##############ECHO OF PROBLEM################# ##############temp/lin_lnpostode.ode################# diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(20.0); x_end=c(30.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.001); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-2.0); 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(10.0) * (c(0.1) * c(x) + c(0.2)) * ln(c(0.1) * c(x) + c(0.2)) - c(x) - c(2.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 20 y[1] (closed_form) = -4.653938071986055 y[1] (numeric) = -4.653938071986055 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 = 22 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 23.91 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.1 y[1] (closed_form) = -4.574865406794476 y[1] (numeric) = -4.574865406794481 absolute error = 4.440892098500626e-15 relative error = 9.707153552332105e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 22.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.02 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.2 y[1] (closed_form) = -4.495340251371015 y[1] (numeric) = -4.495340251371024 absolute error = 8.881784197001252e-15 relative error = 1.975775736729257e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 22.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.13 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.3 y[1] (closed_form) = -4.415364643973778 y[1] (numeric) = -4.415364643973788 absolute error = 1.06581410364015e-14 relative error = 2.413875612957143e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 22.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.24 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.40000000000001 y[1] (closed_form) = -4.33494060458035 y[1] (numeric) = -4.334940604580353 absolute error = 3.552713678800501e-15 relative error = 8.19553023413207e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 Radius of convergence (given) for eq 1 = 22.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.35 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.50000000000001 y[1] (closed_form) = -4.254070135132594 y[1] (numeric) = -4.254070135132602 absolute error = 8.881784197001252e-15 relative error = 2.087832103107632e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 22.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.46 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.60000000000001 y[1] (closed_form) = -4.172755219777191 y[1] (numeric) = -4.172755219777203 absolute error = 1.243449787580175e-14 relative error = 2.97992506650455e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 22.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.57 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.70000000000001 y[1] (closed_form) = -4.09099782510182 y[1] (numeric) = -4.090997825101832 absolute error = 1.243449787580175e-14 relative error = 3.039477997153977e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 22.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.67 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.80000000000001 y[1] (closed_form) = -4.008799900367215 y[1] (numeric) = -4.008799900367232 absolute error = 1.687538997430238e-14 relative error = 4.209586508110958e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 22.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.78 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.90000000000001 y[1] (closed_form) = -3.926163377735193 y[1] (numeric) = -3.926163377735203 absolute error = 9.325873406851315e-15 relative error = 2.375314654437774e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 22.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 24.89 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 22.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.00000000000001 y[1] (closed_form) = -3.843090172492595 y[1] (numeric) = -3.843090172492606 absolute error = 1.110223024625157e-14 relative error = 2.888881017082864e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.10000000000002 y[1] (closed_form) = -3.759582183271462 y[1] (numeric) = -3.759582183271478 absolute error = 1.554312234475219e-14 relative error = 4.134268540241642e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.11 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.20000000000002 y[1] (closed_form) = -3.675641292265308 y[1] (numeric) = -3.675641292265326 absolute error = 1.865174681370263e-14 relative error = 5.074419762600803e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.22 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.30000000000002 y[1] (closed_form) = -3.591269365441683 y[1] (numeric) = -3.591269365441703 absolute error = 2.042810365310288e-14 relative error = 5.688268290226253e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.33 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.40000000000002 y[1] (closed_form) = -3.506468252751109 y[1] (numeric) = -3.506468252751122 absolute error = 1.332267629550188e-14 relative error = 3.799457270160412e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.43 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.50000000000002 y[1] (closed_form) = -3.421239788332393 y[1] (numeric) = -3.421239788332409 absolute error = 1.598721155460225e-14 relative error = 4.672929272342779e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.54 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.60000000000002 y[1] (closed_form) = -3.335585790714532 y[1] (numeric) = -3.335585790714556 absolute error = 2.398081733190338e-14 relative error = 7.189387063183985e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.65 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.70000000000002 y[1] (closed_form) = -3.249508063015128 y[1] (numeric) = -3.249508063015154 absolute error = 2.575717417130363e-14 relative error = 7.926484154467452e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.76 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.80000000000003 y[1] (closed_form) = -3.163008393135449 y[1] (numeric) = -3.163008393135474 absolute error = 2.486899575160351e-14 relative error = 7.862450129938224e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.87 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.90000000000003 y[1] (closed_form) = -3.076088553952253 y[1] (numeric) = -3.076088553952276 absolute error = 2.264854970235319e-14 relative error = 7.362775585005067e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 23.