##############ECHO OF PROBLEM################# ##############temp/div_lin_linpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(0.1); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-1.5); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(1.0); array_given_ord_poles[1][2]=c(0.0); /* 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(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = 0.3407877024514202 y[1] (numeric) = 0.3407877024514202 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.667 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 1.124e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2 y[1] (closed_form) = 0.4059438579055289 y[1] (numeric) = 0.4059438579055289 absolute error = 5.551115123125783e-17 relative error = 1.367458828362822e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.771 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 2.284e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3 y[1] (closed_form) = 0.470233461365516 y[1] (numeric) = 0.4702334613655161 absolute error = 5.551115123125783e-17 relative error = 1.180501937698317e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.875 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4 y[1] (closed_form) = 0.533750266683085 y[1] (numeric) = 0.533750266683085 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 1.979 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.4999999999999999 y[1] (closed_form) = 0.5965735902799726 y[1] (numeric) = 0.5965735902799727 absolute error = 1.110223024625157e-16 relative error = 1.860999284437194e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.083 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 9.84e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6 y[1] (closed_form) = 0.6587711313223307 y[1] (numeric) = 0.6587711313223307 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.188 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.1 Order of pole (three term test) = 1.16e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7000000000000001 y[1] (closed_form) = 0.720401135231054 y[1] (numeric) = 0.7204011352310539 absolute error = 1.110223024625157e-16 relative error = 1.541117816630141e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.292 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.2 Order of pole (three term test) = 2.466e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8000000000000002 y[1] (closed_form) = 0.7815140758737624 y[1] (numeric) = 0.7815140758737623 absolute error = 1.110223024625157e-16 relative error = 1.420605282616164e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.396 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9000000000000002 y[1] (closed_form) = 0.8421539794784615 y[1] (numeric) = 0.8421539794784613 absolute error = 2.220446049250313e-16 relative error = 2.6366271529411e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1 y[1] (closed_form) = 0.9023594781085251 y[1] (numeric) = 0.9023594781085251 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.604 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.5 Order of pole (three term test) = 1.724e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.1 y[1] (closed_form) = 0.9621646563968456 y[1] (numeric) = 0.9621646563968455 absolute error = 1.110223024625157e-16 relative error = 1.153880489419312e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.708 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.6 Order of pole (three term test) = 1.309e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.2 y[1] (closed_form) = 1.021599738392557 y[1] (numeric) = 1.021599738392557 absolute error = 2.220446049250313e-16 relative error = 2.173499038619653e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.813 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.7 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.3 y[1] (closed_form) = 1.080691649435276 y[1] (numeric) = 1.080691649435276 absolute error = 2.220446049250313e-16 relative error = 2.054652731341659e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 2.917 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.8 Order of pole (three term test) = 3.71e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.400000000000001 y[1] (closed_form) = 1.139464479388094 y[1] (numeric) = 1.139464479388093 absolute error = 2.220446049250313e-16 relative error = 1.948675092042114e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 2.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.021 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 2.9 Order of pole (three term test) = 7.766e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.500000000000001 y[1] (closed_form) = 1.197939867307014 y[1] (numeric) = 1.197939867307014 absolute error = 2.220446049250313e-16 relative error = 1.853553846773551e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.125 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3 Order of pole (three term test) = 1.847e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.600000000000001 y[1] (closed_form) = 1.256137323012762 y[1] (numeric) = 1.256137323012761 absolute error = 4.440892098500626e-16 relative error = 3.535355583455988e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.229 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.1 Order of pole (three term test) = 1.043e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.700000000000001 y[1] (closed_form) = 1.314074497591407 y[1] (numeric) = 1.314074497591407 absolute error = 2.220446049250313e-16 relative error = 1.68974137563754e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.333 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.2 Order of pole (three term test) = 1.124e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.800000000000001 y[1] (closed_form) = 1.371767412258095 y[1] (numeric) = 