##############ECHO OF PROBLEM################# ##############temp/diff0postode.ode################# diff ( y , x , 1 ) = y ; ! /* 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=false; 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(exp(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) = 0.006737946999085467 y[1] (numeric) = 0.006737946999085467 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 = 25 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] = -4.9 y[1] (closed_form) = 0.007446583070924338 y[1] (numeric) = 0.007446583070924341 absolute error = 2.602085213965211e-18 relative error = 3.494334501048164e-14 % 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 = 25 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] = -4.800000000000001 y[1] (closed_form) = 0.008229747049020023 y[1] (numeric) = 0.008229747049020028 absolute error = 5.204170427930421e-18 relative error = 6.323609215364792e-14 % 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 = 25 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] = -4.700000000000001 y[1] (closed_form) = 0.009095277101695807 y[1] (numeric) = 0.009095277101695817 absolute error = 1.040834085586084e-17 relative error = 1.144367647019816e-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 = 25 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] = -4.600000000000001 y[1] (closed_form) = 0.01005183574463357 y[1] (numeric) = 0.01005183574463358 absolute error = 1.561251128379126e-17 relative error = 1.553200000519946e-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 = 25 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] = -4.500000000000002 y[1] (closed_form) = 0.01110899653824229 y[1] (numeric) = 0.01110899653824231 absolute error = 2.081668171172169e-17 relative error = 1.873857970885225e-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 = 25 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] = -4.400000000000002 y[1] (closed_form) = 0.01227733990306842 y[1] (numeric) = 0.01227733990306844 absolute error = 2.602085213965211e-17 relative error = 2.119421010177363e-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 = 25 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] = -4.300000000000002 y[1] (closed_form) = 0.0135685590122009 y[1] (numeric) = 0.01356855901220093 absolute error = 3.469446951953614e-17 relative error = 2.556975246106735e-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 = 25 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] = -4.200000000000003 y[1] (closed_form) = 0.01499557682047766 y[1] (numeric) = 0.01499557682047771 absolute error = 4.336808689942018e-17 relative error = 2.892058599586351e-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 = 25 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] = -4.100000000000003 y[1] (closed_form) = 0.0165726754017612 y[1] (numeric) = 0.01657267540176125 absolute error = 5.204170427930421e-17 relative error = 3.140211403270089e-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 = 25 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] = -4.000000000000004 y[1] (closed_form) = 0.01831563888873412 y[1] (numeric) = 0.01831563888873418 absolute error = 6.245004513516506e-17 relative error = 3.409656933866383e-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 = 25 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] = -3.900000000000004 y[1] (closed_form) = 0.02024191144580431 y[1] (numeric) = 0.02024191144580439 absolute error = 7.979727989493313e-17 relative error = 3.942181058769196e-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 = 25 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] = -3.800000000000004 y[1] (closed_form) = 0.0223707718561655 y[1] (numeric) = 0.02237077185616559 absolute error = 9.367506770274758e-17 relative error = 4.187386483802983e-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 = 25 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] = -3.700000000000005 y[1] (closed_form) = 0.02472352647033928 y[1] (numeric) = 0.02472352647033939 absolute error = 1.110223024625157e-16 relative error = 4.490552858456851e-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 = 25 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] = -3.600000000000005 y[1] (closed_form) = 0.02732372244729242 y[1] (numeric) = 0.02732372244729256 absolute error = 1.35308431126191e-16 relative error = 4.952049684562617e-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 = 25 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] = -3.500000000000005 y[1] (closed_form) = 0.03019738342231834 y[1] (numeric) = 0.0301973834223185 absolute error = 1.561251128379126e-16 relative error = 5.17015367372934e-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 = 25 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] = -3.400000000000006 y[1] (closed_form) = 0.03337326996032589 y[1] (numeric) = 0.03337326996032607 absolute error = 1.804112415015879e-16 relative error = 5.405860490028715e-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 = 25 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] = -3.300000000000006 y[1] (closed_form) = 0.03688316740123979 y[1] (numeric) = 0.03688316740123999 absolute error = 2.081668171172169e-16 relative error = 5.64395174776176e-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 = 25 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] = -3.200000000000006 