##############ECHO OF PROBLEM################# ##############temp/div_exp_exppostode.ode################# diff ( y , x , 1 ) = exp ( 0.1 * x ) / exp ( 0.2 * x ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-5.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=3; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=8; glob_max_minutes=(20.0); glob_subiter_method=3; glob_max_iter=1000; glob_upper_ratio_limit=c(1.11); glob_lower_ratio_limit=c(0.99); /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(c(-10.0) * (exp(c(0.1) * c(x))/exp(c(0.2)*c(x)))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (closed_form) = -16.48721270700128 y[1] (numeric) = -16.48721270700128 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 NO POLE (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] = -4.9 y[1] (closed_form) = -16.32316219955379 y[1] (numeric) = -16.32316219955379 absolute error = 3.552713678800501e-15 relative error = 2.176486170613203e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.800000000000001 y[1] (closed_form) = -16.16074402192894 y[1] (numeric) = -16.16074402192893 absolute error = 3.552713678800501e-15 relative error = 2.198360220284246e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.700000000000001 y[1] (closed_form) = -15.99994193217361 y[1] (numeric) = -15.9999419321736 absolute error = 3.552713678800501e-15 relative error = 2.220454107809291e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.600000000000001 y[1] (closed_form) = -15.84073984994482 y[1] (numeric) = -15.84073984994482 absolute error = 3.552713678800501e-15 relative error = 2.242770042595502e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.500000000000002 y[1] (closed_form) = -15.68312185490169 y[1] (numeric) = -15.68312185490169 absolute error = 5.329070518200751e-15 relative error = 3.397965384382429e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.400000000000002 y[1] (closed_form) = -15.52707218511337 y[1] (numeric) = -15.52707218511336 absolute error = 3.552713678800501e-15 relative error = 2.288077002827795e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.300000000000002 y[1] (closed_form) = -15.37257523548282 y[1] (numeric) = -15.37257523548281 absolute error = 5.329070518200751e-15 relative error = 3.466608838511485e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.200000000000003 y[1] (closed_form) = -15.21961555618634 y[1] (numeric) = -15.21961555618634 absolute error = 5.329070518200751e-15 relative error = 3.501448836553979e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.100000000000003 y[1] (closed_form) = -15.06817785112854 y[1] (numeric) = -15.06817785112854 absolute error = 7.105427357601002e-15 relative error = 4.715518643197349e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -4.000000000000004 y[1] (closed_form) = -14.91824697641271 y[1] (numeric) = -14.9182469764127 absolute error = 3.552713678800501e-15 relative error = 2.381455196724997e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.900000000000004 y[1] (closed_form) = -14.76980793882643 y[1] (numeric) = -14.76980793882643 absolute error = 5.329070518200751e-15 relative error = 3.608083829033314e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.800000000000004 y[1] (closed_form) = -14.62284589434225 y[1] (numeric) = -14.62284589434225 absolute error = 5.329070518200751e-15 relative error = 3.644345674368784e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.700000000000005 y[1] (closed_form) = -14.47734614663325 y[1] (numeric) = -14.47734614663325 absolute error = 5.329070518200751e-15 relative error = 3.680971957308655e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.600000000000005 y[1] (closed_form) = -14.33329414560341 y[1] (numeric) = -14.3332941456034 absolute error = 7.105427357601002e-15 relative error = 4.957288454015658e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.500000000000005 y[1] (closed_form) = -14.19067548593258 y[1] (numeric) = -14.19067548593257 absolute error = 8.881784197001252e-15 relative error = 6.258887539078666e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.400000000000006 y[1] (closed_form) = -14.04947590563595 y[1] (numeric) = -14.04947590563594 absolute error = 7.105427357601002e-15 relative error = 5.057432323685939e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.300000000000006 y[1] (closed_form) = -13.90968128463781 y[1] (numeric) = -13.9096812846378 absolute error = 7.105427357601002e-15 relative error = 5.108260363555855e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.200000000000006 y[1] (closed_form) = -13.77127764335958 y[1] (numeric) = -13.77127764335957 absolute error = 7.105427357601002e-15 relative error = 