##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 3 ) = sin(x); ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.5; /* # */ /* # trouble about Pi/2 */ /* # */ array_y_init[0 + 1] = exact_soln_y(x_start); array_y_init[1 + 1] = exact_soln_yp(x_start); array_y_init[2 + 1] = exact_soln_ypp(x_start); glob_look_poles=true; glob_max_iter=20; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(1.0 + cos(x)); } double exact_soln_yp (double x) { return(-sin(x)); } double exact_soln_ypp (double x) { return(-cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 1.4 estimated_steps = 1400000 step_error = 7.142857142857143e-17 est_needed_step_err = 7.142857142857143e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.467208605532302e-183 estimated_step_error = 2.467208605532302e-183 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.655715664606566e-175 estimated_step_error = 1.655715664606566e-175 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.111131969458436e-167 estimated_step_error = 1.111131969458436e-167 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.456680367024187e-160 estimated_step_error = 7.456680367024187e-160 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.004093412037818e-152 estimated_step_error = 5.004093412037818e-152 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.358190142481625e-144 estimated_step_error = 3.358190142481625e-144 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.25364312158092e-136 estimated_step_error = 2.25364312158092e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.512394117654307e-128 estimated_step_error = 1.512394117654307e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.014950270158056e-120 estimated_step_error = 1.014950270158056e-120 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.81121272440811e-113 estimated_step_error = 6.81121272440811e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.570923134360026e-105 estimated_step_error = 4.570923134360026e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.067488750234022e-97 estimated_step_error = 3.067488750234022e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.058549011618091e-89 estimated_step_error = 2.058549011618091e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.381458319740245e-81 estimated_step_error = 1.381458319740245e-81 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.270668118428106e-74 estimated_step_error = 9.270668118428106e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.221249002016116e-66 estimated_step_error = 6.221249002016116e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.174750875079242e-58 estimated_step_error = 4.174750875079242e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.801274754399603e-50 estimated_step_error = 2.801274754399603e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.995004165278026 y[1] (numeric) = 1.995004165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.11 y[1] (analytic) = 1.993956097956697 y[1] (numeric) = 1.993956097956697 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.12 y[1] (analytic) = 1.992808635853866 y[1] (numeric) = 1.992808635853866 absolute error = 2.220446049250313e-16 relative error = 1.114229439445855e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.13 y[1] (analytic) = 1.991561893714788 y[1] (numeric) = 1.991561893714788 absolute error = 2.220446049250313e-16 relative error = 1.114926960722569e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.14 y[1] (analytic) = 1.990215996212637 y[1] (numeric) = 1.990215996212637 absolute error = 2.220446049250313e-16 relative error = 1.115680937886039e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.15 y[1] (analytic) = 1.988771077936042 y[1] (numeric) = 1.988771077936042 absolute error = 4.440892098500626e-16 relative error = 2.232983045544593e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.16 y[1] (analytic) = 1.987227283375627 y[1] (numeric) = 1.987227283375627 absolute error = 4.440892098500626e-16 relative error = 2.234717757576804e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.17 y[1] (analytic) = 1.985584766909561 y[1] (numeric) = 1.98558476690956 absolute error = 4.440892098500626e-16 relative error = 2.236566361965296e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.18 y[1] (analytic) = 1.983843692788121 y[1] (numeric) = 1.983843692788121 absolute error = 2.220446049250313e-16 relative error = 1.119264616119866e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.1900000000000001 