##############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_type_given_pole=1; array_given_rad_poles[1][1]=-0.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=1.0; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { 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 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 900000.0000000001 step_error = 3.513641844631533e-15 est_needed_step_err = 3.513641844631533e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 900000.0000000001 step_error = 3.513641844631533e-15 est_needed_step_err = 3.513641844631533e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.504046601192705e-152 estimated_step_error = 4.504046601192705e-152 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 450000.0000000001 step_error = 4.969039949999532e-15 est_needed_step_err = 4.969039949999532e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.022612082540084e-144 estimated_step_error = 3.022612082540084e-144 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 225000 step_error = 7.027283689263065e-15 est_needed_step_err = 7.027283689263065e-15 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 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 112500 step_error = 9.938079899999064e-15 est_needed_step_err = 9.938079899999064e-15 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 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 56250.00000000001 step_error = 1.405456737852613e-14 est_needed_step_err = 1.405456737852613e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.13518184350067e-121 estimated_step_error = 9.13518184350067e-121 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 28125 step_error = 1.987615979999813e-14 est_needed_step_err = 1.987615979999813e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.13043804872516e-113 estimated_step_error = 6.13043804872516e-113 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 14062.5 step_error = 2.810913475705226e-14 est_needed_step_err = 2.810913475705226e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.113961692974021e-105 estimated_step_error = 4.113961692974021e-105 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 7031.250000000001 step_error = 3.975231959999626e-14 est_needed_step_err = 3.975231959999626e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.760691181215538e-97 estimated_step_error = 2.760691181215538e-97 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 3515.625 step_error = 5.621826951410452e-14 est_needed_step_err = 5.621826951410452e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.852478230639745e-89 estimated_step_error = 1.852478230639745e-89 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 1757.8125 step_error = 7.950463919999252e-14 est_needed_step_err = 7.950463919999252e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.242921813052388e-81 estimated_step_error = 1.242921813052388e-81 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 878.9062500000001 step_error = 1.12436539028209e-13 est_needed_step_err = 1.12436539028209e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.337682848792879e-74 estimated_step_error = 8.337682848792879e-74 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 439.4531250000001 step_error = 1.59009278399985e-13 est_needed_step_err = 1.59009278399985e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.5907339663456e-66 estimated_step_error = 5.5907339663456e-66 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 219.7265625 step_error = 2.248730780564181e-13 est_needed_step_err = 2.248730780564181e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.745732246456583e-58 estimated_step_error = 3.745732246456583e-58 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.0831945138723568 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 0.9 estimated_steps = 109.86328125 step_error = 3.180185567999701e-13 est_needed_step_err = 3.180185567999701e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.505510050253785e-50 estimated_step_error = 2.505510050253785e-50 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3662 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 0.0831945138723568 y[1] (numeric) = 0.0831945138723568 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.6 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 2.777e-13 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) = 0.08998221380235036 absolute error = 1.387390202722827e-12 relative error = 1.54184937680204e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.61 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.61 Order of pole (three term test) = 1.023e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.12 y[1] (analytic) = 0.09654210265235433 y[1] (numeric) = 0.09654210265497812 absolute error = 2.623790074096632e-12 relative error = 2.717767690998853e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.62 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.62 Order of pole (three term test) = 3.35e-13 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) = 0.1028842401780887 absolute error = 3.727684827481426e-12 relative error = 3.623183513008413e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.63 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.63 Order of pole (three term test) = 1.203e-13 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) = 0.1090180583205248 absolute error = 4.715061674431809e-12 relative error = 4.325028116693243e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.64 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.64 Order of pole (three term test) = 3.844e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.15 y[1] (analytic) = 0.1149524095950763 y[1] (numeric) = 0.1149524096006761 absolute error = 5.599756769392172e-12 relative error = 4.871369629499286e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.65 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.65 Order of pole (three term test) = 6.743e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.16 y[1] (analytic) = 0.1206956110713985 y[1] (numeric) = 0.1206956110777923 absolute error = 6.3938160321797e-12 relative error = 5.297471859517232e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.66 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.66 Order of pole (three term test) = 2.105e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.17 y[1] (analytic) = 0.1262554843783553 y[1] (numeric) = 0.1262554843854629 absolute error = 7.107675559225868e-12 relative error = 5.629597473901403e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.67 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.67 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.18 y[1] (analytic) = 0.1316393922248708 y[1] (numeric) = 0.1316393922326212 absolute error = 7.750494690483833e-12 relative error = 5.887671280982658e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.68 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.68 