5.159599233719025e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.100000000000007 y[1] (closed_form) = -13.63425114132179 y[1] (numeric) = -13.63425114132178 absolute error = 8.881784197001252e-15 relative error = 6.514317585131557e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -3.000000000000007 y[1] (closed_form) = -13.49858807576004 y[1] (numeric) = -13.49858807576003 absolute error = 8.881784197001252e-15 relative error = 6.579787565301463e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -2.900000000000007 y[1] (closed_form) = -13.36427488025473 y[1] (numeric) = -13.36427488025472 absolute error = 1.06581410364015e-14 relative error = 7.975098635653289e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -2.800000000000008 y[1] (closed_form) = -13.23129812337438 y[1] (numeric) = -13.23129812337437 absolute error = 1.06581410364015e-14 relative error = 8.055249709454324e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -2.700000000000008 y[1] (closed_form) = -13.09964450733248 y[1] (numeric) = -13.09964450733247 absolute error = 1.243449787580175e-14 relative error = 9.492240700762209e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -2.600000000000009 y[1] (closed_form) = -12.96930086665773 y[1] (numeric) = -12.96930086665772 absolute error = 1.06581410364015e-14 relative error = 8.217976547835438e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (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] = -2.500000000000009 y[1] (closed_form) = -12.84025416687743 y[1] (numeric) = -12.84025416687741 absolute error = 1.4210854715202e-14 relative error = 1.106742478031328e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -2.400000000000009 y[1] (closed_form) = -12.71249150321406 y[1] (numeric) = -12.71249150321404 absolute error = 1.4210854715202e-14 relative error = 1.117865424854689e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -2.30000000000001 y[1] (closed_form) = -12.58600009929479 y[1] (numeric) = -12.58600009929478 absolute error = 1.4210854715202e-14 relative error = 1.129100159152093e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -2.20000000000001 y[1] (closed_form) = -12.46076730587382 y[1] (numeric) = -12.46076730587381 absolute error = 1.4210854715202e-14 relative error = 1.140447804406332e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -2.10000000000001 y[1] (closed_form) = -12.33678059956745 y[1] (numeric) = -12.33678059956743 absolute error = 1.4210854715202e-14 relative error = 1.151909495391388e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -2.000000000000011 y[1] (closed_form) = -12.21402758160171 y[1] (numeric) = -12.2140275816017 absolute error = 1.243449787580175e-14 relative error = 1.018050581000173e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -1.900000000000011 y[1] (closed_form) = -12.09249597657253 y[1] (numeric) = -12.09249597657251 absolute error = 1.598721155460225e-14 relative error = 1.322077062136318e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 268.9 Order of pole (ratio test) = 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] = -1.80000000000001 y[1] (closed_form) = -11.97217363121812 y[1] (numeric) = -11.9721736312181 absolute error = 1.598721155460225e-14 relative error = 1.335364157508934e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -1.70000000000001 y[1] (closed_form) = -11.85304851320367 y[1] (numeric) = -11.85304851320365 absolute error = 1.4210854715202e-14 relative error = 1.198919813697874e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -1.60000000000001 y[1] (closed_form) = -11.73510870991812 y[1] (numeric) = -11.7351087099181 absolute error = 1.598721155460225e-14 relative error = 1.362340302914314e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -1.50000000000001 y[1] (closed_form) = -11.61834242728284 y[1] (numeric) = -11.61834242728283 absolute error = 1.4210854715202e-14 relative error = 1.2231396005192e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -1.40000000000001 y[1] (closed_form) = -11.50273798857229 y[1] (numeric) = -11.50273798857227 absolute error = 1.4210854715202e-14 relative error = 1.23543235787168e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 265.6 Order of pole (ratio test) = 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] = -1.30000000000001 y[1] (closed_form) = -11.38828383324623 y[1] (numeric) = -11.38828383324622 absolute error = 1.243449787580175e-14 relative error = 1.091867577053294e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (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] = -1.20000000000001 y[1] (closed_form) = -11.27496851579377 y[1] (numeric) = -11.27496851579375 absolute error = 1.4210854715202e-14 