y[1] (analytic) = 1.98200423511727 y[1] (numeric) = 1.98200423511727 absolute error = 4.440892098500626e-16 relative error = 2.240606765523823e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2000000000000001 y[1] (analytic) = 1.980066577841242 y[1] (numeric) = 1.980066577841241 absolute error = 4.440892098500626e-16 relative error = 2.242799382706761e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2100000000000001 y[1] (analytic) = 1.978030914724148 y[1] (numeric) = 1.978030914724148 absolute error = 4.440892098500626e-16 relative error = 2.245107528625225e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2200000000000001 y[1] (analytic) = 1.975897449330605 y[1] (numeric) = 1.975897449330605 absolute error = 4.440892098500626e-16 relative error = 2.247531672256124e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2300000000000001 y[1] (analytic) = 1.973666395005375 y[1] (numeric) = 1.973666395005374 absolute error = 4.440892098500626e-16 relative error = 2.250072306920204e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2400000000000001 y[1] (analytic) = 1.97133797485203 y[1] (numeric) = 1.971337974852029 absolute error = 6.661338147750939e-16 relative error = 3.379094925745011e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2500000000000001 y[1] (analytic) = 1.968912421710645 y[1] (numeric) = 1.968912421710644 absolute error = 6.661338147750939e-16 relative error = 3.383257718473525e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2600000000000001 y[1] (analytic) = 1.966389978134513 y[1] (numeric) = 1.966389978134513 absolute error = 4.440892098500626e-16 relative error = 2.258398460062149e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2700000000000001 y[1] (analytic) = 1.96377089636589 y[1] (numeric) = 1.96377089636589 absolute error = 4.440892098500626e-16 relative error = 2.26141048669111e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2800000000000001 y[1] (analytic) = 1.961055438310771 y[1] (numeric) = 1.96105543831077 absolute error = 6.661338147750939e-16 relative error = 3.396812766032221e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.2900000000000001 y[1] (analytic) = 1.958243875512697 y[1] (numeric) = 1.958243875512697 absolute error = 6.661338147750939e-16 relative error = 3.401689764512554e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3000000000000002 y[1] (analytic) = 1.955336489125606 y[1] (numeric) = 1.955336489125605 absolute error = 6.661338147750939e-16 relative error = 3.40674773104131e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3100000000000002 y[1] (analytic) = 1.952333569885713 y[1] (numeric) = 1.952333569885713 absolute error = 6.661338147750939e-16 relative error = 3.411987710758302e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3200000000000002 y[1] (analytic) = 1.949235418082441 y[1] (numeric) = 1.94923541808244 absolute error = 4.440892098500626e-16 relative error = 2.278273859229047e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3300000000000002 y[1] (analytic) = 1.946042343528387 y[1] (numeric) = 1.946042343528386 absolute error = 4.440892098500626e-16 relative error = 2.282012060667089e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3400000000000002 y[1] (analytic) = 1.942754665528346 y[1] (numeric) = 1.942754665528346 absolute error = 4.440892098500626e-16 relative error = 2.285873855972902e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3500000000000002 y[1] (analytic) = 1.939372712847379 y[1] (numeric) = 1.939372712847378 absolute error = 4.440892098500626e-16 relative error = 2.28986005066583e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3600000000000002 y[1] (analytic) = 1.935896823677935 y[1] (numeric) = 1.935896823677934 absolute error = 4.440892098500626e-16 relative error = 2.293971478326799e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3700000000000002 y[1] (analytic) = 1.932327345606034 y[1] (numeric) = 1.932327345606034 absolute error = 4.440892098500626e-16 relative error = 2.298209000974332e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3800000000000002 y[1] (analytic) = 1.92866463557651 y[1] (numeric) = 1.92866463557651 absolute error = 4.440892098500626e-16 relative error = 2.302573509454726e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.3900000000000002 y[1] (analytic) = 1.924909059857313 y[1] (numeric) = 1.924909059857313 absolute error = 2.220446049250313e-16 relative error = 1.153532961923358e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4000000000000002 