.4800000000000003 y[1] (analytic) = 0.235601620174226 y[1] (numeric) = 0.2356016201742263 absolute error = 3.05311331771918e-16 relative error = 1.295879593468594e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.025 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] = 0.4900000000000003 y[1] (analytic) = 0.237689842510686 y[1] (numeric) = 0.2376898425106863 absolute error = 3.05311331771918e-16 relative error = 1.284494652976986e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.035 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] = 0.5000000000000003 y[1] (analytic) = 0.2397127693021016 y[1] (numeric) = 0.2397127693021019 absolute error = 3.33066907387547e-16 relative error = 1.389441657018256e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.045 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.04 Order of pole (six term test) = 2.31e-11 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (analytic) = 0.241671904397479 y[1] (numeric) = 0.2416719043974794 absolute error = 3.608224830031759e-16 relative error = 1.493026191450576e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.056 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.2127 Order of pole (six term test) = -1.816e-11 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (analytic) = 0.2435686950214396 y[1] (numeric) = 0.24356869502144 absolute error = 3.608224830031759e-16 relative error = 1.481399253592155e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.066 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6076 Order of pole (six term test) = -2.102e-11 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (analytic) = 0.2454045345654597 y[1] (numeric) = 0.2454045345654601 absolute error = 3.885780586188048e-16 relative error = 1.58341841281321e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.077 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.6816 Order of pole (six term test) = -4.422e-11 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (analytic) = 0.2471807652178429 y[1] (numeric) = 0.2471807652178433 absolute error = 4.163336342344337e-16 relative error = 1.684328608124158e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.087 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] = 0.5500000000000004 y[1] (analytic) = 0.2488986804431711 y[1] (numeric) = 0.2488986804431715 absolute error = 4.163336342344337e-16 relative error = 1.672703260190612e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.098 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] = 0.5600000000000004 y[1] (analytic) = 0.2505595273211715 y[1] (numeric) = 0.2505595273211719 absolute error = 4.440892098500626e-16 relative error = 1.772390036802797e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.108 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] = 0.5700000000000004 y[1] (analytic) = 0.2521645087541913 y[1] (numeric) = 0.2521645087541918 absolute error = 4.996003610813204e-16 relative error = 1.981247732084012e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.119 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] = 0.5800000000000004 y[1] (analytic) = 0.2537147855517934 y[1] (numeric) = 0.2537147855517939 absolute error = 4.996003610813204e-16 relative error = 1.969141687957842e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.129 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] = 0.5900000000000004 y[1] (analytic) = 0.2552114784003596 y[1] (numeric) = 0.2552114784003601 absolute error = 5.551115123125783e-16 relative error = 2.175104018800262e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.14 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] = 0.6000000000000004 y[1] (analytic) = 0.2566556697250161 y[1] (numeric) = 0.2566556697250167 absolute error = 6.106226635438361e-16 relative error = 2.379151273759369e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.15 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] = 0.6100000000000004 y[1] (analytic) = 0.2580484054506673 y[1] (numeric) = 0.2580484054506679 absolute error = 5.551115123125783e-16 relative error = 2.151191406678552e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.229 Order of pole (six term test) = -4.147e-11 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (analytic) = 0.2593906966684398 y[1] (numeric) = 0.2593906966684404 absolute error = 6.106226635438361e-16 relative error = 2.354065397820919e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.171 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] = 0.6300000000000004 y[1] (analytic) = 0.2606835212133937 y[1] (numeric) = 0.2606835212133942 absolute error = 5.551115123125783e-16 relative error = 2.129446118146333e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.181 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] = 0.6400000000000005 y[1] (analytic) = 0.2619278251589439 y[1] (numeric) = 0.2619278251589445 absolute error = 6.106226635438361e-16 relative error = 2.331263061392183e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.192 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) = 0.2631245242330607 y[1] (numeric) = 0.2631245242330614 absolute error = 6.661338147750939e-16 relative error = 2.531629526805607e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.202 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) = 0.2642745051609629 y[1] (numeric) = 0.2642745051609635 absolute error = 6.106226635438361e-16 relative error = 2.310562129978907e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.213 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.538 Order of pole (six term test) = -1.288e-10 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (analytic) = 0.2653786269387008 y[1] (numeric) = 0.2653786269387014 absolute error = 6.106226635438361e-16 relative error = 2.300948914340726e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.223 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) = 0.266437722041724 y[1] (numeric) = 0.2664377220417247 absolute error = 6.661338147750939e-16 relative error = 2.500148288577462e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.234 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) = 0.2674525975722555 y[1] (numeric) = 0.2674525975722562 absolute error = 7.216449660063518e-16 relative error = 2.698216329012811e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.244 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) = 0.268424036349038 y[1] (numeric) = 0.2684240363490387 absolute error = 6.661338147750939e-16 relative error = 2.481647410699482e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.255 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) = 0.2693527979427838 y[1] (numeric) = 0.2693527979427845 absolute error = 7.216449660063518e-16 relative error = 2.679181250456676e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.265 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) = 0.2702396196604399 y[1] (numeric) = 0.2702396196604406 absolute error = 7.216449660063518e-16 relative error = 2.670389215737905e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.275 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) = 