##############ECHO OF PROBLEM################# ##############temp/sqrt_tonepostode.ode################# diff ( y , x , 1 ) = sqrt ( x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.5; x_end=1.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=0.001; glob_type_given_pole=1; array_given_rad_poles[1][1]=0.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=1.5; 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(2.0*expt(x,1.5)/3.0); } /* 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 = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000 step_error = 7.905694150420948e-14 est_needed_step_err = 7.905694150420948e-14 opt_iter = 1 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.001 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000 step_error = 7.905694150420948e-14 est_needed_step_err = 7.905694150420948e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.285783216869341e-103 estimated_step_error = 9.285783216869341e-103 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.002 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 500 step_error = 1.118033988749895e-13 est_needed_step_err = 1.118033988749895e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.375202760816313e-92 estimated_step_error = 6.375202760816313e-92 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.004 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 250 step_error = 1.58113883008419e-13 est_needed_step_err = 1.58113883008419e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.372866438037111e-81 estimated_step_error = 4.372866438037111e-81 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 min_size = 0.2357022603955159 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 0.008 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 125 step_error = 2.23606797749979e-13 est_needed_step_err = 2.23606797749979e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.993886267121181e-70 estimated_step_error = 2.993886267121181e-70 Double H and LOOP opt_iter = 5 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3125 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y[1] (analytic) = 0.2357022603955159 y[1] (numeric) = 0.2357022603955159 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.5 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.51 y[1] (analytic) = 0.2428085665704569 y[1] (numeric) = 0.2428085665704569 absolute error = 2.775557561562891e-17 relative error = 1.143105286920548e-14 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.51 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.51 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.52 y[1] (analytic) = 0.2499848884321699 y[1] (numeric) = 0.24998488843217 absolute error = 2.775557561562891e-17 relative error = 1.110290137524054e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.52 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.52 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.53 y[1] (analytic) = 0.257230549421245 y[1] (numeric) = 0.257230549421245 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 = 0.53 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.53 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.54 y[1] (analytic) = 0.2645448922205832 y[1] (numeric) = 0.2645448922205832 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 = 0.54 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.54 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.55 y[1] (analytic) = 0.2719272778601743 y[1] (numeric) = 0.2719272778601743 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 = 0.55 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.55 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5600000000000001 y[1] (analytic) = 0.279377084879121 y[1] (numeric) = 0.279377084879121 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 = 0.56 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.56 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5700000000000001 y[1] (analytic) = 0.2868937085402886 y[1] (numeric) = 0.2868937085402885 absolute error = 5.551115123125783e-17 relative error = 1.934903052203474e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.57 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.57 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5800000000000001 y[1] (analytic) = 0.2944765600934045 y[1] (numeric) = 0.2944765600934044 absolute error = 5.551115123125783e-17 relative error = 1.885078772098205e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.58 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.58 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5900000000000001 y[1] (analytic) = 0.302125066082832 y[1] (numeric) = 0.3021250660828319 absolute error = 1.110223024625157e-16 relative error = 3.674713386147089e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.59 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.59 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6000000000000001 y[1] (analytic) = 0.3098386676965934 y[1] (numeric) = 0.3098386676965934 absolute error = 5.551115123125783e-17 relative error = 1.791614702062191e-14 % 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) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6100000000000001 y[1] (analytic) = 0.3176168201535374 y[1] (numeric) = 0.3176168201535373 absolute error = 1.110223024625157e-16 relative error = 3.495479314000026e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.61 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.61 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6200000000000001 y[1] (analytic) = 0.3254589921258216 y[1] (numeric) = 0.3254589921258215 absolute error = 5.551115123125783e-17 relative error = 