relative error = 1.260389747013103e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = -1.10000000000001 y[1] (closed_form) = -11.16278070458872 y[1] (numeric) = -11.16278070458871 absolute error = 1.243449787580175e-14 relative error = 1.113924765241537e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = -1.00000000000001 y[1] (closed_form) = -11.05170918075649 y[1] (numeric) = -11.05170918075648 absolute error = 1.243449787580175e-14 relative error = 1.125119895251407e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 247.8 Order of pole (ratio test) = 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] = -0.9000000000000097 y[1] (closed_form) = -10.94174283705211 y[1] (numeric) = -10.9417428370521 absolute error = 8.881784197001252e-15 relative error = 8.117339558488611e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = -0.8000000000000096 y[1] (closed_form) = -10.83287067674959 y[1] (numeric) = -10.83287067674959 absolute error = 8.881784197001252e-15 relative error = 8.198920177330349e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 264.8 Order of pole (ratio test) = 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] = -0.7000000000000095 y[1] (closed_form) = -10.72508181254218 y[1] (numeric) = -10.72508181254217 absolute error = 8.881784197001252e-15 relative error = 8.281320695022275e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = -0.6000000000000094 y[1] (closed_form) = -10.61836546545361 y[1] (numeric) = -10.6183654654536 absolute error = 8.881784197001252e-15 relative error = 8.364549351684827e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = -0.5000000000000093 y[1] (closed_form) = -10.51271096376025 y[1] (numeric) = -10.51271096376024 absolute error = 7.105427357601002e-15 relative error = 6.758891576202424e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = -0.4000000000000093 y[1] (closed_form) = -10.40810774192389 y[1] (numeric) = -10.40810774192389 absolute error = 5.329070518200751e-15 relative error = 5.120114674385276e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = -0.3000000000000094 y[1] (closed_form) = -10.30454533953518 y[1] (numeric) = -10.30454533953517 absolute error = 5.329070518200751e-15 relative error = 5.171572682352949e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = -0.2000000000000094 y[1] (closed_form) = -10.20201340026757 y[1] (numeric) = -10.20201340026756 absolute error = 5.329070518200751e-15 relative error = 5.223547851898515e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 243.1 Order of pole (ratio test) = 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] = -0.1000000000000094 y[1] (closed_form) = -10.10050167084169 y[1] (numeric) = -10.10050167084168 absolute error = 7.105427357601002e-15 relative error = 7.034727174109655e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = -9.395262345890387e-15 y[1] (closed_form) = -10.00000000000001 y[1] (numeric) = -10 absolute error = 7.105427357601002e-15 relative error = 7.105427357600994e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.09999999999999061 y[1] (closed_form) = -9.900498337491689 y[1] (numeric) = -9.900498337491685 absolute error = 3.552713678800501e-15 relative error = 3.588419044874652e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.1999999999999906 y[1] (closed_form) = -9.801986733067563 y[1] (numeric) = -9.801986733067558 absolute error = 5.329070518200751e-15 relative error = 5.436724883765479e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 239.3 Order of pole (ratio test) = 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] = 0.2999999999999906 y[1] (closed_form) = -9.70445533548509 y[1] (numeric) = -9.704455335485088 absolute error = 1.77635683940025e-15 relative error = 1.830454959079326e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.3999999999999906 y[1] (closed_form) = -9.607894391523242 y[1] (numeric) = -9.607894391523239 absolute error = 3.552713678800501e-15 relative error = 3.697702674516233e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 247.6 Order of pole (ratio test) = 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] = 0.4999999999999906 y[1] (closed_form) = -9.512294245007149 y[1] (numeric) = -9.512294245007146 absolute error = 3.552713678800501e-15 relative error = 3.734865204222696e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.5999999999999907 y[1] (closed_form) = -9.417645335842495 y[1] (numeric) = -9.417645335842494 absolute error = 1.77635683940025e-15 relative error = 1.88620061178099e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.6999999999999907 y[1] (closed_form) = -9.323938199059491 y[1] (numeric) = -9.323938199059489 absolute error = 1.77635683940025e-15 