##############ECHO OF PROBLEM################# ##############temp/lin_exppostode.ode################# diff ( y , x , 1 ) = exp ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ max_terms=30; Digits=32; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(1.0); x_end=c(10.0); 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) + c(0.2))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 13.49858807576003 y[1] (numeric) = 13.49858807576003 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 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.1 y[1] (closed_form) = 13.63425114132178 y[1] (numeric) = 13.63425114132178 absolute error = 1.77635683940025e-15 relative error = 1.302863517026312e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.2 y[1] (closed_form) = 13.77127764335957 y[1] (numeric) = 13.77127764335957 absolute error = 1.77635683940025e-15 relative error = 1.289899808429757e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.3 y[1] (closed_form) = 13.9096812846378 y[1] (numeric) = 13.90968128463781 absolute error = 3.552713678800501e-15 relative error = 2.554130181777929e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.4 y[1] (closed_form) = 14.04947590563594 y[1] (numeric) = 14.04947590563594 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.5 y[1] (closed_form) = 14.19067548593257 y[1] (numeric) = 14.19067548593257 absolute error = 1.77635683940025e-15 relative error = 1.251777507815734e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.600000000000001 y[1] (closed_form) = 14.3332941456034 y[1] (numeric) = 14.33329414560341 absolute error = 1.77635683940025e-15 relative error = 1.239322113503915e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.700000000000001 y[1] (closed_form) = 14.47734614663324 y[1] (numeric) = 14.47734614663325 absolute error = 3.552713678800501e-15 relative error = 2.453981304872438e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.800000000000001 y[1] (closed_form) = 14.62284589434225 y[1] (numeric) = 14.62284589434225 absolute error = 1.77635683940025e-15 relative error = 1.214781891456262e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 1.900000000000001 y[1] (closed_form) = 14.76980793882643 y[1] (numeric) = 14.76980793882643 absolute error = 1.77635683940025e-15 relative error = 1.202694609677772e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.000000000000001 y[1] (closed_form) = 14.91824697641271 y[1] (numeric) = 14.91824697641271 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.100000000000001 y[1] (closed_form) = 15.06817785112854 y[1] (numeric) = 15.06817785112854 absolute error = 1.77635683940025e-15 relative error = 1.178879660799338e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.2 y[1] (closed_form) = 15.21961555618634 y[1] (numeric) = 15.21961555618634 absolute error = 1.77635683940025e-15 relative error = 1.16714961218466e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.3 y[1] (closed_form) = 15.37257523548281 y[1] (numeric) = 15.37257523548282 absolute error = 1.77635683940025e-15 relative error = 1.155536279503829e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.399999999999999 y[1] (closed_form) = 15.52707218511336 y[1] (numeric) = 15.52707218511336 absolute error = 3.552713678800501e-15 relative error = 2.288077002827796e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.499999999999999 y[1] (closed_form) = 15.68312185490169 y[1] (numeric) = 15.68312185490169 absolute error = 3.552713678800501e-15 relative error = 2.265310256254954e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.599999999999999 y[1] (closed_form) = 15.84073984994482 y[1] (numeric) = 15.84073984994482 absolute error = 3.552713678800501e-15 relative error = 2.242770042595503e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.699999999999998 y[1] (closed_form) = 15.9999419321736 y[1] (numeric) = 15.9999419321736 absolute error = 3.552713678800501e-15 relative error = 2.220454107809292e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.799999999999998 y[1] (closed_form) = 16.16074402192893 y[1] (numeric) = 16.16074402192894 absolute error = 7.105427357601002e-15 relative error = 4.396720440568493e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.899999999999998 y[1] (closed_form) = 16.32316219955379 y[1] (numeric) = 16.3231621995538 absolute error = 1.06581410364015e-14 relative error = 6.52945851183961e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 2.999999999999997 y[1] (closed_form) = 16.48721270700128 y[1] (numeric) = 16.48721270700129 absolute error = 1.06581410364015e-14 relative error = 6.464489314118896e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.099999999999997 y[1] (closed_form) = 16.65291194945886 y[1] (numeric) = 16.65291194945887 absolute error = 7.105427357601002e-15 relative error = 4.266777713811124e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.199999999999997 y[1] (closed_form) = 16.82027649698886 y[1] (numeric) = 16.82027649698887 absolute error = 1.4210854715202e-14 relative error = 8.448645132406718e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.299999999999996 y[1] (closed_form) = 16.9893230861855 y[1] (numeric) = 16.98932308618551 absolute error = 1.4210854715202e-14 relative error = 8.36457970874499e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.399999999999996 y[1] (closed_form) = 17.16006862184858 y[1] (numeric) = 17.16006862184859 absolute error = 1.4210854715202e-14 relative error = 8.281350750024642e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.499999999999996 y[1] (closed_form) = 17.33253017867395 y[1] (numeric) = 17.33253017867396 