1.705626594265288e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.62 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.62 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6300000000000001 y[1] (analytic) = 0.3333646651941385 y[1] (numeric) = 0.3333646651941384 absolute error = 5.551115123125783e-17 relative error = 1.665178017560149e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.63 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.63 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6400000000000001 y[1] (analytic) = 0.3413333333333334 y[1] (numeric) = 0.3413333333333334 absolute error = 5.551115123125783e-17 relative error = 1.626303258728256e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.64 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.64 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6500000000000001 y[1] (analytic) = 0.3493645024262706 y[1] (numeric) = 0.3493645024262705 absolute error = 5.551115123125783e-17 relative error = 1.588917902240879e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.65 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.65 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6600000000000001 y[1] (analytic) = 0.3574576898039823 y[1] (numeric) = 0.3574576898039823 absolute error = 5.551115123125783e-17 relative error = 1.55294326614426e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.66 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.66 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6700000000000002 y[1] (analytic) = 0.3656124238103029 y[1] (numeric) = 0.3656124238103028 absolute error = 1.110223024625157e-16 relative error = 3.036611866343998e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.67 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.67 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6800000000000002 y[1] (analytic) = 0.3738282433893347 y[1] (numeric) = 0.3738282433893346 absolute error = 1.110223024625157e-16 relative error = 2.969874653020482e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.68 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.68 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6900000000000002 y[1] (analytic) = 0.3821046976942316 y[1] (numeric) = 0.3821046976942314 absolute error = 1.110223024625157e-16 relative error = 2.905546650760051e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.69 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.69 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000002 y[1] (analytic) = 0.3904413457159021 y[1] (numeric) = 0.3904413457159019 absolute error = 1.665334536937735e-16 relative error = 4.26526174855848e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.7 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100000000000002 y[1] (analytic) = 0.3988377559303478 y[1] (numeric) = 0.3988377559303476 absolute error = 1.665334536937735e-16 relative error = 4.175468626467163e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7200000000000002 y[1] (analytic) = 0.4072935059634515 y[1] (numeric) = 0.4072935059634514 absolute error = 1.665334536937735e-16 relative error = 4.088782444488996e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7300000000000002 y[1] (analytic) = 0.41580818227212 y[1] (numeric) = 0.4158081822721199 absolute error = 1.665334536937735e-16 relative error = 4.005054753462931e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7400000000000002 y[1] (analytic) = 0.4243813798407698 y[1] (numeric) = 0.4243813798407696 absolute error = 2.220446049250313e-16 relative error = 5.232194801014683e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7500000000000002 y[1] (analytic) = 0.4330127018922195 y[1] (numeric) = 0.4330127018922193 absolute error = 1.665334536937735e-16 relative error = 3.845925372767126e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600000000000002 y[1] (analytic) = 0.4417017596121218 y[1] (numeric) = 0.4417017596121215 absolute error = 2.220446049250313e-16 relative error = 5.027025591204769e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700000000000002 y[1] (analytic) = 0.4504481718861291 y[1] (numeric) = 0.4504481718861289 absolute error = 2.220446049250313e-16 relative error = 4.929415164352426e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7800000000000002 y[1] (analytic) = 0.4592515650490482 y[1] (numeric) = 0.459251565049048 absolute error = 2.220446049250313e-16 relative error = 4.834923206006209e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7900000000000003 y[1] (analytic) = 0.4681115726452879 y[1] (numeric) = 0.4681115726452877 absolute error = 1.665334536937735e-16 relative error = 3.557558997157381e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000003 y[1] (analytic) = 0.4770278351999553 y[1] (numeric) = 0.4770278351999551 absolute error = 2.220446049250313e-16 relative error = 4.654751537338635e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100000000000003 y[1] (analytic) = 0.4860000000000003 y[1] (numeric) = 0.486 absolute error = 2.775557561562891e-16 relative error = 5.711023789224053e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8200000000000003 y[1] (analytic) = 0.4950277208848457 y[1] (numeric) = 0.4950277208848454 absolute error = 2.775557561562891e-16 relative error = 5.606872998145788e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8300000000000003 y[1] (analytic) = 0.5041106580459848 y[1] (numeric) = 0.5041106580459845 absolute error = 2.220446049250313e-16 relative error = 4.404679833307085e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8400000000000003 y[1] (analytic) = 0.5132484778350543 y[1] (numeric) = 0.5132484778350541 absolute error = 2.220446049250313e-16 relative error = 