1.371767412258095 absolute error = 4.440892098500626e-16 relative error = 3.237350631613547e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.438 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (closed_form) = 1.429230653045516 y[1] (numeric) = 1.429230653045515 absolute error = 6.661338147750939e-16 relative error = 4.660785950508717e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.542 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.4 Order of pole (three term test) = 2.284e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.000000000000001 y[1] (closed_form) = 1.486477537263829 y[1] (numeric) = 1.486477537263828 absolute error = 6.661338147750939e-16 relative error = 4.481290823951849e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.646 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.5 Order of pole (three term test) = 2.166e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (closed_form) = 1.543520256505503 y[1] (numeric) = 1.543520256505502 absolute error = 4.440892098500626e-16 relative error = 2.877119415688597e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.75 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.6 Order of pole (three term test) = 9.894e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (closed_form) = 1.600370000052531 y[1] (numeric) = 1.600370000052531 absolute error = 2.220446049250313e-16 relative error = 1.387457931089328e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.854 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.7 Order of pole (three term test) = 8.723e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (closed_form) = 1.657037061823071 y[1] (numeric) = 1.657037061823071 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 3.958 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.399999999999999 y[1] (closed_form) = 1.713530933423886 y[1] (numeric) = 1.713530933423886 absolute error = 2.220446049250313e-16 relative error = 1.295830735202157e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.062 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 3.9 Order of pole (three term test) = 1.228e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499999999999999 y[1] (closed_form) = 1.769860385419959 y[1] (numeric) = 1.769860385419959 absolute error = 2.220446049250313e-16 relative error = 1.254588253142599e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.167 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4 Order of pole (three term test) = 2.952e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.599999999999999 y[1] (closed_form) = 1.826033538567551 y[1] (numeric) = 1.826033538567552 absolute error = 6.661338147750939e-16 relative error = 3.647982365634142e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.271 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.1 Order of pole (three term test) = 7.66e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.699999999999998 y[1] (closed_form) = 1.882057926462316 y[1] (numeric) = 1.882057926462317 absolute error = 8.881784197001252e-16 relative error = 4.719187476708672e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.375 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.2 Order of pole (three term test) = 2.321e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.799999999999998 y[1] (closed_form) = 1.937940550814864 y[1] (numeric) = 1.937940550814865 absolute error = 1.110223024625157e-15 relative error = 5.72888071390183e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.479 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.3 Order of pole (three term test) = 8.563e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.899999999999998 y[1] (closed_form) = 1.993687930371039 y[1] (numeric) = 1.99368793037104 absolute error = 1.332267629550188e-15 relative error = 6.68242812355414e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.583 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.999999999999997 y[1] (closed_form) = 2.049306144334053 y[1] (numeric) = 2.049306144334055 absolute error = 1.77635683940025e-15 relative error = 8.66808916916364e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.687 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.5 Order of pole (three term test) = 2.6e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.099999999999997 y[1] (closed_form) = 2.104800871013747 y[1] (numeric) = 2.104800871013749 absolute error = 1.77635683940025e-15 relative error = 8.439548196047135e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.792 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.6 Order of pole (three term test) = 1.191e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.199999999999997 y[1] (closed_form) = 2.160177422318988 y[1] (numeric) = 2.16017742231899 absolute error = 1.77635683940025e-15 relative error = 8.223198803241359e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 4.896 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.7 Order of pole (three term test) = 2.402e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.299999999999996 y[1] (closed_form) = 2.215440774618445 y[1] (numeric) = 2.215440774618448 absolute error = 2.220446049250313e-15 relative error = 1.002259268082998e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.8 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.399999999999996 y[1] (closed_form) = 2.270595596419129 y[1] (numeric) = 2.270595596419132 absolute error = 2.220446049250313e-15 relative error = 9.779134834719555e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.104 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 4.9 Order of pole (three term test) = 6.805e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.499999999999996 y[1] (closed_form) = 2.325646273248509 y[1] (numeric) = 2.325646273248511 absolute error = 2.220446049250313e-15 