Order of pole (three term test) = 0 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) = 0.1368542717304321 absolute error = 8.330225398367475e-12 relative error = 6.08693122512313e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.69 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.69 Order of pole (three term test) = 2.222e-13 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) = 0.141906664862469 absolute error = 8.853834332356314e-12 relative error = 6.239195559623326e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y[1] (analytic) = 0.1468027463704927 y[1] (numeric) = 0.1468027463798202 absolute error = 9.327483230237021e-12 relative error = 6.353752542678482e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 2.919e-13 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) = 0.1515483493714714 absolute error = 9.756501162527798e-12 relative error = 6.437880190460556e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 7.141e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y[1] (analytic) = 0.1561489887227318 y[1] (numeric) = 0.1561489887328775 absolute error = 1.014566208823453e-11 relative error = 6.497424140382887e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 1.385e-13 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) = 0.1606098827315361 absolute error = 1.049915709927518e-11 relative error = 6.537055454745055e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 1.995e-13 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) = 0.1649359728471693 absolute error = 1.082064993163101e-11 relative error = 6.560515420348829e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 1.267e-13 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) = 0.1691319420454261 absolute error = 1.111344349880028e-11 relative error = 6.570872045296826e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 0 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) = 0.1732022316275046 absolute error = 1.13803966250714e-11 relative error = 6.570583137920693e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 1.12e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y[1] (analytic) = 0.1771510567718678 y[1] (numeric) = 0.1771510567834919 absolute error = 1.162409057897662e-11 relative error = 6.561682888488737e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 2.081e-13 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) = 0.1809824209642745 absolute error = 1.184685682886766e-11 relative error = 6.545860513149882e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 9.59e-14 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) = 0.184700129175388 absolute error = 1.205069377618884e-11 relative error = 6.524464184609181e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 0 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) = 0.188307800285968 absolute error = 1.223740553335517e-11 relative error = 6.498618493533706e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 7.961e-14 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) = 0.1918088784368708 absolute error = 1.240862967932799e-11 relative error = 6.469267627887588e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y[1] (analytic) = 0.1952066436113666 y[1] (numeric) = 0.1952066436239324 absolute error = 1.256580950403929e-11 relative error = 6.437183321002302e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 2.567e-13 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) = 0.1985042215250999 absolute error = 1.271030503069426e-11 relative error = 6.403040164010289e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 2.281e-13 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) = 0.201704592633697 absolute error = 1.284319872674189e-11 relative error = 6.367330837569664e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 2.013e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y[1] (analytic) = 0.2048106007413314 y[1] (numeric) = 0.2048106007542971 absolute error = 1.296560081520681e-11 relative error = 6.330532095641821e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 8.822e-14 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) = 0.2078249609124819 absolute error = 1.307839947450873e-11 relative error = 6.292987819128835e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 7.684e-14 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) = 0.2107502667251046 absolute error = 1.318251063864295e-11 relative error = 6.255038650395798e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 0 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) = 0.2135889972734818 absolute error = 1.327865595257549e-11 relative error = 6.216919468187246e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 2.288e-13 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) = 0.2163435235181734 absolute error = 1.336755706127235e-11 relative error = 6.178857053225077e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y[1] (analytic) = 0.2190161142771555 y[1] (numeric) = 0.2190161142906053 absolute error = 1.344976907624584e-11 relative error = 6.140995205140813e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 0 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) = 0.2216089418937272 absolute error = 1.352593037573513e-11 relative error = 6.103512909261153e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 7.023e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y[1] (analytic) = 0.2241240873275327 y[1] (numeric) = 0.2241240873411292 absolute error = 1.359651280452567e-11 relative error = 6.066511175416796e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 1.18e-13 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) = 0.2265635452615342 absolute error = 1.366198820740294e-11 relative error = 6.030091113049994e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 9.86e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y[1] (analytic) = 0.2289292284795949 y[1] (numeric) = 0.2289292284933176 absolute error = 1.372274516242555e-11 relative error = 5.994317655968818e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 1.639e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y[1] (analytic) = 0.2312229723778749 y[1] (numeric) = 0.2312229723916542 absolute error = 1.377922775880336e-11 relative error = 5.959281474975906e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 1.355e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y[1] (analytic) = 0.2334465388551899 y[1] (numeric) = 0.2334465388690216 absolute error = 1.383171355229251e-11 relative error = 5.925002623779534e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 2.228e-13 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) = 0.2356016201881066 absolute error = 1.388056336537602e-11 relative error = 5.891539860851306e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 2.734e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y[1] (analytic) = 0.2376898425106859 y[1] (numeric) = 0.237689842524612 absolute error = 1.392611026496127e-11 