y[1] (closed_form) = 0.04076220397836595 y[1] (numeric) = 0.0407622039783662 absolute error = 2.42861286636753e-16 relative error = 5.95800184812501e-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 = 25 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] = -3.100000000000007 y[1] (closed_form) = 0.0450492023935575 y[1] (numeric) = 0.04504920239355779 absolute error = 2.844946500601964e-16 relative error = 6.315198381867068e-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 = 25 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] = -3.000000000000007 y[1] (closed_form) = 0.04978706836786359 y[1] (numeric) = 0.04978706836786392 absolute error = 3.33066907387547e-16 relative error = 6.689827666224549e-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 = 25 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] = -2.900000000000007 y[1] (closed_form) = 0.05502322005640682 y[1] (numeric) = 0.05502322005640721 absolute error = 3.885780586188048e-16 relative error = 7.062074124714177e-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 = 25 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] = -2.800000000000008 y[1] (closed_form) = 0.06081006262521749 y[1] (numeric) = 0.06081006262521794 absolute error = 4.579669976578771e-16 relative error = 7.531105509303678e-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 = 25 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] = -2.700000000000008 y[1] (closed_form) = 0.06720551273974922 y[1] (numeric) = 0.06720551273974974 absolute error = 5.273559366969494e-16 relative error = 7.846914861569692e-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 = 25 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] = -2.600000000000009 y[1] (closed_form) = 0.07427357821433325 y[1] (numeric) = 0.07427357821433386 absolute error = 6.106226635438361e-16 relative error = 8.221263580189256e-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 = 25 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] = -2.500000000000009 y[1] (closed_form) = 0.08208499862389806 y[1] (numeric) = 0.08208499862389877 absolute error = 7.077671781985373e-16 relative error = 8.622369373987896e-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 = 25 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] = -2.400000000000009 y[1] (closed_form) = 0.09071795328941167 y[1] (numeric) = 0.09071795328941247 absolute error = 8.049116928532385e-16 relative error = 8.872683561162148e-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 = 25 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] = -2.30000000000001 y[1] (closed_form) = 0.1002588437228028 y[1] (numeric) = 0.1002588437228037 absolute error = 9.159339953157541e-16 relative error = 9.13569278584683e-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 = 25 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] = -2.20000000000001 y[1] (closed_form) = 0.1108031583623328 y[1] (numeric) = 0.1108031583623338 absolute error = 1.054711873393899e-15 relative error = 9.518788895393481e-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 = 25 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] = -2.10000000000001 y[1] (closed_form) = 0.1224564282529806 y[1] (numeric) = 0.1224564282529819 absolute error = 1.221245327087672e-15 relative error = 9.97289684592729e-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 = 25 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] = -2.000000000000011 y[1] (closed_form) = 0.1353352832366113 y[1] (numeric) = 0.1353352832366126 absolute error = 1.387778780781446e-15 relative error = 1.025437526409979e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = -1.900000000000011 y[1] (closed_form) = 0.1495686192226335 y[1] (numeric) = 0.149568619222635 absolute error = 1.52655665885959e-15 relative error = 1.020639668129385e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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) = 0.1652988882215848 y[1] (numeric) = 0.1652988882215865 absolute error = 1.693090112553364e-15 relative error = 1.024259830643119e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = -1.70000000000001 y[1] (closed_form) = 0.1826835240527327 y[1] (numeric) = 0.1826835240527346 absolute error = 1.859623566247137e-15 relative error = 1.017948157005306e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = -1.60000000000001 y[1] (closed_form) = 0.2018965179946533 y[1] (numeric) = 0.2018965179946554 absolute error = 2.05391259555654e-15 relative error = 1.017309568266518e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = -1.50000000000001 y[1] (closed_form) = 0.2231301601484275 y[1] (numeric) = 0.2231301601484298 absolute error = 2.275957200481571e-15 relative error = 1.020013250995558e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = -1.40000000000001 y[1] (closed_form) = 0.246596963941604 y[1] (numeric) = 0.2465969639416065 absolute error = 2.470246229790973e-15 relative error = 1.001734242914664e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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) = 0.2725317930340099 y[1] (numeric) = 0.2725317930340126 absolute error = 2.720046410331634e-15 relative error = 9.980657229199651e-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 = 25 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] = -1.20000000000001 y[1] (closed_form) = 