y[1] (analytic) = 1.921060994002885 y[1] (numeric) = 1.921060994002885 absolute error = 2.220446049250313e-16 relative error = 1.155843596940462e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4100000000000003 y[1] (analytic) = 1.917120822816605 y[1] (numeric) = 1.917120822816605 absolute error = 2.220446049250313e-16 relative error = 1.158219149687221e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4200000000000003 y[1] (analytic) = 1.913088940312308 y[1] (numeric) = 1.913088940312308 absolute error = 2.220446049250313e-16 relative error = 1.16066012534045e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4300000000000003 y[1] (analytic) = 1.908965749674885 y[1] (numeric) = 1.908965749674885 absolute error = 2.220446049250313e-16 relative error = 1.163167044578184e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4400000000000003 y[1] (analytic) = 1.904751663219963 y[1] (numeric) = 1.904751663219963 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4500000000000003 y[1] (analytic) = 1.900447102352677 y[1] (numeric) = 1.900447102352677 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4600000000000003 y[1] (analytic) = 1.896052497525525 y[1] (numeric) = 1.896052497525525 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4700000000000003 y[1] (analytic) = 1.891568288195329 y[1] (numeric) = 1.891568288195329 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4800000000000003 y[1] (analytic) = 1.886994922779284 y[1] (numeric) = 1.886994922779284 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.4900000000000003 y[1] (analytic) = 1.882332858610121 y[1] (numeric) = 1.882332858610122 absolute error = 2.220446049250313e-16 relative error = 1.179624548917373e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5000000000000003 y[1] (analytic) = 1.877582561890373 y[1] (numeric) = 1.877582561890373 absolute error = 2.220446049250313e-16 relative error = 1.182609007091939e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5100000000000003 y[1] (analytic) = 1.872744507645751 y[1] (numeric) = 1.872744507645751 absolute error = 2.220446049250313e-16 relative error = 1.18566416304254e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5200000000000004 y[1] (analytic) = 1.86781917967765 y[1] (numeric) = 1.86781917967765 absolute error = 2.220446049250313e-16 relative error = 1.188790688846829e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5300000000000004 y[1] (analytic) = 1.862807070514761 y[1] (numeric) = 1.862807070514761 absolute error = 2.220446049250313e-16 relative error = 1.191989274894004e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5400000000000004 y[1] (analytic) = 1.857708681363824 y[1] (numeric) = 1.857708681363824 absolute error = 2.220446049250313e-16 relative error = 1.195260630219044e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5500000000000004 y[1] (analytic) = 1.852524522059505 y[1] (numeric) = 1.852524522059506 absolute error = 2.220446049250313e-16 relative error = 1.198605482847686e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5600000000000004 y[1] (analytic) = 1.847255111013416 y[1] (numeric) = 1.847255111013416 absolute error = 2.220446049250313e-16 relative error = 1.20202458015242e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5700000000000004 y[1] (analytic) = 1.841900975162269 y[1] (numeric) = 1.841900975162269 absolute error = 2.220446049250313e-16 relative error = 1.205518689219813e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5800000000000004 y[1] (analytic) = 1.836462649915187 y[1] (numeric) = 1.836462649915187 absolute error = 2.220446049250313e-16 relative error = 1.209088597229494e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.5900000000000004 y[1] (analytic) = 1.830940679100163 y[1] (numeric) = 1.830940679100164 absolute error = 4.440892098500626e-16 relative error = 2.425470223690236e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.6000000000000004 y[1] (analytic) = 1.825335614909678 y[1] (numeric) = 1.825335614909678 absolute error = 4.440892098500626e-16 relative error = 2.432918123235311e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.6100000000000004 y[1] (analytic) = 1.819648017845479 y[1] (numeric) = 1.81964801784548 absolute error = 4.440892098500626e-16 relative error = 2.440522592802746e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.6200000000000004 y[1] (analytic) = 1.813878456662534 y[1] (numeric) = 1.813878456662534 absolute error = 4.440892098500626e-16 relative error = 