##############ECHO OF PROBLEM################# ##############temp/diffpostode.ode################# diff ( y , x , 2 ) = diff ( y , x , 1 ) ; ! /* 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); array_y_init[1 + 1] = exact_soln_yp(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(1.0) + exp(c(x))); } double exact_soln_yp (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) = 1.006737946999085 y[1] (numeric) = 1.006737946999085 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) = 1.007446583070924 y[1] (numeric) = 1.00746103905474 absolute error = 1.445598381533131e-05 relative error = 0.001434913181328802 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 5 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) = 1.00822974704902 y[1] (numeric) = 1.008394105082548 absolute error = 0.0001643580335282113 relative error = 0.01630164493849439 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 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) = 1.009095277101696 y[1] (numeric) = 1.009924786802966 absolute error = 0.0008295097012700481 relative error = 0.08220330825970665 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 4 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) = 1.010051835744634 y[1] (numeric) = 1.013156367508092 absolute error = 0.003104531763458374 relative error = 0.3073636078458925 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 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) = 1.011108996538242 y[1] (numeric) = 1.021228947858911 absolute error = 0.01011995132066867 relative error = 1.000876399608409 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 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) = 1.012277339903068 y[1] (numeric) = 1.043079699506376 absolute error = 0.03080235960330802 relative error = 3.042877518749706 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 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) = 1.013568559012201 y[1] (numeric) = 1.104145079985434 absolute error = 0.09057652097323254 relative error = 8.936398052984812 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 3 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) = 1.014995576820478 y[1] (numeric) = 1.276820853548645 absolute error = 0.2618252767281677 relative error = 25.79570617916858 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 2 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) = 1.016572675401761 y[1] (numeric) = 1.767155628753718 absolute error = 0.750582953351957 relative error = 73.83465752267226 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 2 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) = 1.018315638888734 y[1] (numeric) = 3.161592956917451 absolute error = 2.143277318028717 relative error = 210.4727882179664 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 1 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) = 1.020241911445804 y[1] (numeric) = 7.129234324763743 absolute error = 6.108992413317939 relative error = 598.7788136110551 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 1 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) = 1.022370771856165 y[1] (numeric) = 18.42057919081419 absolute error = 17.39820841895803 relative error = 1701.751350673954 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 0 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) = 1.024723526470339 y[1] (numeric) = 50.55622248887887 absolute error = 49.53149896240853 relative error = 4833.645142609324 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 0 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) = 1.027323722447292 y[1] (numeric) = 142.017694205504 absolute error = 140.9903704830567 relative error = 13724.04505049189 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -1 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) = 1.030197383422318 y[1] (numeric) = 402.328884180954 absolute error = 401.2986867975317 relative error = 38953.57270899062 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -1 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) = 1.033373269960326 y[1] (numeric) = 1143.210310022929 absolute error = 1142.176936752969 relative error = 110528.980181268 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -2 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) = 1.03688316740124 y[1] (numeric) = 3251.8627572343 absolute error = 3250.825874066898 relative error = 313519.0131608082 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -2 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) = 1.040762203978366 y[1] (numeric) = 9253.385439167152 absolute error = 9252.344676963174 relative error = 888996.9910125118 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -2 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) = 1.045049202393558 y[1] (numeric) = 26334.56869850284 absolute error = 26333.52364930044 relative error = 2519835.773185294 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -3 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) = 1.049787068367864 y[1] (numeric) = 74950.03671655906 absolute error = 74948.9869294907 relative error = 7139446.578058559 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -3 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) = 1.055023220056407 y[1] (numeric) = 213316.5497505784 absolute error = 213315.4947273584 relative error = 20219033.16174912 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -4 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) = 1.060810062625217 y[1] (numeric) = 607127.2608404878 absolute error = 607126.2000304252 relative error = 57232319.09470696 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -4 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) = 1.067205512739749 y[1] (numeric) = 1727968.37373587 absolute error = 1727967.306530357 relative error = 161915140.6081372 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -5 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) = 1.074273578214333 y[1] (numeric) = 4918041.080741595 absolute error = 4918040.006468018 relative error = 457801448.9235438 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -5 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) = 