relative error = 1.905157243083649e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.7999999999999908 y[1] (closed_form) = -9.231163463866366 y[1] (numeric) = -9.231163463866364 absolute error = 1.77635683940025e-15 relative error = 1.924304391698253e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.8999999999999909 y[1] (closed_form) = -9.139311852712289 y[1] (numeric) = -9.139311852712289 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 0.999999999999991 y[1] (closed_form) = -9.048374180359604 y[1] (numeric) = -9.048374180359604 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 234.6 Order of pole (ratio test) = 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] = 1.099999999999991 y[1] (closed_form) = -8.95834135296529 y[1] (numeric) = -8.95834135296529 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 1.199999999999991 y[1] (closed_form) = -8.869204367171582 y[1] (numeric) = -8.869204367171582 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 1.299999999999991 y[1] (closed_form) = -8.780954309205621 y[1] (numeric) = -8.780954309205621 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 271.9 Order of pole (ratio test) = 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] = 1.399999999999991 y[1] (closed_form) = -8.693582353988065 y[1] (numeric) = -8.693582353988065 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 1.499999999999991 y[1] (closed_form) = -8.607079764250585 y[1] (numeric) = -8.607079764250585 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 1.599999999999991 y[1] (closed_form) = -8.521437889662121 y[1] (numeric) = -8.521437889662121 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 1.699999999999992 y[1] (closed_form) = -8.436648165963845 y[1] (numeric) = -8.436648165963843 absolute error = 1.77635683940025e-15 relative error = 2.105524379417226e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 1.799999999999992 y[1] (closed_form) = -8.352702114112727 y[1] (numeric) = -8.352702114112727 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 1.899999999999992 y[1] (closed_form) = -8.26959133943363 y[1] (numeric) = -8.26959133943363 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 273.4 Order of pole (ratio test) = 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] = 1.999999999999992 y[1] (closed_form) = -8.187307530779824 y[1] (numeric) = -8.187307530779824 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.099999999999992 y[1] (closed_form) = -8.105842459701879 y[1] (numeric) = -8.105842459701877 absolute error = 1.77635683940025e-15 relative error = 2.191452459422191e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.199999999999991 y[1] (closed_form) = -8.025187979624791 y[1] (numeric) = -8.025187979624791 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.299999999999991 y[1] (closed_form) = -7.945336025033347 y[1] (numeric) = -7.945336025033346 absolute error = 8.881784197001252e-16 relative error = 1.117861367853725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.399999999999991 y[1] (closed_form) = -7.866278610665542 y[1] (numeric) = -7.866278610665541 absolute error = 1.77635683940025e-15 relative error = 2.258192122755182e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.49999999999999 y[1] (closed_form) = -7.788007830714056 y[1] (numeric) = -7.788007830714055 absolute error = 8.881784197001252e-16 relative error = 1.140443665448512e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.59999999999999 y[1] (closed_form) = -7.71051585803567 y[1] (numeric) = -7.710515858035669 absolute error = 8.881784197001252e-16 relative error = 1.151905314836351e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.69999999999999 y[1] (closed_form) = -7.633794943368539 y[1] (numeric) = -7.633794943368538 absolute error = 8.881784197001252e-16 relative error = 1.163482155715597e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.799999999999989 y[1] (closed_form) = -7.557837414557263 y[1] (numeric) = -7.557837414557261 absolute error = 2.664535259100376e-15 relative error = 3.52552603733996e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.899999999999989 y[1] (closed_form) = -7.48263567578566 y[1] (numeric) = -7.482635675785658 absolute error = 1.77635683940025e-15 relative error = 2.373972108716541e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 2.999999999999988 y[1] (closed_form) = -7.408182206817187 y[1] (numeric) = -7.408182206817184 absolute error = 3.552713678800501e-15 relative error = 4.795661850124594e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.099999999999988 y[1] (closed_form) = -7.334469562242901 y[1] (numeric) = -7.334469562242898 absolute error = 3.552713678800501e-15 