0.3011942119121991 y[1] (numeric) = 0.3011942119122021 absolute error = 2.997602166487923e-15 relative error = 9.95238968058839e-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 = 25 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] = -1.10000000000001 y[1] (closed_form) = 0.3328710836980763 y[1] (numeric) = 0.3328710836980796 absolute error = 3.275157922644212e-15 relative error = 9.839118154266818e-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 = 25 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] = -1.00000000000001 y[1] (closed_form) = 0.3678794411714387 y[1] (numeric) = 0.3678794411714423 absolute error = 3.608224830031759e-15 relative error = 9.808171988470153e-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 = 25 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) = 0.4065696597405952 y[1] (numeric) = 0.4065696597405992 absolute error = 3.996802888650564e-15 relative error = 9.830548819606105e-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 = 25 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] = -0.8000000000000096 y[1] (closed_form) = 0.4493289641172173 y[1] (numeric) = 0.4493289641172216 absolute error = 4.329869796038111e-15 relative error = 9.636302446126239e-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 = 25 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) = 0.4965853037914048 y[1] (numeric) = 0.4965853037914096 absolute error = 4.773959005888173e-15 relative error = 9.613572873460464e-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 = 25 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] = -0.6000000000000094 y[1] (closed_form) = 0.5488116360940213 y[1] (numeric) = 0.5488116360940265 absolute error = 5.218048215738236e-15 relative error = 9.507903755240878e-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 = 25 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] = -0.5000000000000093 y[1] (closed_form) = 0.6065306597126278 y[1] (numeric) = 0.6065306597126335 absolute error = 5.773159728050814e-15 relative error = 9.518331242786833e-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 = 25 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] = -0.4000000000000093 y[1] (closed_form) = 0.670320046035633 y[1] (numeric) = 0.6703200460356394 absolute error = 6.439293542825908e-15 relative error = 9.606297142549735e-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 = 25 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] = -0.3000000000000094 y[1] (closed_form) = 0.7408182206817109 y[1] (numeric) = 0.740818220681718 absolute error = 7.105427357601002e-15 relative error = 9.59132370024929e-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 = 25 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] = -0.2000000000000094 y[1] (closed_form) = 0.8187307530779742 y[1] (numeric) = 0.8187307530779819 absolute error = 7.771561172376096e-15 relative error = 9.492206251150737e-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 = 25 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) = 0.9048374180359511 y[1] (numeric) = 0.9048374180359597 absolute error = 8.659739592076221e-15 relative error = 9.570492355271001e-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 = 25 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] = -9.395262345890387e-15 y[1] (closed_form) = 0.9999999999999906 y[1] (numeric) = 1 absolute error = 9.658940314238862e-15 relative error = 9.658940314238953e-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 = 25 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] = 0.09999999999999061 y[1] (closed_form) = 1.105170918075637 y[1] (numeric) = 1.105170918075648 absolute error = 1.06581410364015e-14 relative error = 9.643884816440732e-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 = 25 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] = 0.1999999999999906 y[1] (closed_form) = 1.221402758160158 y[1] (numeric) = 1.22140275816017 absolute error = 1.199040866595169e-14 relative error = 9.816916316787481e-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 = 25 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) = 1.349858807575991 y[1] (numeric) = 1.349858807576004 absolute error = 1.310063169057685e-14 relative error = 9.705186658819756e-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 = 25 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] = 0.3999999999999906 y[1] (closed_form) = 1.491824697641256 y[1] (numeric) = 1.491824697641271 absolute error = 1.443289932012704e-14 relative error = 9.674661736695391e-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 = 25 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) = 1.648721270700113 y[1] (numeric) = 1.648721270700129 absolute error = 1.598721155460225e-14 relative error = 9.696733971178432e-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 = 25 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] = 0.5999999999999907 y[1] (closed_form) = 1.822118800390492 y[1] (numeric) = 1.82211880039051 absolute error = 1.754152378907747e-14 relative error = 9.626992370265983e-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 = 25 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] = 0.6999999999999907 y[1] (closed_form) = 2.013752707470458 y[1] (numeric) = 2.013752707470477 absolute error = 1.909583602355269e-14 relative error = 9.482711532906943e-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 = 25 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] = 0.7999999999999908 y[1] (closed_form) = 2.225540928492447 y[1] (numeric) = 2.225540928492468 absolute error = 2.131628207280301e-14 relative error = 9.578022942603164e-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 = 25 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] = 0.8999999999999909 y[1] (closed_form) = 2.459603111156927 y[1] (numeric) = 2.45960311115695 absolute error = 2.309263891220326e-14 relative error = 9.388766345047083e-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 = 25 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] = 0.999999999999991 y[1] (closed_form) = 2.718281828459021 y[1] (numeric) = 2.718281828459046 absolute error = 2.531308496145357e-14 relative error = 9.312163549944863e-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 = 25 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) = 3.004166023946406 y[1] (numeric) = 3.004166023946434 absolute error = 2.842170943040401e-14 relative error = 9.460765218650596e-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 = 25 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] = 1.199999999999991 y[1] (closed_form) = 3.320116922736518 y[1] (numeric) = 3.320116922736549 absolute error = 3.108624468950438e-14 relative error = 9.362996970565234e-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 = 25 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] = 1.299999999999991 y[1] (closed_form) = 3.669296667619212 y[1] (numeric) = 3.669296667619246 absolute error = 3.463895836830488e-14 relative error = 9.440217432944729e-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 = 25 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) = 4.055199966844639 y[1] (numeric) = 4.055199966844676 absolute error = 3.730349362740526e-14 relative error = 9.198928272933282e-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 = 25 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] = 1.499999999999991 y[1] (closed_form) = 4.481689070338026 y[1] (numeric) = 4.481689070338067 absolute error = 4.085620730620576e-14 relative error = 9.116252079291218e-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 = 25 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] = 1.599999999999991 y[1] (closed_form) = 4.953032424395072 y[1] (numeric) = 4.953032424395118 absolute error = 4.529709940470639e-14 relative error = 9.145326645068077e-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 = 25 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] = 1.699999999999992 y[1] (closed_form) = 5.473947391727154 y[1] (numeric) = 5.473947391727203 absolute error = 4.884981308350689e-14 relative error = 8.924056003412498e-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 = 25 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] = 1.799999999999992 y[1] (closed_form) = 6.049647464412895 y[1] (numeric) = 6.049647464412949 absolute error = 5.417888360170764e-14 relative error = 8.955709224449095e-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 = 25 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] = 1.899999999999992 y[1] (closed_form) = 6.685894442279213 y[1] (numeric) = 6.685894442279272 absolute error = 5.861977570020827e-14 relative error = 8.767678910620798e-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 = 25 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) = 7.389056098930589 y[1] (numeric) = 7.389056098930653 absolute error = 6.394884621840902e-14 relative error = 8.654535215623044e-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 = 25 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] = 2.099999999999992 y[1] (closed_form) = 8.166169912567582 y[1] (numeric) = 8.166169912567653 absolute error = 7.105427357601002e-14 relative error = 8.701052554228492e-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 = 25 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] = 2.199999999999991 y[1] (closed_form) = 9.025013499434042 y[1] (numeric) = 9.025013499434126 absolute error = 8.348877145181177e-14 relative error = 9.25081956465188e-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 = 25 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] = 2.299999999999991 y[1] (closed_form) = 9.974182454814631 y[1] (numeric) = 9.974182454814725 absolute error = 9.414691248821327e-14 relative error = 9.439060586140338e-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 = 25 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] = 2.399999999999991 y[1] (closed_form) = 11.0231763806415 y[1] (numeric) = 11.02317638064161 absolute error = 1.083577672034153e-13 relative error = 9.829994863704554e-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 = 25 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] = 2.49999999999999 y[1] (closed_form) = 12.18249396070335 y[1] (numeric) = 12.18249396070348 absolute error = 1.261213355974178e-13 relative error = 1.035266965895842e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 2.59999999999999 y[1] (closed_form) = 13.46373803500155 y[1] (numeric) = 13.4637380350017 absolute error = 1.438849039914203e-13 relative error = 1.068684667046878e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 2.69999999999999 y[1] (closed_form) = 14.87973172487268 y[1] (numeric) = 14.87973172487284 absolute error = 1.652011860642233e-13 