1.082084998623898 y[1] (numeric) = 13997440.25804542 absolute error = 13997439.17596042 relative error = 1293561891.511401 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -6 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) = 1.090717953289412 y[1] (numeric) = 39838697.49535345 absolute error = 39838696.4046355 relative error = 3652520459.985926 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -6 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) = 1.100258843722803 y[1] (numeric) = 113386579.0878752 absolute error = 113386577.9876164 relative error = 10305445726.2043 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -7 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) = 1.110803158362333 y[1] (numeric) = 322714276.9288173 absolute error = 322714275.8180141 relative error = 29052336895.92625 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -7 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) = 1.122456428252981 y[1] (numeric) = 918490581.2186861 absolute error = 918490580.0962297 relative error = 81828617750.96173 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -7 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) = 1.135335283236611 y[1] (numeric) = 2614154406.000429 absolute error = 2614154404.865094 relative error = 230253956118.8188 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -8 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) = 1.149568619222634 y[1] (numeric) = 7440254044.356895 absolute error = 7440254043.207327 relative error = 647221394077.2504 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -8 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) = 1.165298888221585 y[1] (numeric) = 21176017807.75845 absolute error = 21176017806.59315 relative error = 1817217713037.624 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -9 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) = 1.182683524052733 y[1] (numeric) = 60269948787.64954 absolute error = 60269948786.46686 relative error = 5096033517059.428 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -9 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) = 1.201896517994653 y[1] (numeric) = 171536818674.6166 absolute error = 171536818673.4147 relative error = 14272178686366.56 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -10 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) = 1.223130160148427 y[1] (numeric) = 488218104596.2462 absolute error = 488218104595.0231 relative error = 39915466113253.03 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -10 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) = 1.246596963941604 y[1] (numeric) = 1389537940005.079 absolute error = 1389537940003.832 relative error = 111466494801195.8 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -11 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) = 1.27253179303401 y[1] (numeric) = 3954821971036.983 absolute error = 3954821971035.711 relative error = 310783745654519.3 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -11 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) = 1.301194211912199 y[1] (numeric) = 11255984001807.5 absolute error = 11255984001806.2 relative error = 865050266805653.8 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -11 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) = 1.332871083698076 y[1] (numeric) = 32036126221818.12 absolute error = 32036126221816.79 relative error = 2403542744203884 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -12 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) = 1.367879441171439 y[1] (numeric) = 91179356965636.66 absolute error = 91179356965635.28 relative error = 6665745110369533 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -12 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) = 1.406569659740595 y[1] (numeric) = 259509376355406.6 absolute error = 259509376355405.2 relative error = 1.844980620464008e+16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -13 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) = 1.449328964117217 y[1] (numeric) = 738600475563270 absolute error = 738600475563268.5 relative error = 5.096154798873754e+16 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -13 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) = 1.496585303791405 y[1] (numeric) = 2102161664305984 absolute error = 2102161664305982 relative error = 1.404638719209943e+17 % 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] = -0.6000000000000094 y[1] (closed_form) = 1.548811636094021 y[1] (numeric) = 5983050118547019 absolute error = 5983050118547017 relative error = 3.862994039504888e+17 % 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] = -0.5000000000000093 y[1] (closed_form) = 1.606530659712628 y[1] (numeric) = 1.702860885005418e+16 absolute error = 1.702860885005418e+16 relative error = 1.059961647610274e+18 % 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) = 1.670320046035633 y[1] (numeric) = 4.846583492076171e+16 absolute error = 4.846583492076171e+16 relative error = 2.90158973041073e+18 % 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) = 1.740818220681711 y[1] (numeric) = 1.379406371507002e+17 absolute error = 1.379406371507002e+17 relative error = 7.923896677545236e+18 % 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) = 1.818730753077974 y[1] (numeric) = 3.92598609074825e+17 absolute error = 3.92598609074825e+17 relative error = 2.158640625669308e+19 % 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 = 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) = 1.904837418035951 y[1] (numeric) = 1.117391299846586e+18 absolute error = 1.117391299846586e+18 relative error = 5.866071766895002e+19 % 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 = 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) = 1.999999999999991 y[1] (numeric) = 3.180254051116319e+18 absolute error = 3.180254051116319e+18 relative error = 1.590127025558167e+20 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -17 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) = 2.105170918075637 y[1] (numeric) = 9.051453891783814e+18 absolute error = 9.051453891783814e+18 relative error = 4.29962898217208e+20 