4.326259395091496e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8500000000000003 y[1] (analytic) = 0.5224408525799306 y[1] (numeric) = 0.5224408525799303 absolute error = 2.220446049250313e-16 relative error = 4.250138629636734e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8600000000000003 y[1] (analytic) = 0.5316874604084206 y[1] (numeric) = 0.5316874604084204 absolute error = 2.220446049250313e-16 relative error = 4.176224219289763e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8700000000000003 y[1] (analytic) = 0.5409879850791516 y[1] (numeric) = 0.5409879850791514 absolute error = 2.220446049250313e-16 relative error = 4.104427659193653e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8800000000000003 y[1] (analytic) = 0.5503421158192827 y[1] (numeric) = 0.5503421158192825 absolute error = 2.220446049250313e-16 relative error = 4.034664957350723e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8900000000000003 y[1] (analytic) = 0.5597495471686922 y[1] (numeric) = 0.559749547168692 absolute error = 2.220446049250313e-16 relative error = 3.966856356528923e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000004 y[1] (analytic) = 0.5692099788303085 y[1] (numeric) = 0.5692099788303084 absolute error = 1.110223024625157e-16 relative error = 1.950463038098166e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100000000000004 y[1] (analytic) = 0.5787231155262808 y[1] (numeric) = 0.5787231155262805 absolute error = 2.220446049250313e-16 relative error = 3.836802072837678e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200000000000004 y[1] (analytic) = 0.5882886668596939 y[1] (numeric) = 0.5882886668596937 absolute error = 2.220446049250313e-16 relative error = 3.774415817158495e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300000000000004 y[1] (analytic) = 0.5979063471815635 y[1] (numeric) = 0.5979063471815633 absolute error = 2.220446049250313e-16 relative error = 3.713702086818691e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400000000000004 y[1] (analytic) = 0.607575875462847 y[1] (numeric) = 0.6075758754628466 absolute error = 3.33066907387547e-16 relative error = 5.48189816018977e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500000000000004 y[1] (analytic) = 0.6172969751712348 y[1] (numeric) = 0.6172969751712345 absolute error = 3.33066907387547e-16 relative error = 5.395570054351165e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9600000000000004 y[1] (analytic) = 0.627069374152494 y[1] (numeric) = 0.6270693741524938 absolute error = 2.220446049250313e-16 relative error = 3.540989467475306e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9700000000000004 y[1] (analytic) = 0.6368928045161485 y[1] (numeric) = 0.6368928045161483 absolute error = 2.220446049250313e-16 relative error = 3.486373269575875e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9800000000000004 y[1] (analytic) = 0.646767002525296 y[1] (numeric) = 0.6467670025252956 absolute error = 3.33066907387547e-16 relative error = 5.149720163321416e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9900000000000004 y[1] (analytic) = 0.6566917084903696 y[1] (numeric) = 0.6566917084903693 absolute error = 3.33066907387547e-16 relative error = 5.071891468726095e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (analytic) = 0.6666666666666671 y[1] (numeric) = 0.6666666666666667 absolute error = 3.33066907387547e-16 relative error = 4.996003610813201e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.01 y[1] (analytic) = 0.6766916251554737 y[1] (numeric) = 0.6766916251554733 absolute error = 3.33066907387547e-16 relative error = 4.921989500180721e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.01 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.02 y[1] (analytic) = 0.6867663358086218 y[1] (numeric) = 0.6867663358086213 absolute error = 4.440892098500626e-16 relative error = 6.466379999933704e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.02 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.03 y[1] (analytic) = 0.6968905541363329 y[1] (numeric) = 0.6968905541363325 absolute error = 4.440892098500626e-16 relative error = 6.37243835799194e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.04 y[1] (analytic) = 0.7070640392182 y[1] (numeric) = 0.7070640392181996 absolute error = 4.440892098500626e-16 relative error = 6.280749482622417e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.04 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.04 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.05 y[1] (analytic) = 0.7172865536171723 y[1] (numeric) = 0.717286553617172 absolute error = 3.33066907387547e-16 relative error = 4.643428845946418e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.06 y[1] (analytic) = 0.7275578632964153 y[1] (numeric) = 0.7275578632964148 absolute error = 4.440892098500626e-16 relative error = 6.103833554048685e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.06 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.070000000000001 y[1] (analytic) = 0.7378777375389207 y[1] (numeric) = 0.7378777375389203 absolute error = 4.440892098500626e-16 relative error = 6.018466031124002e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.080000000000001 y[1] (analytic) = 0.7482459488697555 y[1] (numeric) = 0.7482459488697552 absolute error = 3.33066907387547e-16 relative error = 4.451302514776765e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.08 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.08 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.090000000000001 y[1] (analytic) = 0.7586622729808338 y[1] (numeric) = 0.7586622729808334 absolute error = 3.33066907387547e-16 relative error = 4.390186770180429e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.09 