absolute error = 1.4210854715202e-14 relative error = 8.198949933280444e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.599999999999995 y[1] (closed_form) = 17.50672500296101 y[1] (numeric) = 17.50672500296102 absolute error = 1.06581410364015e-14 relative error = 6.088026763771542e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.699999999999995 y[1] (closed_form) = 17.68267051433734 y[1] (numeric) = 17.68267051433736 absolute error = 1.4210854715202e-14 relative error = 8.036599847110002e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.799999999999994 y[1] (closed_form) = 17.86038430750072 y[1] (numeric) = 17.86038430750074 absolute error = 1.4210854715202e-14 relative error = 7.956634342539849e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.899999999999994 y[1] (closed_form) = 18.03988415397856 y[1] (numeric) = 18.03988415397857 absolute error = 1.4210854715202e-14 relative error = 7.877464508034498e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 3.999999999999994 y[1] (closed_form) = 18.22118800390508 y[1] (numeric) = 18.22118800390509 absolute error = 1.4210854715202e-14 relative error = 7.799082426544525e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.099999999999993 y[1] (closed_form) = 18.40431398781636 y[1] (numeric) = 18.40431398781638 absolute error = 1.77635683940025e-14 relative error = 9.651850324745583e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.199999999999993 y[1] (closed_form) = 18.58928041846341 y[1] (numeric) = 18.58928041846342 absolute error = 1.77635683940025e-14 relative error = 9.55581280938622e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.299999999999993 y[1] (closed_form) = 18.77610579264342 y[1] (numeric) = 18.77610579264343 absolute error = 1.77635683940025e-14 relative error = 9.460730883270998e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.399999999999992 y[1] (closed_form) = 18.9648087930495 y[1] (numeric) = 18.96480879304952 absolute error = 1.77635683940025e-14 relative error = 9.366595038128071e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.499999999999992 y[1] (closed_form) = 19.15540829013895 y[1] (numeric) = 19.15540829013896 absolute error = 1.77635683940025e-14 relative error = 9.273395860294479e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.599999999999992 y[1] (closed_form) = 19.3479233440203 y[1] (numeric) = 19.34792334402032 absolute error = 1.4210854715202e-14 relative error = 7.344899223819818e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.699999999999991 y[1] (closed_form) = 19.54237320635938 y[1] (numeric) = 19.5423732063594 absolute error = 1.77635683940025e-14 relative error = 9.089770319309005e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 4.799999999999991 y[1] (closed_form) = 19.73877732230446 y[1] (numeric) = 19.73877732230448 absolute error = 2.131628207280301e-14 relative error = 1.079919071214e-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 = 250 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] = 4.899999999999991 y[1] (closed_form) = 19.93715533243081 y[1] (numeric) = 19.93715533243083 absolute error = 2.131628207280301e-14 relative error = 1.069173696917977e-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 = 250 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] = 4.99999999999999 y[1] (closed_form) = 20.13752707470475 y[1] (numeric) = 20.13752707470477 absolute error = 2.131628207280301e-14 relative error = 1.058535240882627e-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 = 250 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] = 5.09999999999999 y[1] (closed_form) = 20.33991258646749 y[1] (numeric) = 20.33991258646751 absolute error = 2.486899575160351e-14 relative error = 1.222669745795727e-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 = 250 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] = 5.19999999999999 y[1] (closed_form) = 20.54433210643886 y[1] (numeric) = 20.54433210643888 absolute error = 2.486899575160351e-14 relative error = 1.210503978555197e-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 = 250 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] = 5.299999999999989 y[1] (closed_form) = 20.7508060767412 y[1] (numeric) = 20.75080607674123 absolute error = 2.842170943040401e-14 relative error = 1.369667728824319e-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 = 250 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] = 5.399999999999989 y[1] (closed_form) = 20.95935514494362 y[1] (numeric) = 20.95935514494365 absolute error = 2.842170943040401e-14 relative error = 1.356039307214118e-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 = 250 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] = 5.499999999999988 y[1] (closed_form) = 21.17000016612672 y[1] (numeric) = 21.17000016612675 absolute error = 3.197442310920451e-14 relative error = 1.510364801997759e-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 = 250 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] = 5.599999999999988 y[1] (closed_form) = 21.38276220496816 y[1] (numeric) = 21.38276220496819 absolute error = 2.842170943040401e-14 relative error = 1.32918792988309e-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 = 250 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] = 5.699999999999988 y[1] (closed_form) = 21.59766253784912 y[1] (numeric) = 21.59766253784916 absolute error = 3.197442310920451e-14 relative error = 1.480457575127423e-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 = 250 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] = 5.799999999999987 y[1] (closed_form) = 