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -17 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) = 2.221402758160158 y[1] (numeric) = 2.576172099406022e+19 absolute error = 2.576172099406022e+19 relative error = 1.159705096224737e+21 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -18 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) = 2.34985880757599 y[1] (numeric) = 7.332151016956805e+19 absolute error = 7.332151016956805e+19 relative error = 3.12025173313299e+21 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -18 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) = 2.491824697641256 y[1] (numeric) = 2.086834126798285e+20 absolute error = 2.086834126798285e+20 relative error = 8.374722863826125e+21 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -18 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) = 2.648721270700113 y[1] (numeric) = 5.939425773826249e+20 absolute error = 5.939425773826249e+20 relative error = 2.242374778927317e+22 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -19 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) = 2.822118800390492 y[1] (numeric) = 1.690444778038721e+21 absolute error = 1.690444778038721e+21 relative error = 5.989984467715592e+22 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -19 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) = 3.013752707470458 y[1] (numeric) = 4.811245491426486e+21 absolute error = 4.811245491426486e+21 relative error = 1.596430085156099e+23 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -20 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) = 3.225540928492447 y[1] (numeric) = 1.369348675537833e+22 absolute error = 1.369348675537833e+22 relative error = 4.24533033650836e+23 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -20 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) = 3.459603111156927 y[1] (numeric) = 3.897360462147742e+22 absolute error = 3.897360462147742e+22 relative error = 1.126533980033456e+24 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -21 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) = 3.718281828459021 y[1] (numeric) = 1.109244040123425e+23 absolute error = 1.109244040123425e+23 relative error = 2.983216687969917e+24 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -21 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) = 4.004166023946405 y[1] (numeric) = 3.157065794913107e+23 absolute error = 3.157065794913107e+23 relative error = 7.884452782508711e+24 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -21 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) = 4.320116922736518 y[1] (numeric) = 8.985456827247235e+23 absolute error = 8.985456827247235e+23 relative error = 2.079910564447298e+25 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -22 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) = 4.669296667619212 y[1] (numeric) = 2.557388399203322e+24 absolute error = 2.557388399203322e+24 relative error = 5.477031298821472e+25 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -22 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) = 5.055199966844639 y[1] (numeric) = 7.278689943228385e+24 absolute error = 7.278689943228385e+24 relative error = 1.439842140957207e+26 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -23 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) = 5.481689070338026 y[1] (numeric) = 2.071618347301418e+25 absolute error = 2.071618347301418e+25 relative error = 3.77916062133322e+26 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -23 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) = 5.953032424395072 y[1] (numeric) = 5.896119508248158e+25 absolute error = 5.896119508248158e+25 relative error = 9.904396764389038e+26 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -23 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) = 6.473947391727154 y[1] (numeric) = 1.678119200905415e+26 absolute error = 1.678119200905415e+26 relative error = 2.592111272096262e+27 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -24 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) = 7.049647464412895 y[1] (numeric) = 4.776165151516979e+26 absolute error = 4.776165151516979e+26 relative error = 6.77504112883288e+27 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -24 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) = 7.685894442279213 y[1] (numeric) = 1.359364313468156e+27 absolute error = 1.359364313468156e+27 relative error = 1.768648169288471e+28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -25 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) = 8.389056098930588 y[1] (numeric) = 3.868943552221685e+27 absolute error = 3.868943552221685e+27 relative error = 4.611893765634594e+28 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -25 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) = 9.166169912567582 y[1] (numeric) = 1.101156184694001e+28 absolute error = 1.101156184694001e+28 relative error = 1.201326393900057e+29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -26 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) = 10.02501349943404 y[1] (numeric) = 3.134046611751578e+28 absolute error = 3.134046611751578e+28 relative error = 3.126226824461144e+29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -26 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) = 10.97418245481463 y[1] (numeric) = 8.919940968556647e+28 absolute error = 8.919940968556647e+28 relative error = 8.12811433132612e+29 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -26 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) = 12.0231763806415 y[1] (numeric) = 2.53874165700641e+29 absolute error = 2.53874165700641e+29 relative error = 2.111539893146735e+30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -27 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) = 13.18249396070335 y[1] (numeric) = 7.225618671400878e+29 absolute error = 7.225618671400878e+29 relative error = 5.481222819399915e+30 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -27 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) = 14.46373803500155 y[1] (numeric) = 2.056513510951743e+30 absolute error = 2.056513510951743e+30 relative error = 1.421840955619549e+31 