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.09 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y[1] (analytic) = 0.7691264886581117 y[1] (numeric) = 0.7691264886581113 absolute error = 4.440892098500626e-16 relative error = 5.773942471086404e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.110000000000001 y[1] (analytic) = 0.7796383777111032 y[1] (numeric) = 0.7796383777111028 absolute error = 4.440892098500626e-16 relative error = 5.696092221035082e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.11 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.120000000000001 y[1] (analytic) = 0.7901977249046249 y[1] (numeric) = 0.7901977249046245 absolute error = 4.440892098500626e-16 relative error = 5.6199758092655e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.12 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.12 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.130000000000001 y[1] (analytic) = 0.8008043178926775 y[1] (numeric) = 0.800804317892677 absolute error = 4.440892098500626e-16 relative error = 5.545539652167295e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.13 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.13 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.140000000000001 y[1] (analytic) = 0.8114579471543802 y[1] (numeric) = 0.8114579471543798 absolute error = 4.440892098500626e-16 relative error = 5.472732276606497e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.14 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.14 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.150000000000001 y[1] (analytic) = 0.8221584059318773 y[1] (numeric) = 0.8221584059318768 absolute error = 4.440892098500626e-16 relative error = 5.401504219210758e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.160000000000001 y[1] (analytic) = 0.8329054901701373 y[1] (numeric) = 0.8329054901701368 absolute error = 4.440892098500626e-16 relative error = 5.331807931285802e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.16 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.170000000000001 y[1] (analytic) = 0.8436989984585742 y[1] (numeric) = 0.8436989984585737 absolute error = 5.551115123125783e-16 relative error = 6.579497111253646e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.17 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.180000000000001 y[1] (analytic) = 0.8545387319744177 y[1] (numeric) = 0.8545387319744171 absolute error = 5.551115123125783e-16 relative error = 6.496036885653963e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.18 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.190000000000001 y[1] (analytic) = 0.8654244944277673 y[1] (numeric) = 0.8654244944277668 absolute error = 4.440892098500626e-16 relative error = 5.131461065747875e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.19 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.19 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y[1] (analytic) = 0.8763560920082664 y[1] (numeric) = 0.8763560920082659 absolute error = 4.440892098500626e-16 relative error = 5.067451620406761e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.210000000000001 y[1] (analytic) = 0.8873333333333341 y[1] (numeric) = 0.8873333333333335 absolute error = 5.551115123125783e-16 relative error = 6.255952430269472e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.21 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.220000000000001 y[1] (analytic) = 0.8983560293978979 y[1] (numeric) = 0.8983560293978974 absolute error = 5.551115123125783e-16 relative error = 6.179192816066796e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.230000000000001 y[1] (analytic) = 0.9094239935255729 y[1] (numeric) = 0.9094239935255723 absolute error = 5.551115123125783e-16 relative error = 6.103990176909365e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.23 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.240000000000001 y[1] (analytic) = 0.9205370413212309 y[1] (numeric) = 0.9205370413212305 absolute error = 4.440892098500626e-16 relative error = 4.824240523908403e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.24 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.250000000000001 y[1] (analytic) = 0.9316949906249131 y[1] (numeric) = 0.9316949906249126 absolute error = 5.551115123125783e-16 relative error = 5.95808196779345e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.260000000000001 y[1] (analytic) = 0.942897661467034 y[1] (numeric) = 0.9428976614670335 absolute error = 5.551115123125783e-16 relative error = 5.887293340497763e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.26 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.26 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.270000000000001 y[1] (analytic) = 0.954144876024834 y[1] (numeric) = 0.9541448760248336 absolute error = 4.440892098500626e-16 relative error = 4.654316351833598e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.27 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.280000000000001 y[1] (analytic) = 0.9654364585800336 y[1] (numeric) = 0.9654364585800331 absolute error = 4.440892098500626e-16 relative error = 4.599880250050119e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.28 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.290000000000001 y[1] (analytic) = 0.9767722354776479 y[1] (numeric) = 0.9767722354776474 absolute error = 5.551115123125783e-16 relative error = 5.683121327062754e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.29 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.29 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y[1] (analytic) = 0.9881520350859204 y[1] (numeric) = 0.9881520350859199 