relative error = 4.843859052997517e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.199999999999988 y[1] (closed_form) = -7.261490370736919 y[1] (numeric) = -7.261490370736914 absolute error = 4.440892098500626e-15 relative error = 6.115675807265377e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.299999999999987 y[1] (closed_form) = -7.18923733431927 y[1] (numeric) = -7.189237334319267 absolute error = 3.552713678800501e-15 relative error = 4.941711496768799e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.399999999999987 y[1] (closed_form) = -7.117703227626105 y[1] (numeric) = -7.117703227626102 absolute error = 3.552713678800501e-15 relative error = 4.99137652299308e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.499999999999987 y[1] (closed_form) = -7.046880897187143 y[1] (numeric) = -7.046880897187139 absolute error = 4.440892098500626e-15 relative error = 6.301925863786442e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.599999999999986 y[1] (closed_form) = -6.97676326071032 y[1] (numeric) = -6.976763260710315 absolute error = 5.329070518200751e-15 relative error = 7.638313526003441e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.699999999999986 y[1] (closed_form) = -6.907343306373557 y[1] (numeric) = -6.907343306373551 absolute error = 6.217248937900877e-15 relative error = 9.000926495377876e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.799999999999986 y[1] (closed_form) = -6.838614092123568 y[1] (numeric) = -6.838614092123563 absolute error = 5.329070518200751e-15 relative error = 7.792617694773205e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.899999999999985 y[1] (closed_form) = -6.770568744981657 y[1] (numeric) = -6.770568744981651 absolute error = 6.217248937900877e-15 relative error = 9.182757272066841e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 3.999999999999985 y[1] (closed_form) = -6.703200460356403 y[1] (numeric) = -6.703200460356396 absolute error = 6.217248937900877e-15 relative error = 9.275045516944471e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 4.099999999999985 y[1] (closed_form) = -6.636502501363203 y[1] (numeric) = -6.636502501363196 absolute error = 6.217248937900877e-15 relative error = 9.368261274103028e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.05 NO POLE (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] = 4.199999999999984 y[1] (closed_form) = -6.570468198150579 y[1] (numeric) = -6.570468198150571 absolute error = 7.993605777301127e-15 relative error = 1.21659606838233e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = 4.299999999999984 y[1] (closed_form) = -6.505090947233176 y[1] (numeric) = -6.505090947233168 absolute error = 7.993605777301127e-15 relative error = 1.228823062143515e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = 4.399999999999983 y[1] (closed_form) = -6.440364210831424 y[1] (numeric) = -6.440364210831416 absolute error = 7.993605777301127e-15 relative error = 1.241172939234936e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 264.6 Order of pole (ratio test) = 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] = 4.499999999999983 y[1] (closed_form) = -6.376281516217745 y[1] (numeric) = -6.376281516217736 absolute error = 8.881784197001252e-15 relative error = 1.392941038505105e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = 4.599999999999983 y[1] (closed_form) = -6.31283645506927 y[1] (numeric) = -6.312836455069262 absolute error = 7.993605777301127e-15 relative error = 1.266246295812429e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = 4.699999999999982 y[1] (closed_form) = -6.250022682827019 y[1] (numeric) = -6.25002268282701 absolute error = 8.881784197001252e-15 relative error = 1.421080314061169e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = 4.799999999999982 y[1] (closed_form) = -6.187833918061419 y[1] (numeric) = -6.18783391806141 absolute error = 8.881784197001252e-15 relative error = 1.435362408657506e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = 4.899999999999982 y[1] (closed_form) = -6.126263941844171 y[1] (numeric) = -6.126263941844162 absolute error = 9.769962616701378e-15 relative error = 1.594766844759933e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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] = 4.999999999999981 y[1] (closed_form) = -6.065306597126345 y[1] (numeric) = -6.065306597126335 absolute error = 1.06581410364015e-14 relative error = 1.757230383283703e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (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 , 1 ) = exp ( 0.1 * x ) / exp ( 0.2 * x ) ; Iterations = 201 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 101 %