2.448285375565735e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.6300000000000004 y[1] (analytic) = 1.808027508312152 y[1] (numeric) = 1.808027508312152 absolute error = 4.440892098500626e-16 relative error = 2.456208259047084e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y[1] (analytic) = 1.802095757884292 y[1] (numeric) = 1.802095757884293 absolute error = 2.220446049250313e-16 relative error = 1.232146538015924e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y[1] (analytic) = 1.796083798549056 y[1] (numeric) = 1.796083798549056 absolute error = 2.220446049250313e-16 relative error = 1.236270852754239e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y[1] (analytic) = 1.789992231497365 y[1] (numeric) = 1.789992231497365 absolute error = 2.220446049250313e-16 relative error = 1.240478036819671e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y[1] (analytic) = 1.783821665880849 y[1] (numeric) = 1.783821665880849 absolute error = 2.220446049250313e-16 relative error = 1.244769077380759e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y[1] (analytic) = 1.777572718750928 y[1] (numeric) = 1.777572718750928 absolute error = 2.220446049250313e-16 relative error = 1.249144986209389e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y[1] (analytic) = 1.771246014997106 y[1] (numeric) = 1.771246014997107 absolute error = 2.220446049250313e-16 relative error = 1.253606800212866e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y[1] (analytic) = 1.764842187284488 y[1] (numeric) = 1.764842187284488 absolute error = 2.220446049250313e-16 relative error = 1.258155581982574e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y[1] (analytic) = 1.758361875990508 y[1] (numeric) = 1.758361875990508 absolute error = 4.440892098500626e-16 relative error = 2.525584840719442e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y[1] (analytic) = 1.751805729140895 y[1] (numeric) = 1.751805729140895 absolute error = 4.440892098500626e-16 relative error = 2.535036862037487e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y[1] (analytic) = 1.74517440234487 y[1] (numeric) = 1.745174402344871 absolute error = 4.440892098500626e-16 relative error = 2.544669514137788e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y[1] (analytic) = 1.738468558729588 y[1] (numeric) = 1.738468558729588 absolute error = 4.440892098500626e-16 relative error = 2.554485139349242e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y[1] (analytic) = 1.731688868873821 y[1] (numeric) = 1.731688868873821 absolute error = 4.440892098500626e-16 relative error = 2.564486137390661e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y[1] (analytic) = 1.724836010740905 y[1] (numeric) = 1.724836010740905 absolute error = 4.440892098500626e-16 relative error = 2.574674966690333e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y[1] (analytic) = 1.717910669610943 y[1] (numeric) = 1.717910669610943 absolute error = 4.440892098500626e-16 relative error = 2.585054145746915e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y[1] (analytic) = 1.710913538012277 y[1] (numeric) = 1.710913538012277 absolute error = 4.440892098500626e-16 relative error = 2.595626254533009e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y[1] (analytic) = 1.703845315652236 y[1] (numeric) = 1.703845315652236 absolute error = 2.220446049250313e-16 relative error = 1.303196967971427e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y[1] (analytic) = 1.696706709347165 y[1] (numeric) = 1.696706709347165 absolute error = 2.220446049250313e-16 relative error = 1.308679948642783e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y[1] (analytic) = 1.689498432951747 y[1] (numeric) = 1.689498432951747 absolute error = 2.220446049250313e-16 relative error = 1.314263455912735e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y[1] (analytic) = 1.682221207287613 y[1] (numeric) = 1.682221207287613 absolute error = 4.440892098500626e-16 relative error = 2.63989782037111e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y[1] (analytic) = 1.674875760071267 y[1] (numeric) = 1.674875760071267 absolute error = 2.220446049250313e-16 relative error = 1.325737766457276e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y[1] (analytic) = 1.667462825841308 y[1] (numeric) = 1.667462825841308 absolute error = 4.440892098500626e-16 relative error = 2.663263030322732e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y[1] (analytic) = 1.659983145884982 y[1] (numeric) = 1.659983145884982 absolute