21.81472265498198 y[1] (numeric) = 21.81472265498202 absolute error = 3.197442310920451e-14 relative error = 1.465726776127602e-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 = 250 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] = 5.899999999999987 y[1] (closed_form) = 22.03396426255934 y[1] (numeric) = 22.03396426255937 absolute error = 3.552713678800501e-14 relative error = 1.612380612252041e-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 = 250 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] = 5.999999999999987 y[1] (closed_form) = 22.25540928492465 y[1] (numeric) = 22.25540928492468 absolute error = 3.552713678800501e-14 relative error = 1.596337157100515e-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 = 250 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] = 6.099999999999986 y[1] (closed_form) = 22.47907986676469 y[1] (numeric) = 22.47907986676472 absolute error = 3.552713678800501e-14 relative error = 1.580453336994984e-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 = 250 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] = 6.199999999999986 y[1] (closed_form) = 22.70499837532403 y[1] (numeric) = 22.70499837532406 absolute error = 3.197442310920451e-14 relative error = 1.408254807186182e-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 = 250 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] = 6.299999999999986 y[1] (closed_form) = 22.9331874026418 y[1] (numeric) = 22.93318740264183 absolute error = 3.907985046680551e-14 relative error = 1.70407409056029e-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 = 250 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] = 6.399999999999985 y[1] (closed_form) = 23.16366976781088 y[1] (numeric) = 23.16366976781092 absolute error = 3.907985046680551e-14 relative error = 1.68711827005548e-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 = 250 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] = 6.499999999999985 y[1] (closed_form) = 23.39646851925988 y[1] (numeric) = 23.39646851925991 absolute error = 3.552713678800501e-14 relative error = 1.518482875257829e-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 = 250 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] = 6.599999999999985 y[1] (closed_form) = 23.63160693705792 y[1] (numeric) = 23.63160693705795 absolute error = 3.552713678800501e-14 relative error = 1.503373718199972e-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 = 250 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] = 6.699999999999984 y[1] (closed_form) = 23.86910853524273 y[1] (numeric) = 23.86910853524277 absolute error = 3.552713678800501e-14 relative error = 1.488414899766751e-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 = 250 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] = 6.799999999999984 y[1] (closed_form) = 24.10899706417206 y[1] (numeric) = 24.1089970641721 absolute error = 4.263256414560601e-14 relative error = 1.768325908876628e-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 = 250 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] = 6.899999999999983 y[1] (closed_form) = 24.3512965128987 y[1] (numeric) = 24.35129651289875 absolute error = 4.618527782440651e-14 relative error = 1.89662500310579e-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 = 250 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] = 6.999999999999983 y[1] (closed_form) = 24.59603111156945 y[1] (numeric) = 24.5960311115695 absolute error = 4.618527782440651e-14 relative error = 1.877753269009403e-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 = 250 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] = 7.099999999999983 y[1] (closed_form) = 24.84322533384812 y[1] (numeric) = 24.84322533384817 absolute error = 4.263256414560601e-14 relative error = 1.71606398012743e-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 = 250 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] = 7.199999999999982 y[1] (closed_form) = 25.09290389936293 y[1] (numeric) = 25.09290389936298 absolute error = 4.618527782440651e-14 relative error = 1.840571263080439e-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 = 250 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] = 7.299999999999982 y[1] (closed_form) = 25.3450917761785 y[1] (numeric) = 25.34509177617855 absolute error = 5.329070518200751e-14 relative error = 2.102604545788022e-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 = 250 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] = 7.399999999999982 y[1] (closed_form) = 25.59981418329267 y[1] (numeric) = 25.59981418329272 absolute error = 5.329070518200751e-14 relative error = 2.081683280997676e-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 = 250 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] = 7.499999999999981 y[1] (closed_form) = 25.85709659315842 y[1] (numeric) = 25.85709659315847 absolute error = 4.973799150320701e-14 relative error = 1.92357217385216e-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 = 250 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] = 7.599999999999981 y[1] (closed_form) = 26.11696473423113 y[1] (numeric) = 26.11696473423118 absolute error = 4.973799150320701e-14 relative error = 1.904432310926857e-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 = 250 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] = 7.699999999999981 y[1] (closed_form) = 26.37944459354148 y[1] (numeric) = 26.37944459354152 absolute error = 4.618527782440651e-14 relative error = 1.750805543332559e-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 = 250 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] = 