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 25.98 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 23.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.00000000000003 y[1] (closed_form) = -2.988750303506375 y[1] (numeric) = -2.988750303506399 absolute error = 2.353672812205332e-14 relative error = 7.875106894824984e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 24 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.09 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.10000000000003 y[1] (closed_form) = -2.900995385188185 y[1] (numeric) = -2.900995385188214 absolute error = 2.842170943040401e-14 relative error = 9.797226695195281e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 Radius of convergence (given) for eq 1 = 24.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.2 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.20000000000003 y[1] (closed_form) = -2.812825527919966 y[1] (numeric) = -2.812825527919997 absolute error = 3.153033389935445e-14 relative error = 1.120948796375244e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.3 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.30000000000003 y[1] (closed_form) = -2.724242446335253 y[1] (numeric) = -2.724242446335289 absolute error = 3.597122599785507e-14 relative error = 1.320412067077394e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.41 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.40000000000003 y[1] (closed_form) = -2.635247840955273 y[1] (numeric) = -2.6352478409553 absolute error = 2.708944180085382e-14 relative error = 1.027965619773886e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.52 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.50000000000004 y[1] (closed_form) = -2.545843398362393 y[1] (numeric) = -2.545843398362424 absolute error = 3.019806626980426e-14 relative error = 1.18617139959312e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.63 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.60000000000004 y[1] (closed_form) = -2.456030791370885 y[1] (numeric) = -2.456030791370919 absolute error = 3.33066907387547e-14 relative error = 1.35611861446427e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.74 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.70000000000004 y[1] (closed_form) = -2.365811679194778 y[1] (numeric) = -2.365811679194816 absolute error = 3.819167204710538e-14 relative error = 1.614315813171749e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.85 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.80000000000004 y[1] (closed_form) = -2.275187707613064 y[1] (numeric) = -2.275187707613104 absolute error = 3.952393967665557e-14 relative error = 1.737172697637364e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 26.96 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.90000000000004 y[1] (closed_form) = -2.184160509132219 y[1] (numeric) = -2.184160509132251 absolute error = 3.153033389935445e-14 relative error = 1.443590513037965e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 24.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.07 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 24.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.00000000000004 y[1] (closed_form) = -2.092731703146082 y[1] (numeric) = -2.092731703146119 absolute error = 3.641531520770513e-14 relative error = 1.740085227024593e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.17 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.10000000000004 y[1] (closed_form) = -2.000902896093272 y[1] (numeric) = -2.000902896093313 absolute error = 4.04121180963557e-14 relative error = 2.019694117853477e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.28 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.20000000000005 y[1] (closed_form) = -1.908675681611985 y[1] (numeric) = -1.90867568161203 absolute error = 4.485301019485632e-14 relative error = 2.349954506518122e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.39 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.30000000000005 y[1] (closed_form) = -1.8160516406924 y[1] (numeric) = -1.816051640692444 absolute error = 4.39648317751562e-14 relative error = 2.420902070735933e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.40000000000005 y[1] (closed_form) = -1.723032341826645 y[1] (numeric) = -1.723032341826686 absolute error = 4.085620730620576e-14 relative error = 2.371180523686091e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.61 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.50000000000005 y[1] (closed_form) = -1.629619341156417 y[1] (numeric) = -1.629619341156457 absolute error = 4.04121180963557e-14 relative error = 2.479850175788801e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.72 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.60000000000005 y[1] (closed_form) = -1.535814182618285 y[1] (numeric) = -1.535814182618334 absolute error = 4.840572387365683e-14 relative error = 3.151795602716328e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.83 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.70000000000005 y[1] (closed_form) = -1.441618398086742 y[1] (numeric) = -1.441618398086793 absolute error = 5.084821452783217e-14 relative error = 3.52716187552239e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 27.93 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.80000000000005 y[1] (closed_form) = -1.347033507514968 y[1] (numeric) = -1.347033507515021 absolute error = 5.284661597215745e-14 relative error = 3.923184959938364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.04 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.90000000000006 y[1] (closed_form) = -1.252061019073484 y[1] (numeric) = -1.252061019073532 absolute error = 4.840572387365683e-14 relative error = 3.866083452504314e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 25.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.15 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 25.