0.271085217481178 y[1] (numeric) = 0.2710852174811786 absolute error = 6.106226635438361e-16 relative error = 2.252511845601588e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.286 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) = 0.2718902869468327 y[1] (numeric) = 0.2718902869468333 absolute error = 5.551115123125783e-16 relative error = 2.041674671596962e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.296 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) = 0.2726555040093337 y[1] (numeric) = 0.2726555040093343 absolute error = 6.106226635438361e-16 relative error = 2.23953910544543e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.307 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) = 0.2733815258375204 y[1] (numeric) = 0.2733815258375211 absolute error = 6.661338147750939e-16 relative error = 2.436645317324767e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.317 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) = 0.2740689915855736 y[1] (numeric) = 0.2740689915855742 absolute error = 6.106226635438361e-16 relative error = 2.227988872477677e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.328 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) = 0.2747185231251603 y[1] (numeric) = 0.274718523125161 absolute error = 7.216449660063518e-16 relative error = 2.626852233322375e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.338 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) = 0.2753307257432589 y[1] (numeric) = 0.2753307257432596 absolute error = 7.216449660063518e-16 relative error = 2.621011382068825e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.349 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.479 Order of pole (six term test) = -1.843e-11 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 0.2759061888075088 y[1] (numeric) = 0.2759061888075095 absolute error = 7.216449660063518e-16 relative error = 2.615544686131782e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.359 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) = 0.2764454864008178 y[1] (numeric) = 0.2764454864008185 absolute error = 7.216449660063518e-16 relative error = 2.610442208342082e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.37 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) = 0.2769491779268545 y[1] (numeric) = 0.2769491779268554 absolute error = 8.326672684688674e-16 relative error = 3.006570644845115e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.38 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) = 0.277417808687956 y[1] (numeric) = 0.2774178086879568 absolute error = 8.326672684688674e-16 relative error = 3.001491765820503e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.39 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) = 0.2778519104368878 y[1] (numeric) = 0.2778519104368887 absolute error = 8.326672684688674e-16 relative error = 2.996802387140693e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.401 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) = 0.2782520019038122 y[1] (numeric) = 0.278252001903813 absolute error = 8.326672684688674e-16 relative error = 2.992493361311768e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.411 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) = 0.2786185892997342 y[1] (numeric) = 0.2786185892997351 absolute error = 8.881784197001252e-16 relative error = 3.187793111480564e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.422 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) = 0.2789521667976296 y[1] (numeric) = 0.2789521667976305 absolute error = 8.881784197001252e-16 relative error = 3.183981074233665e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.432 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) = 0.2792532169923802 y[1] (numeric) = 0.2792532169923811 absolute error = 9.436895709313831e-16 relative error = 3.379332854586713e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.443 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) = 0.2795222113405841 y[1] (numeric) = 0.2795222113405851 absolute error = 9.992007221626409e-16 relative error = 3.574673788428082e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.453 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) = 0.2797596105812441 y[1] (numeric) = 0.279759610581245 absolute error = 9.436895709313831e-16 relative error = 3.373215915516615e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.464 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) = 0.2799658651382803 y[1] (numeric) = 0.2799658651382813 absolute error = 9.992007221626409e-16 relative error = 3.569009106410587e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.474 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) = 0.2801414155057627 y[1] (numeric) = 0.2801414155057638 absolute error = 1.054711873393899e-15 relative error = 3.764926622826329e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.485 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) = 0.2802866926167053 y[1] (numeric) = 0.2802866926167064 absolute error = 1.054711873393899e-15 relative error = 3.762975200667936e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.495 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) = 0.2804021181962202 y[1] (numeric) = 0.2804021181962212 absolute error = 9.992007221626409e-16 relative error = 3.563456398226702e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.505 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] = 0.9500000000000007 y[1] (analytic) = 0.2804881050997841 y[1] (numeric) = 0.2804881050997851 absolute error = 9.992007221626409e-16 relative error = 3.562363979061336e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.516 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] = 0.9600000000000007 y[1] (analytic) = 0.2805450576373282 y[1] (numeric) = 0.2805450576373292 absolute error = 9.992007221626409e-16 relative error = 3.561640795163633e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.526 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] = 0.9700000000000008 y[1] (analytic) = 0.2805733718838265 y[1] (numeric) = 0.2805733718838276 absolute error = 1.110223024625157e-15 relative error = 3.956979299820557e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.537 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] = 0.9800000000000008 y[1] (analytic) = 0.2805734359770171 y[1] (numeric) = 0.2805734359770181 absolute error = 9.992007221626409e-16 relative error = 3.561280556312143e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.547 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] = 0.9900000000000008 y[1] (analytic) = 0.2805456304028592 y[1] (numeric) = 0.2805456304028602 absolute error = 9.992007221626409e-16 relative error = 3.561633523672438e-13 % Correct digits = 15 h = 0.001 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.558 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 Finished! diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ; Iterations = 900 Total Elapsed Time = 1 Seconds Elapsed Time(since restart) = 1 Seconds Time to Timeout = 2 Minutes 59 Seconds Percent Done = 100.1 %