7.79999999999998 y[1] (closed_form) = 26.64456241929411 y[1] (numeric) = 26.64456241929417 absolute error = 5.684341886080801e-14 relative error = 2.133396599512027e-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 = 250 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] = 7.89999999999998 y[1] (closed_form) = 26.91234472349257 y[1] (numeric) = 26.91234472349262 absolute error = 5.684341886080801e-14 relative error = 2.112168948667923e-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 = 250 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] = 7.99999999999998 y[1] (closed_form) = 27.1828182845904 y[1] (numeric) = 27.18281828459045 absolute error = 5.684341886080801e-14 relative error = 2.091152516478832e-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 = 250 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] = 8.09999999999998 y[1] (closed_form) = 27.45601015016911 y[1] (numeric) = 27.45601015016917 absolute error = 5.684341886080801e-14 relative error = 2.070345201284022e-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 = 250 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] = 8.199999999999982 y[1] (closed_form) = 27.73194763964293 y[1] (numeric) = 27.73194763964298 absolute error = 5.329070518200751e-14 relative error = 1.921635864688719e-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 = 250 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] = 8.299999999999983 y[1] (closed_form) = 28.01065834699074 y[1] (numeric) = 28.01065834699079 absolute error = 5.329070518200751e-14 relative error = 1.902515268361505e-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 = 250 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] = 8.399999999999984 y[1] (closed_form) = 28.29217014351556 y[1] (numeric) = 28.2921701435156 absolute error = 4.263256414560601e-14 relative error = 1.506867940117249e-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 = 250 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] = 8.499999999999986 y[1] (closed_form) = 28.5765111806316 y[1] (numeric) = 28.57651118063164 absolute error = 3.552713678800501e-14 relative error = 1.243228627995861e-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 = 250 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] = 8.599999999999987 y[1] (closed_form) = 28.86370989267954 y[1] (numeric) = 28.86370989267958 absolute error = 3.907985046680551e-14 relative error = 1.353944126105459e-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 = 250 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] = 8.699999999999989 y[1] (closed_form) = 29.15379499976994 y[1] (numeric) = 29.15379499976997 absolute error = 3.197442310920451e-14 relative error = 1.096749946600668e-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 = 250 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] = 8.79999999999999 y[1] (closed_form) = 29.44679551065521 y[1] (numeric) = 29.44679551065524 absolute error = 3.197442310920451e-14 relative error = 1.085837102296401e-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 = 250 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] = 8.899999999999991 y[1] (closed_form) = 29.74274072563063 y[1] (numeric) = 29.74274072563065 absolute error = 2.486899575160351e-14 relative error = 8.361366553611786e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 8.999999999999993 y[1] (closed_form) = 30.04166023946431 y[1] (numeric) = 30.04166023946433 absolute error = 1.77635683940025e-14 relative error = 5.912978261656572e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.099999999999994 y[1] (closed_form) = 30.34358394435674 y[1] (numeric) = 30.34358394435676 absolute error = 1.4210854715202e-14 relative error = 4.683314515932426e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.199999999999996 y[1] (closed_form) = 30.64854203293001 y[1] (numeric) = 30.64854203293002 absolute error = 7.105427357601002e-15 relative error = 2.318357378946982e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.299999999999997 y[1] (closed_form) = 30.95656500124711 y[1] (numeric) = 30.95656500124711 absolute error = 7.105427357601002e-15 relative error = 2.295289337597616e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.399999999999999 y[1] (closed_form) = 31.26768365186155 y[1] (numeric) = 31.26768365186156 absolute error = 3.552713678800501e-15 relative error = 1.136225413547379e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.5 y[1] (closed_form) = 31.58192909689768 y[1] (numeric) = 31.58192909689768 absolute error = 3.552713678800501e-15 relative error = 1.124919781784162e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.600000000000001 y[1] (closed_form) = 31.89933276116185 y[1] (numeric) = 31.89933276116185 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.700000000000003 y[1] (closed_form) = 32.21992638528501 y[1] (numeric) = 32.21992638528501 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.800000000000004 y[1] (closed_form) = 32.54374202889672 y[1] (numeric) = 32.54374202889672 absolute error = 7.105427357601002e-15 relative error = 2.183346755665604e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 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] = 9.900000000000006 y[1] (closed_form) = 32.8708120738312 y[1] (numeric) = 32.87081207383119 absolute error = 1.4210854715202e-14 relative error = 4.323244184927033e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 250 Order of pole (ratio test) = 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 + 0.2 ) ; Iterations = 180 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.6 %