error = 4.440892098500626e-16 relative error = 2.675263366082592e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y[1] (analytic) = 1.652437468164051 y[1] (numeric) = 1.652437468164052 absolute error = 2.220446049250313e-16 relative error = 1.343739834050937e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y[1] (analytic) = 1.644826547240001 y[1] (numeric) = 1.644826547240001 absolute error = 2.220446049250313e-16 relative error = 1.349957570283745e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y[1] (analytic) = 1.63715114419858 y[1] (numeric) = 1.63715114419858 absolute error = 2.220446049250313e-16 relative error = 1.356286532931734e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y[1] (analytic) = 1.629412026573696 y[1] (numeric) = 1.629412026573697 absolute error = 2.220446049250313e-16 relative error = 1.362728403275281e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y[1] (analytic) = 1.621609968270664 y[1] (numeric) = 1.621609968270664 absolute error = 2.220446049250313e-16 relative error = 1.369284903704845e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y[1] (analytic) = 1.613745749488811 y[1] (numeric) = 1.613745749488811 absolute error = 2.220446049250313e-16 relative error = 1.375957798775729e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y[1] (analytic) = 1.605820156643462 y[1] (numeric) = 1.605820156643462 absolute error = 2.220446049250313e-16 relative error = 1.382748896297056e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y[1] (analytic) = 1.597833982287298 y[1] (numeric) = 1.597833982287298 absolute error = 2.220446049250313e-16 relative error = 1.38966004845619e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y[1] (analytic) = 1.589788025031098 y[1] (numeric) = 1.589788025031098 absolute error = 2.220446049250313e-16 relative error = 1.396693152979863e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 12.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y[1] (analytic) = 1.581683089463883 y[1] (numeric) = 1.581683089463883 absolute error = 2.220446049250313e-16 relative error = 1.403850154333344e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.9600000000000007 y[1] (analytic) = 1.573519986072456 y[1] (numeric) = 1.573519986072456 absolute error = 2.220446049250313e-16 relative error = 1.411133044959029e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.9700000000000008 y[1] (analytic) = 1.565299531160354 y[1] (numeric) = 1.565299531160354 absolute error = 2.220446049250313e-16 relative error = 1.418543866555879e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.9800000000000008 y[1] (analytic) = 1.557022546766217 y[1] (numeric) = 1.557022546766217 absolute error = 2.220446049250313e-16 relative error = 1.426084711401233e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 0.9900000000000008 y[1] (analytic) = 1.548689860581587 y[1] (numeric) = 1.548689860581587 absolute error = 2.220446049250313e-16 relative error = 1.433757723716522e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.000000000000001 y[1] (analytic) = 1.540302305868139 y[1] (numeric) = 1.540302305868139 absolute error = 2.220446049250313e-16 relative error = 1.44156510107854e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.010000000000001 y[1] (analytic) = 1.531860721374355 y[1] (numeric) = 1.531860721374355 absolute error = 2.220446049250313e-16 relative error = 1.449509095877968e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.020000000000001 y[1] (analytic) = 1.523365951251649 y[1] (numeric) = 1.523365951251649 absolute error = 2.220446049250313e-16 relative error = 1.457592016826895e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.030000000000001 y[1] (analytic) = 1.514818844969955 y[1] (numeric) = 1.514818844969955 absolute error = 4.440892098500626e-16 relative error = 2.931632461034447e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.040000000000001 y[1] (analytic) = 1.506220257232778 y[1] (numeric) = 1.506220257232778 absolute error = 2.220446049250313e-16 relative error = 1.474184163031845e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.050000000000001 y[1] (analytic) = 1.497571047891726 y[1] (numeric) = 1.497571047891727 absolute error = 2.220446049250313e-16 relative error = 1.482698301610629e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.060000000000001 y[1] (analytic) = 1.488872081860527 y[1] (numeric) = 1.488872081860527 absolute error = 2.220446049250313e-16 relative error = 1.491361196373294e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.070000000000001 