absolute error = 5.551115123125783e-16 relative error = 5.617673117116143e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.310000000000001 y[1] (analytic) = 0.9995756877573391 y[1] (numeric) = 0.9995756877573384 absolute error = 6.661338147750939e-16 relative error = 6.66416583490181e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.31 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.320000000000001 y[1] (analytic) = 1.011043025790694 y[1] (numeric) = 1.011043025790693 absolute error = 6.661338147750939e-16 relative error = 6.588580285731549e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.32 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.330000000000001 y[1] (analytic) = 1.022553883394145 y[1] (numeric) = 1.022553883394144 absolute error = 6.661338147750939e-16 relative error = 6.514412840172372e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.33 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.33 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.340000000000001 y[1] (analytic) = 1.034108096649261 y[1] (numeric) = 1.03410809664926 absolute error = 6.661338147750939e-16 relative error = 6.441626527570133e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.34 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.34 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.350000000000001 y[1] (analytic) = 1.045705503476003 y[1] (numeric) = 1.045705503476003 absolute error = 6.661338147750939e-16 relative error = 6.370185607332229e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.35 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.360000000000001 y[1] (analytic) = 1.057345943598615 y[1] (numeric) = 1.057345943598615 absolute error = 6.661338147750939e-16 relative error = 6.300055519274479e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.36 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.370000000000001 y[1] (analytic) = 1.069029258512393 y[1] (numeric) = 1.069029258512393 absolute error = 4.440892098500626e-16 relative error = 4.154135224212989e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.37 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.37 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.380000000000001 y[1] (analytic) = 1.080755291451308 y[1] (numeric) = 1.080755291451308 absolute error = 4.440892098500626e-16 relative error = 4.109063479612586e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.38 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.38 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.390000000000001 y[1] (analytic) = 1.092523887356449 y[1] (numeric) = 1.092523887356448 absolute error = 4.440892098500626e-16 relative error = 4.064800916386492e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.39 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y[1] (analytic) = 1.104334892845263 y[1] (numeric) = 1.104334892845262 absolute error = 2.220446049250313e-16 relative error = 2.010663670627528e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.410000000000001 y[1] (analytic) = 1.116188156181565 y[1] (numeric) = 1.116188156181565 absolute error = 2.220446049250313e-16 relative error = 1.989311602128417e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.41 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.41 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.420000000000001 y[1] (analytic) = 1.128083527246297 y[1] (numeric) = 1.128083527246297 absolute error = 2.220446049250313e-16 relative error = 1.968334786937739e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.42 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.430000000000001 y[1] (analytic) = 1.140020857509001 y[1] (numeric) = 1.140020857509001 absolute error = 4.440892098500626e-16 relative error = 3.895448113295211e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.43 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.43 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.440000000000001 y[1] (analytic) = 1.152000000000001 y[1] (numeric) = 1.152000000000001 absolute error = 4.440892098500626e-16 relative error = 3.854941057726234e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.44 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.450000000000001 y[1] (analytic) = 1.164020809283256 y[1] (numeric) = 1.164020809283256 absolute error = 4.440892098500626e-16 relative error = 3.815131192744825e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.45 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.460000000000001 y[1] (analytic) = 1.176083141429873 y[1] (numeric) = 1.176083141429872 absolute error = 4.440892098500626e-16 relative error = 3.776001833596071e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.470000000000001 y[1] (analytic) = 1.188186853992251 y[1] (numeric) = 1.18818685399225 absolute error = 4.440892098500626e-16 relative error = 3.737536805410228e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.47 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.480000000000001 y[1] (analytic) = 1.20033180597885 y[1] (numeric) = 1.200331805978849 absolute error = 4.440892098500626e-16 relative error = 3.699720424286479e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.48 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.490000000000001 y[1] (analytic) = 1.212517857829549 y[1] (numeric) = 1.212517857829548 absolute error = 6.661338147750939e-16 relative error = 5.49380621880075e-14 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 1.49 Order of pole (given) = 1.5 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.49 Order of pole (three term test) = 1.5 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sqrt ( x ) ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 101 %