relative error = 1.110243041466105e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 2.799999999999989 y[1] (closed_form) = 16.44464677109687 y[1] (numeric) = 16.44464677109706 absolute error = 1.918465386552271e-13 relative error = 1.166620003005578e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 2.899999999999989 y[1] (closed_form) = 18.17414536944286 y[1] (numeric) = 18.17414536944307 absolute error = 2.167155344068306e-13 relative error = 1.192438653930906e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 2.999999999999988 y[1] (closed_form) = 20.08553692318744 y[1] (numeric) = 20.08553692318768 absolute error = 2.451372438372346e-13 relative error = 1.220466471843427e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.099999999999988 y[1] (closed_form) = 22.19795128144137 y[1] (numeric) = 22.19795128144165 absolute error = 2.806643806252396e-13 relative error = 1.264370648744911e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.199999999999988 y[1] (closed_form) = 24.53253019710905 y[1] (numeric) = 24.53253019710937 absolute error = 3.197442310920451e-13 relative error = 1.303347956867997e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.299999999999987 y[1] (closed_form) = 27.11263892065755 y[1] (numeric) = 27.11263892065791 absolute error = 3.623767952376511e-13 relative error = 1.336560400107533e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.399999999999987 y[1] (closed_form) = 29.96410004739662 y[1] (numeric) = 29.96410004739704 absolute error = 4.121147867408581e-13 relative error = 1.375361803254505e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.499999999999987 y[1] (closed_form) = 33.11545195869187 y[1] (numeric) = 33.11545195869234 absolute error = 4.689582056016661e-13 relative error = 1.416131074359617e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.599999999999986 y[1] (closed_form) = 36.59823444367748 y[1] (numeric) = 36.59823444367802 absolute error = 5.329070518200751e-13 relative error = 1.456100437413689e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.699999999999986 y[1] (closed_form) = 40.44730436006682 y[1] (numeric) = 40.44730436006742 absolute error = 5.968558980384842e-13 relative error = 1.475638259413286e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.799999999999986 y[1] (closed_form) = 44.70118449330018 y[1] (numeric) = 44.70118449330085 absolute error = 6.679101716144942e-13 relative error = 1.494166606960047e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.899999999999985 y[1] (closed_form) = 49.40244910552945 y[1] (numeric) = 49.40244910553021 absolute error = 7.602807272633072e-13 relative error = 1.538953515521585e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 3.999999999999985 y[1] (closed_form) = 54.59815003314341 y[1] (numeric) = 54.59815003314428 absolute error = 8.668621376273222e-13 relative error = 1.587713387909846e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.099999999999985 y[1] (closed_form) = 60.34028759736103 y[1] (numeric) = 60.34028759736201 absolute error = 9.805489753489383e-13 relative error = 1.62503198839878e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.199999999999984 y[1] (closed_form) = 66.68633104092409 y[1] (numeric) = 66.6863310409252 absolute error = 1.108446667785756e-12 relative error = 1.66217971581841e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.299999999999984 y[1] (closed_form) = 73.69979369959461 y[1] (numeric) = 73.69979369959586 absolute error = 1.250555214937776e-12 relative error = 1.696823223189911e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.399999999999983 y[1] (closed_form) = 81.45086866496678 y[1] (numeric) = 81.45086866496818 absolute error = 1.406874616804998e-12 relative error = 1.727267787151441e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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) = 90.01713130052029 y[1] (numeric) = 90.01713130052188 absolute error = 1.591615728102624e-12 relative error = 1.768125361370436e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.599999999999983 y[1] (closed_form) = 99.4843156419321 y[1] (numeric) = 99.48431564193389 absolute error = 1.790567694115452e-12 relative error = 1.799849235089614e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.699999999999982 y[1] (closed_form) = 109.9471724521216 y[1] (numeric) = 109.9471724521236 absolute error = 2.032152224273887e-12 relative error = 1.848298759259883e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.799999999999982 y[1] (closed_form) = 121.5104175187327 y[1] (numeric) = 121.510417518735 absolute error = 2.302158463862725e-12 relative error = 1.894618182435108e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.899999999999982 y[1] (closed_form) = 134.289779684933 y[1] (numeric) = 134.2897796849356 absolute error = 2.586375558166765e-12 relative error = 1.925966044649748e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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] = 4.999999999999981 y[1] (closed_form) = 148.4131591025738 y[1] (numeric) = 148.4131591025767 absolute error = 2.899014361901209e-12 relative error = 1.953340512007828e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 NO POLE (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 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 ) = y ; 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 %