y[1] (analytic) = 1.480124229028533 y[1] (numeric) = 1.480124229028534 absolute error = 2.220446049250313e-16 relative error = 1.500175462101369e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.080000000000001 y[1] (analytic) = 1.471328364173739 y[1] (numeric) = 1.47132836417374 absolute error = 2.220446049250313e-16 relative error = 1.509143780081518e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.090000000000001 y[1] (analytic) = 1.4624853668753 y[1] (numeric) = 1.4624853668753 absolute error = 2.220446049250313e-16 relative error = 1.518268900012619e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.100000000000001 y[1] (analytic) = 1.453596121425577 y[1] (numeric) = 1.453596121425577 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.110000000000001 y[1] (analytic) = 1.444661516741706 y[1] (numeric) = 1.444661516741706 absolute error = 2.220446049250313e-16 relative error = 1.537000898493035e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.120000000000001 y[1] (analytic) = 1.435682446276711 y[1] (numeric) = 1.435682446276711 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.130000000000001 y[1] (analytic) = 1.426659807930157 y[1] (numeric) = 1.426659807930157 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.140000000000001 y[1] (analytic) = 1.417594503958357 y[1] (numeric) = 1.417594503958358 absolute error = 2.220446049250313e-16 relative error = 1.566347811768562e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.150000000000001 y[1] (analytic) = 1.408487440884157 y[1] (numeric) = 1.408487440884157 absolute error = 2.220446049250313e-16 relative error = 1.576475575711532e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.160000000000001 y[1] (analytic) = 1.399339529406272 y[1] (numeric) = 1.399339529406273 absolute error = 2.220446049250313e-16 relative error = 1.586781479826007e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.170000000000001 y[1] (analytic) = 1.39015168430823 y[1] (numeric) = 1.39015168430823 absolute error = 2.220446049250313e-16 relative error = 1.59726889828951e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.180000000000001 y[1] (analytic) = 1.380924824366881 y[1] (numeric) = 1.380924824366881 absolute error = 2.220446049250313e-16 relative error = 1.607941294174599e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.190000000000001 y[1] (analytic) = 1.371659872260532 y[1] (numeric) = 1.371659872260532 absolute error = 2.220446049250313e-16 relative error = 1.618802222150713e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.200000000000001 y[1] (analytic) = 1.362357754476673 y[1] (numeric) = 1.362357754476673 absolute error = 2.220446049250313e-16 relative error = 1.6298553312843e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.210000000000001 y[1] (analytic) = 1.35301940121933 y[1] (numeric) = 1.35301940121933 absolute error = 2.220446049250313e-16 relative error = 1.641104367941262e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.220000000000001 y[1] (analytic) = 1.343645746316046 y[1] (numeric) = 1.343645746316046 absolute error = 2.220446049250313e-16 relative error = 1.652553178796005e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.230000000000001 y[1] (analytic) = 1.334237727124502 y[1] (numeric) = 1.334237727124502 absolute error = 2.220446049250313e-16 relative error = 1.664205713951541e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.240000000000001 y[1] (analytic) = 1.324796284438776 y[1] (numeric) = 1.324796284438776 absolute error = 2.220446049250313e-16 relative error = 1.67606603017532e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.250000000000001 y[1] (analytic) = 1.315322362395268 y[1] (numeric) = 1.315322362395268 absolute error = 2.220446049250313e-16 relative error = 1.688138294255691e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.260000000000001 y[1] (analytic) = 1.305816908378288 y[1] (numeric) = 1.305816908378289 absolute error = 2.220446049250313e-16 relative error = 1.700426786484113e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.270000000000001 y[1] (analytic) = 1.296280872925318 y[1] (numeric) = 1.296280872925318 absolute error = 2.220446049250313e-16 relative error = 1.712935904268518e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.280000000000001 y[1] (analytic) = 1.286715209631955 y[1] (numeric) = 1.286715209631955 absolute error = 2.220446049250313e-16 relative error = 1.725670165883434e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.290000000000001 