relative error = 9.547651656194258e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.208 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.599999999999995 y[1] (closed_form) = 2.380596930072554 y[1] (numeric) = 2.380596930072556 absolute error = 2.664535259100376e-15 relative error = 1.119271904219068e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.312 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.1 Order of pole (three term test) = 1.071e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.699999999999995 y[1] (closed_form) = 2.435451451536829 y[1] (numeric) = 2.435451451536832 absolute error = 2.664535259100376e-15 relative error = 1.094062153207361e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.417 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.2 Order of pole (three term test) = 1.309e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.799999999999994 y[1] (closed_form) = 2.490213500279503 y[1] (numeric) = 2.490213500279505 absolute error = 2.664535259100376e-15 relative error = 1.070002736231776e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.521 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.899999999999994 y[1] (closed_form) = 2.54488653353254 y[1] (numeric) = 2.544886533532543 absolute error = 2.664535259100376e-15 relative error = 1.047015347832326e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.625 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.4 Order of pole (three term test) = 1.857e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.999999999999994 y[1] (closed_form) = 2.599473818199589 y[1] (numeric) = 2.599473818199592 absolute error = 2.664535259100376e-15 relative error = 1.025028696363577e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.729 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.5 Order of pole (three term test) = 2.159e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.099999999999993 y[1] (closed_form) = 2.653978444575259 y[1] (numeric) = 2.653978444575261 absolute error = 2.664535259100376e-15 relative error = 1.003977731826231e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.833 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.6 Order of pole (three term test) = 1.237e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.199999999999993 y[1] (closed_form) = 2.708403338850109 y[1] (numeric) = 2.708403338850112 absolute error = 3.108624468950438e-15 relative error = 1.147770136138678e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 5.937 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.7 Order of pole (three term test) = 1.396e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.299999999999993 y[1] (closed_form) = 2.762751274528076 y[1] (numeric) = 2.762751274528079 absolute error = 3.108624468950438e-15 relative error = 1.125191578992736e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.042 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.8 Order of pole (three term test) = 7.766e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999992 y[1] (closed_form) = 2.817024882867901 y[1] (numeric) = 2.817024882867904 absolute error = 3.552713678800501e-15 relative error = 1.261158075104976e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 5.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.146 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 5.9 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.499999999999992 y[1] (closed_form) = 2.871226662446996 y[1] (numeric) = 2.871226662446999 absolute error = 3.108624468950438e-15 relative error = 1.082681666901602e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.25 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6 Order of pole (three term test) = 9.234e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.599999999999992 y[1] (closed_form) = 2.925358987934798 y[1] (numeric) = 2.925358987934802 absolute error = 3.552713678800501e-15 relative error = 1.214453916067441e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 6.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.354 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.1 Order of pole (three term test) = 1.975e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999991 y[1] (closed_form) = 2.979424118152743 y[1] (numeric) = 2.979424118152747 absolute error = 3.996802888650564e-15 relative error = 1.341468260359187e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 6.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.458 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.2 Order of pole (three term test) = 1.043e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999991 y[1] (closed_form) = 3.033424203489353 y[1] (numeric) = 3.033424203489357 absolute error = 3.996802888650564e-15 relative error = 1.317587854693397e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 6.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.562 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.3 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999991 y[1] (closed_form) = 3.087361292731388 y[1] (numeric) = 3.087361292731392 absolute error = 3.996802888650564e-15 relative error = 1.294569216132976e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 6.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.667 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.99999999999999 y[1] (closed_form) = 3.141237339365379 y[1] (numeric) = 3.141237339365383 absolute error = 4.440892098500626e-15 relative error = 1.413739752437113e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 6.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 6.771 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 6.5 Order of pole (three term test) = 3.439e-13 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; Iterations = 99 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 102 %