##############ECHO OF PROBLEM################# ##############temp/sinh_sqrt_sm_hpostode.ode################# diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=2.0; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_h=0.0000001; glob_type_given_pole=1; array_given_rad_poles[1][1]=-2.0; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; 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(20.0 * sqrt(0.1 * x + 0.2) * cosh( sqrt(0.1 * x + 0.2)) - 20.0 * sinh( sqrt(0.1 * x + 0.2))); } /* 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 = 1 estimated_steps = 1000000 step_error = 2.5e-15 est_needed_step_err = 2.5e-15 opt_iter = 1 SETTING H FOR MAX H Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 1.754980921980319 y[1] (numeric) = 1.754980921980319 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 1e-07 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.010000099983634 y[1] (analytic) = 1.761740464293613 y[1] (numeric) = 1.761740464256989 absolute error = 3.662425918093959e-11 relative error = 2.078868024162937e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.020000099967268 y[1] (analytic) = 1.768509471621774 y[1] (numeric) = 1.768509471548585 absolute error = 7.318989858617897e-11 relative error = 4.138507582832548e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.030000099950902 y[1] (analytic) = 1.775288003860249 y[1] (numeric) = 1.775288003750553 absolute error = 1.096958079926935e-10 relative error = 6.179042935803491e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.040000099934537 y[1] (analytic) = 1.782076053391838 y[1] (numeric) = 1.782076053245697 absolute error = 1.461413212666685e-10 relative error = 8.200622021070122e-09 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 11 h = 1e-07 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.050000099918171 y[1] (analytic) = 1.788873612633523 y[1] (numeric) = 1.788873612450971 absolute error = 1.825521955822751e-10 relative error = 1.020486826419937e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.060000099901805 y[1] (analytic) = 1.795680674036266 y[1] (numeric) = 1.795680673817359 absolute error = 2.189068926128357e-10 relative error = 1.219074726247316e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.070000099885439 y[1] (analytic) = 1.802497230084796 y[1] (numeric) = 1.802497229829578 absolute error = 2.552178468562261e-10 relative error = 1.415912560621353e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.080000099869074 y[1] (analytic) = 1.809323273297387 y[1] (numeric) = 1.809323273005926 absolute error = 2.914610774951143e-10 relative error = 1.610884477067181e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.090000099852708 y[1] (analytic) = 1.816158796225663 y[1] (numeric) = 1.816158795898015 absolute error = 3.276479088043516e-10 relative error = 1.804070819607122e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000099836342 y[1] (analytic) = 1.823003791454365 y[1] (numeric) = 1.823003791090578 absolute error = 3.637872225681349e-10 relative error = 1.995537388750634e-08 % Desired digits = 10 Estimated correct digits = 10 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.110000099819976 y[1] (analytic) = 1.82985825160117 y[1] (numeric) = 1.829858251201298 absolute error = 3.998719133591067e-10 relative error = 2.185261689036345e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.12000009980361 y[1] (analytic) = 1.836722169316474 y[1] (numeric) = 1.836722168880566 absolute error = 4.359079763815998e-10 relative error = 2.373292943612809e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.130000099787245 y[1] (analytic) = 1.843595537283178 y[1] (numeric) = 1.843595536811292 absolute error = 4.718863078068125e-10 relative error = 2.559597798236209e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.140000099770879 y[1] (analytic) = 1.850478348216516 y[1] (numeric) = 1.850478347708724 absolute error = 5.077920306462147e-10 relative error = 2.744112251492284e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.150000099754513 y[1] (analytic) = 1.857370594863831 y[1] (numeric) = 1.857370594320156 absolute error = 5.436744388020998e-10 relative error = 2.927118800661093e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.160000099738147 y[1] (analytic) = 1.864272270004376 y[1] (numeric) = 1.86427226942487 absolute error = 5.795057766988521e-10 relative error = 3.108482521694601e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.170000099721781 y[1] (analytic) = 1.871183366449136 y[1] (numeric) = 