y[1] (analytic) = 1.277120875056557 y[1] (numeric) = 1.277120875056557 absolute error = 2.220446049250313e-16 relative error = 1.738634214362819e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.300000000000001 y[1] (analytic) = 1.267498828624587 y[1] (numeric) = 1.267498828624587 absolute error = 2.220446049250313e-16 relative error = 1.751832821541782e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.310000000000001 y[1] (analytic) = 1.257850032532669 y[1] (numeric) = 1.257850032532669 absolute error = 2.220446049250313e-16 relative error = 1.765270892253719e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.320000000000001 y[1] (analytic) = 1.248175451652372 y[1] (numeric) = 1.248175451652372 absolute error = 2.220446049250313e-16 relative error = 1.778953468689695e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.330000000000001 y[1] (analytic) = 1.238476053433722 y[1] (numeric) = 1.238476053433722 absolute error = 2.220446049250313e-16 relative error = 1.792885734927245e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.340000000000001 y[1] (analytic) = 1.228752807808458 y[1] (numeric) = 1.228752807808459 absolute error = 2.220446049250313e-16 relative error = 1.807073021636133e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.350000000000001 y[1] (analytic) = 1.219006687093041 y[1] (numeric) = 1.219006687093041 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.360000000000001 y[1] (analytic) = 1.209238665891418 y[1] (numeric) = 1.209238665891418 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.370000000000001 y[1] (analytic) = 1.199449720997572 y[1] (numeric) = 1.199449720997572 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.380000000000001 y[1] (analytic) = 1.189640831297833 y[1] (numeric) = 1.189640831297833 absolute error = 2.220446049250313e-16 relative error = 1.866484396662754e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.390000000000001 y[1] (analytic) = 1.179812977672998 y[1] (numeric) = 1.179812977672999 absolute error = 2.220446049250313e-16 relative error = 1.882032229913087e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.400000000000001 y[1] (analytic) = 1.16996714290024 y[1] (numeric) = 1.16996714290024 absolute error = 2.220446049250313e-16 relative error = 1.897870433990166e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.410000000000001 y[1] (analytic) = 1.16010431155483 y[1] (numeric) = 1.16010431155483 absolute error = 2.220446049250313e-16 relative error = 1.914005514102744e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.420000000000001 y[1] (analytic) = 1.150225469911685 y[1] (numeric) = 1.150225469911685 absolute error = 2.220446049250313e-16 relative error = 1.930444167108211e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.430000000000001 y[1] (analytic) = 1.140331605846736 y[1] (numeric) = 1.140331605846736 absolute error = 2.220446049250313e-16 relative error = 1.947193288220364e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.440000000000001 y[1] (analytic) = 1.130423708738144 y[1] (numeric) = 1.130423708738145 absolute error = 4.440892098500626e-16 relative error = 3.928519955988761e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.450000000000001 y[1] (analytic) = 1.120502769367365 y[1] (numeric) = 1.120502769367366 absolute error = 4.440892098500626e-16 relative error = 3.963303099204251e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.460000000000001 y[1] (analytic) = 1.110569779820068 y[1] (numeric) = 1.110569779820069 absolute error = 4.440892098500626e-16 relative error = 3.998751072823292e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.470000000000001 y[1] (analytic) = 1.100625733386931 y[1] (numeric) = 1.100625733386931 absolute error = 2.220446049250313e-16 relative error = 2.017439699885432e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.480000000000001 y[1] (analytic) = 1.090671624464309 y[1] (numeric) = 1.090671624464309 absolute error = 2.220446049250313e-16 relative error = 2.035852037812849e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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] = 1.490000000000001 y[1] (analytic) = 1.0807084484548 y[1] (numeric) = 1.0807084484548 absolute error = 2.220446049250313e-16 relative error = 2.054620792892953e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 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 , 3 ) = sin(x); Iterations = 140 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.7 %