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.00000000000006 y[1] (closed_form) = -1.1567024292866 y[1] (numeric) = -1.156702429286648 absolute error = 4.75175454539567e-14 relative error = 4.10801812556608e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 26 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.26 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.10000000000006 y[1] (closed_form) = -1.060959223166826 y[1] (numeric) = -1.06095922316688 absolute error = 5.373479439185758e-14 relative error = 5.064737005769758e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 26.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.37 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.20000000000006 y[1] (closed_form) = -0.9648328743471914 y[1] (numeric) = -0.964832874347249 absolute error = 5.750955267558311e-14 relative error = 5.960571432072547e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 26.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.48 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.30000000000006 y[1] (closed_form) = -0.8683248452115286 y[1] (numeric) = -0.8683248452115877 absolute error = 5.906386491005833e-14 relative error = 6.802047095136389e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 26.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.59 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.40000000000006 y[1] (closed_form) = -0.7714365870227908 y[1] (numeric) = -0.7714365870228576 absolute error = 6.672440377997191e-14 relative error = 8.649369877241853e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 26.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.7 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.50000000000006 y[1] (closed_form) = -0.6741695400494692 y[1] (numeric) = -0.6741695400495247 absolute error = 5.551115123125783e-14 relative error = 8.234004643280759e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 26.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.8 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.60000000000007 y[1] (closed_form) = -0.5765251336899624 y[1] (numeric) = -0.5765251336900267 absolute error = 6.428191312579656e-14 relative error = 1.114988911487169e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 26.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 28.91 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.70000000000007 y[1] (closed_form) = -0.4785047865953018 y[1] (numeric) = -0.4785047865953684 absolute error = 6.661338147750939e-14 relative error = 1.392115258689106e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 26.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.02 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.80000000000007 y[1] (closed_form) = -0.3801099067898122 y[1] (numeric) = -0.3801099067898808 absolute error = 6.861178292183467e-14 relative error = 1.805051162735799e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 26.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.13 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.90000000000007 y[1] (closed_form) = -0.281341891790106 y[1] (numeric) = -0.2813418917901767 absolute error = 7.061018436615996e-14 relative error = 2.509764326843952e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 26.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.24 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 26.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.00000000000007 y[1] (closed_form) = -0.1822021287222739 y[1] (numeric) = -0.182202128722339 absolute error = 6.50868248186498e-14 relative error = 3.572231854538867e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.35 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.10000000000007 y[1] (closed_form) = -0.08269199443730102 y[1] (numeric) = -0.08269199443737194 absolute error = 7.091549569793187e-14 relative error = 8.575859873799712e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.46 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.20000000000007 y[1] (closed_form) = 0.01718714437512503 y[1] (numeric) = 0.01718714437505187 absolute error = 7.316369732279782e-14 relative error = 4.256885013934467e-10 % Desired digits = 8 Estimated correct digits = 10 Correct digits = 12 h = 0.05 Radius of convergence (given) for eq 1 = 27.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.57 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.30000000000008 y[1] (closed_form) = 0.11743393107459 y[1] (numeric) = 0.1174339310745167 absolute error = 7.331635298868378e-14 relative error = 6.243200097092531e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.67 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.40000000000008 y[1] (closed_form) = 0.2180470189595098 y[1] (numeric) = 0.2180470189594313 absolute error = 7.854827899222983e-14 relative error = 3.602355096027056e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.78 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.50000000000008 y[1] (closed_form) = 0.3190250711582756 y[1] (numeric) = 0.3190250711582088 absolute error = 6.677991493120317e-14 relative error = 2.09324974644617e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 29.89 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.60000000000008 y[1] (closed_form) = 0.4203667605221035 y[1] (numeric) = 0.4203667605220295 absolute error = 7.405187574249794e-14 relative error = 1.761601598816331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.70000000000008 y[1] (closed_form) = 0.5220707695192388 y[1] (numeric) = 0.5220707695191571 absolute error = 8.171241461241152e-14 relative error = 1.565159732801327e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.11 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.80000000000008 y[1] (closed_form) = 0.6241357901308646 y[1] (numeric) = 0.6241357901307824 absolute error = 8.22675261247241e-14 relative error = 1.318103006197975e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.22 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.90000000000008 y[1] (closed_form) = 0.7265605237484465 y[1] (numeric) = 0.7265605237483641 absolute error = 8.237854842718662e-14 relative error = 1.133815363408158e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = 0.05 Radius of convergence (given) for eq 1 = 27.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.33 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 27.