1.871183365833853 absolute error = 6.152836018458174e-10 relative error = 3.288205810707983e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.180000099705416 y[1] (analytic) = 1.878103877040619 y[1] (numeric) = 1.878103876389616 absolute error = 6.510028072170826e-10 relative error = 3.466276893282846e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.19000009968905 y[1] (analytic) = 1.885033794652674 y[1] (numeric) = 1.88503379396599 absolute error = 6.866842650055105e-10 relative error = 3.642822038275633e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000099672684 y[1] (analytic) = 1.89197311219027 y[1] (numeric) = 1.89197311146797 absolute error = 7.222995535016707e-10 relative error = 3.817705171642161e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.210000099656318 y[1] (analytic) = 1.898921822589358 y[1] (numeric) = 1.898921821831488 absolute error = 7.578702110322411e-10 relative error = 3.991055355816671e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.220000099639952 y[1] (analytic) = 1.905879918816645 y[1] (numeric) = 1.905879918023251 absolute error = 7.933935730619623e-10 relative error = 4.162872829651188e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.230000099623587 y[1] (analytic) = 1.912847393869402 y[1] (numeric) = 1.912847393040517 absolute error = 8.288847386239695e-10 relative error = 4.33325074065245e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.240000099607221 y[1] (analytic) = 1.919824240775307 y[1] (numeric) = 1.919824239910998 absolute error = 8.643095128491041e-10 relative error = 4.502024167066766e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.250000099590855 y[1] (analytic) = 1.926810452592248 y[1] (numeric) = 1.926810451692568 absolute error = 8.996796641014271e-10 relative error = 4.669269169113323e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.260000099574489 y[1] (analytic) = 1.933806022408136 y[1] (numeric) = 1.933806021473121 absolute error = 9.350156204845916e-10 relative error = 4.835105536181092e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.270000099558124 y[1] (analytic) = 1.940810943340734 y[1] (numeric) = 1.940810942370448 absolute error = 9.702867398431181e-10 relative error = 4.999388235996626e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.280000099541758 y[1] (analytic) = 1.947825208537468 y[1] (numeric) = 1.947825207531961 absolute error = 1.005507455076327e-09 relative error = 5.162205780421723e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.290000099525392 y[1] (analytic) = 1.954848811175264 y[1] (numeric) = 1.954848810134576 absolute error = 1.040687758191439e-09 relative error = 5.323622738710788e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300000099509026 y[1] (analytic) = 1.961881744460355 y[1] (numeric) = 1.961881743384545 absolute error = 1.075809441530851e-09 relative error = 5.483559060420169e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.31000009949266 y[1] (analytic) = 1.968924001628118 y[1] (numeric) = 1.968924000517234 absolute error = 1.110883829369413e-09 relative error = 5.642085872541629e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.320000099476295 y[1] (analytic) = 1.975975575942902 y[1] (numeric) = 1.975975574796991 absolute error = 1.145911365796337e-09 relative error = 5.799218268421802e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.330000099459929 y[1] (analytic) = 1.983036460697846 y[1] (numeric) = 1.983036459516955 absolute error = 1.180891384677807e-09 relative error = 5.954965569630736e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.340000099443563 y[1] (analytic) = 1.990106649214715 y[1] (numeric) = 1.990106647998903 absolute error = 1.215811673560552e-09 relative error = 6.109278987838688e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.350000099427197 y[1] (analytic) = 1.997186134843748 y[1] (numeric) = 1.997186133593047 absolute error = 1.250700432109397e-09 relative error = 6.262312812457249e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.360000099410831 y[1] (analytic) = 2.004274910963442 y[1] (numeric) = 2.004274909677874 absolute error = 1.285568096420775e-09 relative error = 6.414130563570296e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.370000099394466 y[1] (analytic) = 2.011372970980451 y[1] (numeric) = 2.011372969660099 absolute error = 1.320352271960701e-09 relative error = 6.564432807889876e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3800000993781 y[1] (analytic) = 2.018480308329362 y[1] (numeric) = 2.018480306974277 absolute error = 1.355084933152284e-09 relative error = 6.713391889732373e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.390000099361734 y[1] (analytic) = 2.025596916472569 y[1] (numeric) = 2.02559691508279 absolute error = 1.38977940267182e-09 relative error = 6.861085694640673e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400000099345368 y[1] (analytic) = 2.032722788900106 y[1] (numeric) = 2.032722787475677 absolute error = 1.424429019181161e-09 relative error = 7.007492743031191e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.410000099329002 y[1] (analytic) = 2.039857919129469 y[1] (numeric) = 2.039857917670453 absolute error = 1.459015575022704e-09 relative error = 7.152535288562424e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.420000099312637 y[1] (analytic) = 2.04700230070546 y[1] (numeric) = 2.047002299211902 absolute error = 1.493557277854052e-09 relative error = 7.296314602769749e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.430000099296271 y[1] (analytic) = 2.054155927200057 y[1] (numeric) = 2.054155925672 absolute error = 1.528056792210464e-09 relative error = 7.438854918347415e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.440000099279905 y[1] (analytic) = 2.061318792212219 y[1] (numeric) = 2.061318790649706 absolute error = 1.56251322991352e-09 relative error = 7.580162931695888e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.450000099263539 y[1] (analytic) = 2.068490889367759 y[1] (numeric) = 2.068490887770834 absolute error = 1.596924370517172e-09 relative error = 7.720238840429592e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.460000099247174 y[1] (analytic) = 2.075672212319169 y[1] (numeric) = 2.0756722106879 absolute error = 1.631269785917766e-09 relative error = 7.858995154611296e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.470000099230808 y[1] (analytic) = 2.082862754745477 y[1] (numeric) = 2.082862753079893 absolute error = 1.66558455916288e-09 relative error = 7.99661214051721e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.480000099214442 y[1] (analytic) = 2.090062510352094 y[1] (numeric) = 2.090062508652253 absolute error = 1.699841600810714e-09 relative error = 8.132970149894497e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.490000099198076 y[1] (analytic) = 2.097271472870666 y[1] (numeric) = 2.097271471136598 absolute error = 1.734068000303068e-09 relative error = 8.268209541464564e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.50000009918171 y[1] (analytic) = 2.104489636058908 y[1] (numeric) = 2.104489634290666 absolute error = 1.76824155317945e-09 relative error = 8.402234550752403e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.510000099165345 y[1] (analytic) = 2.111716993700494 y[1] (numeric) = 2.111716991898117 absolute error = 1.802376470294575e-09 relative error = 8.535123199137392e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.520000099148979 y[1] (analytic) = 2.118953539604867 y[1] (numeric) = 2.118953537768391 absolute error = 1.836476304362122e-09 relative error = 8.666902176177871e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.530000099132613 y[1] (analytic) = 2.126199267607095 y[1] (numeric) = 2.126199265736557 absolute error = 1.870537946757622e-09 relative error = 8.797566508725196e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.540000099116247 y[1] (analytic) = 2.133454171567779 y[1] (numeric) = 2.133454169663242 absolute error = 1.904536972574533e-09 relative error = 8.92701140692877e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.550000099099881 y[1] (analytic) = 2.140718245372836 y[1] (numeric) = 2.140718243434359 absolute error = 1.938477378615744e-09 relative error = 9.055266300484726e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.560000099083516 y[1] (analytic) = 2.147991482933412 y[1] (numeric) = 2.147991480961053 absolute error = 1.972359164881254e-09 relative error = 9.182341645916098e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.57000009906715 y[1] (analytic) = 2.155273878185715 y[1] (numeric) = 2.155273876179506 absolute error = 2.006209864902075e-09 relative error = 9.308375539682592e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.580000099050784 y[1] (analytic) = 2.162565425090881 y[1] (numeric) = 2.162565423050864 absolute error = 2.040016600091121e-09 relative error = 9.433317375844899e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.590000099034418 y[1] (analytic) = 2.169866117634822 y[1] (numeric) = 2.169866115561027 absolute error = 2.073794469481527e-09 