relative error = 5.858942106175692e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y[1] (analytic) = 0.2397127693021015 y[1] (numeric) = 0.2397127693160701 absolute error = 1.396854854007756e-11 relative error = 5.827202522729816e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1.202e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y[1] (analytic) = 0.2416719043974791 y[1] (numeric) = 0.2416719044114871 absolute error = 1.40080447241786e-11 relative error = 5.796306674167427e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.01 Order of pole (three term test) = 9.693e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y[1] (analytic) = 0.2435686950214396 y[1] (numeric) = 0.2435686950354846 absolute error = 1.404504290647424e-11 relative error = 5.766357989986337e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.02 Order of pole (three term test) = 1.556e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y[1] (analytic) = 0.2454045345654598 y[1] (numeric) = 0.2454045345795393 absolute error = 1.407948757581323e-11 relative error = 5.737256485803703e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 1.243e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y[1] (analytic) = 0.2471807652178429 y[1] (numeric) = 0.2471807652319546 absolute error = 1.411176731025421e-11 relative error = 5.709087961523772e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.04 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.04 Order of pole (three term test) = 0 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) = 0.248898680457313 absolute error = 1.414190986537278e-11 relative error = 5.681793828795201e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 1.565e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y[1] (analytic) = 0.2505595273211714 y[1] (numeric) = 0.2505595273353416 absolute error = 1.417022055250072e-11 relative error = 5.655430748932207e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.06 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 1.233e-13 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) = 0.2521645087683879 absolute error = 1.41966438604868e-11 relative error = 5.629913555489929e-09 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 1.936e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y[1] (analytic) = 0.2537147855517933 y[1] (numeric) = 0.2537147855660148 absolute error = 1.422145734508717e-11 relative error = 5.60529309088453e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.08 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.08 Order of pole (three term test) = 1.513e-13 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) = 0.2552114784146042 absolute error = 1.424460549515061e-11 relative error = 5.581490920562974e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.09 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.09 Order of pole (three term test) = 1.178e-13 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) = 0.2566556697392826 absolute error = 1.426653239988696e-11 relative error = 5.558627407363448e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 9.134e-14 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) = 0.2580484054649543 absolute error = 1.428696050354006e-11 relative error = 5.536542835282655e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.11 Order of pole (three term test) = 7.054e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y[1] (analytic) = 0.2593906966684398 y[1] (numeric) = 0.2593906966827461 absolute error = 1.430627838416854e-11 relative error = 5.515339820554632e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.12 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.12 Order of pole (three term test) = 0 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) = 0.260683521227718 absolute error = 1.432431950831869e-11 relative error = 5.494907941109523e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.13 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.13 Order of pole (three term test) = 2.495e-13 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) = 0.2619278251732853 absolute error = 1.434141694289792e-11 relative error = 5.475331585789031e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.14 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.14 Order of pole (three term test) = 1.27e-13 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) = 0.2631245242474182 absolute error = 1.435745966560376e-11 relative error = 5.456526603687742e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 2.898e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (analytic) = 0.2642745051609628 y[1] (numeric) = 0.2642745051753355 absolute error = 1.437261420988989e-11 relative error = 5.438517121103262e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.16 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 2.929e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (analytic) = 0.2653786269387008 y[1] (numeric) = 0.2653786269530876 absolute error = 1.438676955345386e-11 relative error = 5.421223901643378e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.17 Order of pole (three term test) = 1.106e-13 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) = 0.2664377220561242 absolute error = 1.440020325205182e-11 relative error = 5.404716397401401e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.18 Order of pole (three term test) = 8.325e-14 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) = 0.2674525975866684 absolute error = 1.441291530568378e-11 relative error = 5.388960674345278e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.19 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.19 Order of pole (three term test) = 2.498e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 0.2684240363490379 y[1] (numeric) = 0.2684240363634628 absolute error = 1.442490571434973e-11 relative error = 5.373924746289373e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 1.867e-13 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) = 0.2693527979572199 absolute error = 1.443611896689845e-11 relative error = 5.359557827932785e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.21 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 2.087e-13 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) = 0.2702396196748867 absolute error = 1.444683261908608e-11 relative error = 5.345934336807735e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 2.067e-13 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) = 0.271085217495635 absolute error = 1.445693564861017e-11 relative error = 5.332985613505075e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.23 Order of pole (three term test) = 2.295e-13 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) = 0.2718902869612992 absolute error = 1.446653907777318e-11 relative error = 5.320726694661978e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.24 Order of pole (three term test) = 2.258e-13 