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.00000000000009 y[1] (closed_form) = 0.8293436810725225 y[1] (numeric) = 0.8293436810724433 absolute error = 7.926992395823618e-14 relative error = 9.558151314991976e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.43 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.10000000000009 y[1] (closed_form) = 0.932483982012986 y[1] (numeric) = 0.9324839820129015 absolute error = 8.448797217397441e-14 relative error = 9.060527988007607e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.54 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.20000000000009 y[1] (closed_form) = 1.035980155590721 y[1] (numeric) = 1.03598015559064 absolute error = 8.126832540256146e-14 relative error = 7.844583215613995e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.65 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.30000000000009 y[1] (closed_form) = 1.139830939840742 y[1] (numeric) = 1.139830939840653 absolute error = 8.926193117986259e-14 relative error = 7.831155310833581e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.76 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.40000000000009 y[1] (closed_form) = 1.244035081716564 y[1] (numeric) = 1.244035081716471 absolute error = 9.370282327836321e-14 relative error = 7.532168879760905e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.87 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.50000000000009 y[1] (closed_form) = 1.348591336996037 y[1] (numeric) = 1.34859133699595 absolute error = 8.681944052568724e-14 relative error = 6.437787203874228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 30.98 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.60000000000009 y[1] (closed_form) = 1.453498470188475 y[1] (numeric) = 1.453498470188386 absolute error = 8.881784197001252e-14 relative error = 6.11062507403228e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.09 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.7000000000001 y[1] (closed_form) = 1.55875525444301 y[1] (numeric) = 1.558755254442919 absolute error = 9.170442183403793e-14 relative error = 5.883182851999857e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.2 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.8000000000001 y[1] (closed_form) = 1.664360471458323 y[1] (numeric) = 1.664360471458227 absolute error = 9.658940314238862e-14 relative error = 5.803394444819779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.3 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.9000000000001 y[1] (closed_form) = 1.770312911393564 y[1] (numeric) = 1.770312911393465 absolute error = 9.903189379656396e-14 relative error = 5.594033301073737e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 28.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.41 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 28.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.0000000000001 y[1] (closed_form) = 1.876611372780527 y[1] (numeric) = 1.876611372780438 absolute error = 8.859579736508749e-14 relative error = 4.721051926367545e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.52 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.1000000000001 y[1] (closed_form) = 1.983254662437091 y[1] (numeric) = 1.98325466243699 absolute error = 1.005862060310392e-13 relative error = 5.071774590330999e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.63 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.2000000000001 y[1] (closed_form) = 2.090241595381674 y[1] (numeric) = 2.090241595381576 absolute error = 9.725553695716371e-14 relative error = 4.652837125241739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.74 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.3000000000001 y[1] (closed_form) = 2.197570994749114 y[1] (numeric) = 2.197570994749012 absolute error = 1.016964290556643e-13 relative error = 4.627674341291282e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.85 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.40000000000011 y[1] (closed_form) = 2.305241691707483 y[1] (numeric) = 2.305241691707371 absolute error = 1.119104808822158e-13 relative error = 4.854609444414661e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 31.96 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.50000000000011 y[1] (closed_form) = 2.413252525376109 y[1] (numeric) = 2.413252525376008 absolute error = 1.008082506359642e-13 relative error = 4.177277329079066e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.07 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.60000000000011 y[1] (closed_form) = 2.521602342744806 y[1] (numeric) = 2.521602342744702 absolute error = 1.048050535246148e-13 relative error = 4.156287918519806e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.17 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.70000000000011 y[1] (closed_form) = 2.630289998593987 y[1] (numeric) = 2.630289998593885 absolute error = 1.025846074753645e-13 relative error = 3.900125367552654e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.28 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.80000000000011 y[1] (closed_form) = 2.739314355416063 y[1] (numeric) = 2.73931435541595 absolute error = 1.127986593019159e-13 relative error = 4.117769801735055e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.39 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.90000000000011 y[1] (closed_form) = 2.848674283337729 y[1] (numeric) = 2.848674283337613 absolute error = 1.159072837708663e-13 relative error = 4.068814902736452e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 29.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.5 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 29.