relative error = 9.557246194258224e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000099018053 y[1] (analytic) = 2.177175949828115 y[1] (numeric) = 2.177175947720595 absolute error = 2.10751993634517e-09 relative error = 9.680062543918677e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.610000099001687 y[1] (analytic) = 2.184494915705841 y[1] (numeric) = 2.184494913564632 absolute error = 2.141208543804396e-09 relative error = 9.801847229809374e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.620000098985321 y[1] (analytic) = 2.191823009327441 y[1] (numeric) = 2.191823007152614 absolute error = 2.174827429257675e-09 relative error = 9.922459158438248e-08 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 10 h = 1e-07 Radius of convergence (given) for eq 1 = 4.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.630000098968955 y[1] (analytic) = 2.199160224776627 y[1] (numeric) = 2.199160222568212 absolute error = 2.208414784377055e-09 relative error = 1.004208224346804e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.640000098952589 y[1] (analytic) = 2.206506556161191 y[1] (numeric) = 2.206506553919238 absolute error = 2.241953289683352e-09 relative error = 1.016064640018034e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.650000098936224 y[1] (analytic) = 2.213861997612916 y[1] (numeric) = 2.213861995337463 absolute error = 2.275453603317601e-09 relative error = 1.027820887558075e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.660000098919858 y[1] (analytic) = 2.221226543287408 y[1] (numeric) = 2.221226540978486 absolute error = 2.308921942528741e-09 relative error = 1.039480619167978e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.670000098903492 y[1] (analytic) = 2.228600187363998 y[1] (numeric) = 2.228600185021639 absolute error = 2.342358751405982e-09 relative error = 1.051044850793331e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.680000098887126 y[1] (analytic) = 2.235982924045574 y[1] (numeric) = 2.235982921669853 absolute error = 2.375720953295968e-09 relative error = 1.062495123619981e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.69000009887076 y[1] (analytic) = 2.243374747558505 y[1] (numeric) = 2.24337474514945 absolute error = 2.409054733476523e-09 relative error = 1.073853013678758e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000098854395 y[1] (analytic) = 2.250775652152463 y[1] (numeric) = 2.250775649710127 absolute error = 2.442335222951897e-09 relative error = 1.085108247290769e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.710000098838029 y[1] (analytic) = 2.258185632100313 y[1] (numeric) = 2.258185629624738 absolute error = 2.475574856219964e-09 relative error = 1.096267207190341e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.720000098821663 y[1] (analytic) = 2.265604681697997 y[1] (numeric) = 2.265604679189214 absolute error = 2.508782959154132e-09 relative error = 1.10733482298151e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.730000098805297 y[1] (analytic) = 2.273032795264399 y[1] (numeric) = 2.273032792722471 absolute error = 2.541928001420501e-09 relative error = 1.118297987920066e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.740000098788931 y[1] (analytic) = 2.280469967141219 y[1] (numeric) = 2.28046996456619 absolute error = 2.575028634765886e-09 relative error = 1.129165773664594e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.750000098772566 y[1] (analytic) = 2.287916191692851 y[1] (numeric) = 2.287916189084747 absolute error = 2.608104399115518e-09 relative error = 1.139947524557601e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7600000987562 y[1] (analytic) = 2.295371463306267 y[1] (numeric) = 2.295371460665146 absolute error = 2.641121099600241e-09 relative error = 1.150629055828704e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.770000098739834 y[1] (analytic) = 2.302835776390893 y[1] (numeric) = 2.302835773716796 absolute error = 2.674096943877657e-09 relative error = 1.161219124391328e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.780000098723468 y[1] (analytic) = 2.31030912537847 y[1] (numeric) = 2.310309122671444 absolute error = 2.707026602877249e-09 relative error = 1.171716188600428e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.790000098707103 y[1] (analytic) = 2.317791504722965 y[1] (numeric) = 2.317791501983058 absolute error = 2.739907856152968e-09 relative error = 1.182120070148612e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000098690737 y[1] (analytic) = 2.325282908900444 