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) = 0.2726555040238093 absolute error = 1.447553188427264e-11 relative error = 5.309092122261762e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 0 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) = 0.2733815258520046 absolute error = 1.448419162386472e-11 relative error = 5.298160356480396e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.26 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.26 Order of pole (three term test) = 0 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) = 0.2740689916000659 absolute error = 1.449229625194448e-11 relative error = 5.287827772161339e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.27 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 0 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) = 0.2747185231396603 absolute error = 1.450001230196563e-11 relative error = 5.278134192414648e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.28 Order of pole (three term test) = 1.3e-13 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) = 0.2753307257577662 absolute error = 1.450733977392815e-11 relative error = 5.269059504624992e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.29 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.29 Order of pole (three term test) = 1.89e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 0.2759061888075087 y[1] (numeric) = 0.2759061888220231 absolute error = 1.451438969013452e-11 relative error = 5.260624907642346e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 6.851e-14 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) = 0.2764454864153387 absolute error = 1.452094000597981e-11 relative error = 5.252731811625937e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.31 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 1.981e-13 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) = 0.2769491779413817 absolute error = 1.452721276606894e-11 relative error = 5.245443541235478e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.32 Order of pole (three term test) = 3.571e-13 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) = 0.2774178087024891 absolute error = 1.453315245925069e-11 relative error = 5.238723688282684e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.33 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.33 Order of pole (three term test) = 2.054e-13 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) = 0.2778519104514267 absolute error = 1.453892561897874e-11 relative error = 5.23261675477346e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.34 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.34 Order of pole (three term test) = 0 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) = 0.2782520019183564 absolute error = 1.454425468949694e-11 relative error = 5.227008104159007e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.35 Order of pole (three term test) = 0 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) = 0.2786185893142836 absolute error = 1.454941722656145e-11 relative error = 5.221983667037153e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.36 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 2.255e-13 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) = 0.2789521668121839 absolute error = 1.45543022078698e-11 relative error = 5.217490286938137e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.37 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.37 Order of pole (three term test) = 1.07e-13 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) = 0.2792532170069392 absolute error = 1.455902065572445e-11 relative error = 5.213555214342155e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.38 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.38 Order of pole (three term test) = 7.595e-14 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) = 0.2795222113551477 absolute error = 1.456351705897418e-11 relative error = 5.210146624530403e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.39 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 1.076e-13 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) = 0.2797596105958119 absolute error = 1.456779141761899e-11 relative error = 5.207253251229561e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 1.519e-13 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) = 0.2799658651528522 absolute error = 1.45718992428101e-11 relative error = 5.204884258162249e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.41 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.41 Order of pole (three term test) = 2.142e-13 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) = 0.2801414155203385 absolute error = 1.457584053454752e-11 relative error = 5.203029515729598e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.42 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 2.258e-13 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) = 0.2802866926312848 absolute error = 1.457950427052879e-11 relative error = 5.201639840413828e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.43 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.43 Order of pole (three term test) = 2.112e-13 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) = 0.2804021182108033 absolute error = 1.458311249535882e-11 relative error = 5.200785425291912e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.44 Order of pole (three term test) = 2.956e-13 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) = 0.2804881051143705 absolute error = 1.458644316443269e-11 relative error = 5.200378518455727e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.45 Order of pole (three term test) = 2.064e-13 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) = 0.2805450576519179 absolute error = 1.458971832235534e-11 relative error = 5.200490233271566e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 7.191e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y[1] (analytic) = 0.2805733718838266 y[1] (numeric) = 0.2805733718984194 absolute error = 1.459282694682429e-11 relative error = 5.201073376580637e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.47 Order of pole (three term test) = 2e-13 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) = 0.2805734359916129 absolute error = 1.459582454899078e-11 relative error = 5.202140572632964e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.48 Order of pole (three term test) = 2.775e-13 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) = 0.2805456304174579 absolute error = 1.45987111288548e-11 relative error = 5.203685086055797e-09 % Desired digits = 10 Estimated correct digits = 11 Correct digits = 11 h = 0.01 Radius of convergence (given) for eq 1 = 1.49 Order of pole (given) = 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.49 Order of pole (three term test) = 1.921e-13 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 = 90 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 101.1 %