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.00000000000011 y[1] (closed_form) = 2.958368660043419 y[1] (numeric) = 2.958368660043313 absolute error = 1.06581410364015e-13 relative error = 3.602708878157557e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.61 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.10000000000012 y[1] (closed_form) = 3.068396370699745 y[1] (numeric) = 3.068396370699631 absolute error = 1.13242748511766e-13 relative error = 3.690616688023949e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.72 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.20000000000012 y[1] (closed_form) = 3.178756307880839 y[1] (numeric) = 3.178756307880726 absolute error = 1.127986593019159e-13 relative error = 3.548515468841166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.83 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.30000000000012 y[1] (closed_form) = 3.289447371494859 y[1] (numeric) = 3.289447371494739 absolute error = 1.194599974496668e-13 relative error = 3.631612971980134e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 32.93 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.40000000000012 y[1] (closed_form) = 3.40046846871131 y[1] (numeric) = 3.400468468711185 absolute error = 1.247890679678676e-13 relative error = 3.66976106722023e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.04 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.50000000000012 y[1] (closed_form) = 3.511818513889402 y[1] (numeric) = 3.511818513889291 absolute error = 1.105782132526656e-13 relative error = 3.14874509645996e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.15 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.60000000000012 y[1] (closed_form) = 3.623496428507401 y[1] (numeric) = 3.62349642850728 absolute error = 1.216804434989172e-13 relative error = 3.358094754602532e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.26 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.70000000000012 y[1] (closed_form) = 3.735501141092691 y[1] (numeric) = 3.735501141092572 absolute error = 1.185718190299667e-13 relative error = 3.174187734159885e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.37 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.80000000000013 y[1] (closed_form) = 3.847831587153031 y[1] (numeric) = 3.847831587152904 absolute error = 1.270095140171179e-13 relative error = 3.300807510421496e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.48 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.90000000000013 y[1] (closed_form) = 3.960486709108466 y[1] (numeric) = 3.960486709108337 absolute error = 1.287858708565182e-13 relative error = 3.251768792970114e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 30.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.59 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 30.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.00000000000013 y[1] (closed_form) = 4.073465456224262 y[1] (numeric) = 4.073465456224143 absolute error = 1.199040866595169e-13 relative error = 2.943540038526735e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.7 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.10000000000013 y[1] (closed_form) = 4.186766784544695 y[1] (numeric) = 4.186766784544566 absolute error = 1.287858708565182e-13 relative error = 3.076022083005119e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.1 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.8 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.1 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.20000000000013 y[1] (closed_form) = 4.300389656827555 y[1] (numeric) = 4.300389656827424 absolute error = 1.305622276959184e-13 relative error = 3.036055755752971e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.2 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 33.91 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.2 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.30000000000013 y[1] (closed_form) = 4.414333042479697 y[1] (numeric) = 4.414333042479561 absolute error = 1.358912982141192e-13 relative error = 3.078410643384168e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.3 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 34.02 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.3 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.40000000000013 y[1] (closed_form) = 4.528595917493256 y[1] (numeric) = 4.528595917493113 absolute error = 1.429967255717202e-13 relative error = 3.157639325234257e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.4 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 34.13 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.4 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.50000000000014 y[1] (closed_form) = 4.643177264382714 y[1] (numeric) = 4.64317726438259 absolute error = 1.243449787580175e-13 relative error = 2.678014895357404e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.5 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 34.24 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.5 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.60000000000014 y[1] (closed_form) = 4.758076072122897 y[1] (numeric) = 4.758076072122763 absolute error = 1.341149413747189e-13 relative error = 2.818680057691495e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.6 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 34.35 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.6 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.70000000000014 y[1] (closed_form) = 4.873291336087462 y[1] (numeric) = 4.873291336087327 absolute error = 1.35003119794419e-13 relative error = 2.770265729748198e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.7 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 34.46 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.7 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.80000000000014 y[1] (closed_form) = 4.988822057988486 y[1] (numeric) = 4.988822057988346 absolute error = 1.394440118929197e-13 relative error = 2.795128995824399e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.8 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 34.57 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.8 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.90000000000014 y[1] (closed_form) = 5.1046672458166 y[1] (numeric) = 5.104667245816456 absolute error = 1.438849039914203e-13 relative error = 2.818693110884701e-12 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 14 h = 0.05 Radius of convergence (given) for eq 1 = 31.9 Order of pole (given) = 1 Radius of convergence (ratio test) for eq 1 = 34.67 Order of pole (ratio test) = 1 Radius of convergence (three term test) for eq 1 = 31.9 Order of pole (three term test) = 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ln ( 0.1 * x + 0.2 ) ; Iterations = 200 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100.5 %