y[1] (numeric) = 2.325282906127693 absolute error = 2.772751805935059e-09 relative error = 1.192436324767987e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.810000098674371 y[1] (analytic) = 2.332783332408935 y[1] (numeric) = 2.332783329603374 absolute error = 2.805561116758781e-09 relative error = 1.20266682198112e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.820000098658005 y[1] (analytic) = 2.340292769768313 y[1] (numeric) = 2.340292766929992 absolute error = 2.838321133680211e-09 relative error = 1.212806008865806e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.830000098641639 y[1] (analytic) = 2.347811215520217 y[1] (numeric) = 2.347811212649166 absolute error = 2.87105050844616e-09 relative error = 1.222862591961001e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.840000098625274 y[1] (analytic) = 2.355338664227894 y[1] (numeric) = 2.355338661324166 absolute error = 2.903727480685347e-09 relative error = 1.232828011014383e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.850000098608908 y[1] (analytic) = 2.362875110476111 y[1] (numeric) = 2.362875107539747 absolute error = 2.936363596717229e-09 relative error = 1.242707912787469e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.860000098592542 y[1] (analytic) = 2.370420548871035 y[1] (numeric) = 2.370420545902068 absolute error = 2.968966850147581e-09 relative error = 1.252506375529699e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.870000098576176 y[1] (analytic) = 2.377974974040102 y[1] (numeric) = 2.377974971038581 absolute error = 3.00152080967564e-09 relative error = 1.262217156379974e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.88000009855981 y[1] (analytic) = 2.385538380631937 y[1] (numeric) = 2.385538377597899 absolute error = 3.034037909799281e-09 relative error = 1.271846193895884e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.890000098543445 y[1] (analytic) = 2.393110763316216 y[1] (numeric) = 2.393110760249698 absolute error = 3.066517262340085e-09 relative error = 1.281393786424957e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000098527079 y[1] (analytic) = 2.400692116783567 y[1] (numeric) = 2.400692113684621 absolute error = 3.098945988710966e-09 relative error = 1.290855235890438e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.910000098510713 y[1] (analytic) = 2.40828243574547 y[1] (numeric) = 2.408282432614127 absolute error = 3.131343184747948e-09 relative error = 1.300239182194865e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.920000098494347 y[1] (analytic) = 2.415881714934109 y[1] (numeric) = 2.415881711770422 absolute error = 3.163687090079748e-09 relative error = 1.309537247011299e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.930000098477981 y[1] (analytic) = 2.42348994910232 y[1] (numeric) = 2.423489945906329 absolute error = 3.195991027382661e-09 relative error = 1.318755635263303e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.940000098461616 y[1] (analytic) = 2.431107133023447 y[1] (numeric) = 2.431107129795187 absolute error = 3.228260325727206e-09 relative error = 1.327897188024116e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.95000009844525 y[1] (analytic) = 2.438733261491237 y[1] (numeric) = 2.438733258230747 absolute error = 3.260489656042864e-09 relative error = 1.336960342292269e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.960000098428884 y[1] (analytic) = 2.446368329319759 y[1] (numeric) = 2.446368326027077 absolute error = 3.292681682864895e-09 relative error = 1.34594682387033e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.970000098412518 y[1] (analytic) = 2.454012331343254 y[1] (numeric) = 2.454012328018427 absolute error = 3.324826636230682e-09 relative error = 1.354853271829637e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.980000098396153 y[1] (analytic) = 2.461665262416071 y[1] (numeric) = 2.461665259059136 absolute error = 3.356934730192052e-09 relative error = 1.363684486857199e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.990000098379787 y[1] (analytic) = 2.469327117412575 y[1] (numeric) = 2.469327114023574 absolute error = 3.389001967946115e-09 relative error = 1.372439456906462e-07 % Desired digits = 10 Estimated correct digits = 9 Correct digits = 9 h = 1e-07 Radius of convergence (given) for eq 1 = 4.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 10000001 Total Elapsed Time = 9 Minutes 50.0 Seconds Elapsed Time(since restart) = 9 Minutes 50.0 Seconds Time to Timeout = 10.0 Seconds Percent Done = 100 %