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -28 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) = 15.87973172487268 y[1] (numeric) = 5.853129002595307e+30 absolute error = 5.853129002595307e+30 relative error = 3.685911767279706e+31 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -28 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) = 17.44464677109687 y[1] (numeric) = 1.665883493523337e+31 absolute error = 1.665883493523337e+31 relative error = 9.549539840975475e+31 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -28 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) = 19.17414536944286 y[1] (numeric) = 4.741340593660239e+31 absolute error = 4.741340593660239e+31 relative error = 2.472778057277245e+32 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -29 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) = 21.08553692318744 y[1] (numeric) = 1.349452750596901e+32 absolute error = 1.349452750596901e+32 relative error = 6.399897500892798e+32 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -29 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) = 23.19795128144137 y[1] (numeric) = 3.840733839135023e+32 absolute error = 3.840733839135023e+32 relative error = 1.655634927644518e+33 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -30 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) = 25.53253019710905 y[1] (numeric) = 1.093127300422484e+33 absolute error = 1.093127300422484e+33 relative error = 4.281312082992286e+33 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -30 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) = 28.11263892065755 y[1] (numeric) = 3.111195268865748e+33 absolute error = 3.111195268865748e+33 relative error = 1.106689157729551e+34 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -31 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) = 30.96410004739662 y[1] (numeric) = 8.854902807085292e+33 absolute error = 8.854902807085292e+33 relative error = 2.85973201014437e+34 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -31 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) = 34.11545195869187 y[1] (numeric) = 2.520230874210372e+34 absolute error = 2.520230874210372e+34 relative error = 7.387358893154784e+34 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -31 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) = 37.59823444367748 y[1] (numeric) = 7.172934359303119e+34 absolute error = 7.172934359303119e+34 relative error = 1.90778489081668e+35 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -32 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) = 41.44730436006682 y[1] (numeric) = 2.041518808827055e+35 absolute error = 2.041518808827055e+35 relative error = 4.925576802514555e+35 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -32 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) = 45.70118449330018 y[1] (numeric) = 5.810451954560417e+35 absolute error = 5.810451954560417e+35 relative error = 1.271400734791071e+36 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -33 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) = 50.40244910552945 y[1] (numeric) = 1.653737000623198e+36 absolute error = 1.653737000623198e+36 relative error = 3.281064769612104e+36 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -33 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) = 55.59815003314341 y[1] (numeric) = 4.706769952866965e+36 absolute error = 4.706769952866965e+36 relative error = 8.465695261553028e+36 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -33 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) = 61.34028759736103 y[1] (numeric) = 1.339613456121672e+37 absolute error = 1.339613456121672e+37 relative error = 2.183904752639771e+37 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -34 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) = 67.68633104092409 y[1] (numeric) = 3.81272981214889e+37 absolute error = 3.81272981214889e+37 relative error = 5.63293910825756e+37 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -34 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) = 74.69979369959461 y[1] (numeric) = 1.085156957331173e+38 absolute error = 1.085156957331173e+38 relative error = 1.452690701791138e+38 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -35 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) = 82.45086866496678 y[1] (numeric) = 3.088510542478129e+38 absolute error = 3.088510542478129e+38 relative error = 3.745879931269216e+38 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -35 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) = 91.01713130052029 y[1] (numeric) = 8.790338859788945e+38 absolute error = 8.790338859788945e+38 relative error = 9.657894875597662e+38 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -35 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) = 100.4843156419321 y[1] (numeric) = 2.50185505949144e+39 absolute error = 2.50185505949144e+39 relative error = 2.489796585177136e+39 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -36 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) = 110.9471724521216 y[1] (numeric) = 7.120634185487135e+39 absolute error = 7.120634185487135e+39 relative error = 6.418040251147447e+39 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -36 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) = 122.5104175187327 y[1] (numeric) = 2.026633437903261e+40 absolute error = 2.026633437903261e+40 relative error = 1.654253963825872e+40 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -37 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) = 135.289779684933 y[1] (numeric) = 5.768086078623078e+40 absolute error = 5.768086078623078e+40 relative error = 4.263504672752053e+40 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -37 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) = 149.4131591025738 y[1] (numeric) = 1.641679071713485e+41 absolute error = 1.641679071713485e+41 relative error = 1.098751329249691e+41 % Desired digits = 8 Estimated correct digits = 13 Correct digits = -38 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 , 2 ) = diff ( y , x , 1 ) ; 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 %