##############ECHO OF PROBLEM################# ##############temp/sub_full_linpostode.ode################# diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* 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=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(-0.05) * c(x) * c(x) - c(0.2) * c(x) - cos(c(0.3) * c(x) + c(0.1)) / c(0.3)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (closed_form) = -3.325706312382627 y[1] (numeric) = -3.325706312382627 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4285 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.2285402759460775 y[1] (closed_form) = -3.334409648535198 y[1] (numeric) = -3.334409648535198 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5513 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3142337932434625 y[1] (closed_form) = -3.338413339394996 y[1] (numeric) = -3.338413339394996 absolute error = 4.440892098500626e-16 relative error = 1.330240340851689e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6314 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.3999273105408474 y[1] (closed_form) = -3.340989914782487 y[1] (numeric) = -3.340989914782488 absolute error = 4.440892098500626e-16 relative error = 1.329214457922046e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7098 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.5284675864869248 y[1] (closed_form) = -3.342204800388032 y[1] (numeric) = -3.342204800388032 absolute error = 4.440892098500626e-16 relative error = 1.328731290788953e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8239 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6141611037843098 y[1] (closed_form) = -3.341267643268262 y[1] (numeric) = -3.341267643268262 absolute error = 4.440892098500626e-16 relative error = 1.329103972693659e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8973 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.6998546210816947 y[1] (closed_form) = -3.338950327776619 y[1] (numeric) = -3.33895032777662 absolute error = 4.440892098500626e-16 relative error = 1.330026404273519e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9683 Order of pole (three term test) = 32.09 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8283948970277721 y[1] (closed_form) = -3.332923202762318 y[1] (numeric) = -3.332923202762319 absolute error = 4.440892098500626e-16 relative error = 1.332431570826482e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9140884143251571 y[1] (closed_form) = -3.327231052461505 y[1] (numeric) = -3.327231052461505 absolute error = 4.440892098500626e-16 relative error = 1.33471106408893e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.134 Order of pole (three term test) = 32.13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.999781931622542 y[1] (closed_form) = -3.320222808463408 y[1] (numeric) = -3.320222808463408 absolute error = 4.440892098500626e-16 relative error = 1.337528339116453e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.195 Order of pole (three term test) = 32.15 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.128322207568619 y[1] (closed_form) = -3.307289896607874 y[1] (numeric) = -3.307289896607875 absolute error = 4.440892098500626e-16 relative error = 1.34275864448878e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.281 Order of pole (three term test) = 32.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.214015724866004 y[1] (closed_form) = -3.297087873098187 y[1] (numeric) = -3.297087873098187 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.334 Order of pole (three term test) = 32.2 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299709242163389 y[1] (closed_form) = -3.285650409817375 y[1] (numeric) = -3.285650409817376 absolute error = 4.440892098500626e-16 relative error = 1.351602131873629e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.384 Order of pole (three term test) = 32.22 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.428249518109467 y[1] (closed_form) = -3.26623499849367 y[1] (numeric) = -3.266234998493671 absolute error = 8.881784197001252e-16 relative error = 2.719272863433701e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.451 Order of pole (three term test) = 32.25 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.513943035406852 y[1] (closed_form) = -3.251825503749719 y[1] (numeric) = -3.251825503749719 absolute error = 8.881784197001252e-16 relative error = 2.731322510005399e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.492 Order of pole (three term test) = 32.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599636552704237 y[1] (closed_form) = -3.236277159872545 y[1] (numeric) = -3.236277159872545 absolute error = 4.440892098500626e-16 relative error = 1.372222426918318e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.528 Order of pole (three term test) = 32.3 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.728176828650314 y[1] (closed_form) = -3.210886175393215 y[1] (numeric) = -3.210886175393215 absolute error = 4.440892098500626e-16 relative error = 1.383073661263243e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.575 Order of pole (three term test) = 32.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.813870345947699 y[1] (closed_form) = -3.192626446774244 y[1] (numeric) = -3.192626446774244 absolute error = 4.440892098500626e-16 relative error = 1.390983935182145e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.601 Order of pole (three term test) = 32.36 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.899563863245084 y[1] (closed_form) = -3.173339614894078 y[1] (numeric) = -3.173339614894079 absolute error = 4.440892098500626e-16 relative error = 1.399438017178271e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.622 Order of pole (three term test) = 32.39 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.028104139191162 y[1] (closed_form) = -3.14255952116577 y[1] (numeric) = -3.14255952116577 absolute error = 4.440892098500626e-16 relative error = 1.413144943982867e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.647 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.113797656488547 y[1] (closed_form) = -3.120858741145895 y[1] (numeric) = -3.120858741145896 absolute error = 8.881784197001252e-16 relative error = 2.84594239396433e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.658 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.199491173785932 y[1] (closed_form) = -3.098256854878205 y[1] (numeric) = -3.098256854878206 absolute error = 8.881784197001252e-16 relative error = 2.866703637891379e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.664 Order of pole (three term test) = 32.47 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.32803144973201 y[1] (closed_form) = -3.06274890854827 y[1] (numeric) = -3.062748908548272 absolute error = 1.332267629550188e-15 relative error = 4.349908103245972e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.666 Order of pole (three term test) = 32.51 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.413724967029396 y[1] (closed_form) = -3.038064894178812 y[1] (numeric) = -3.038064894178814 absolute error = 1.332267629550188e-15 relative error = 4.385250730170131e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.662 Order of pole (three term test) = 32.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.499418484326781 y[1] (closed_form) = -3.012619002323006 y[1] (numeric) = -3.012619002323007 absolute error = 1.332267629550188e-15 relative error = 4.422290467274114e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.653 Order of pole (three term test) = 32.56 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.627958760272859 y[1] (closed_form) = -2.973113902806872 y[1] (numeric) = -2.973113902806874 absolute error = 1.332267629550188e-15 relative error = 4.481051426561269e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.631 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.713652277570245 y[1] (closed_form) = -2.945949401695077 y[1] (numeric) = -2.945949401695078 absolute error = 8.881784197001252e-16 relative error = 3.014914034806823e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.612 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.79934579486763 y[1] (closed_form) = -2.918174357160248 y[1] (numeric) = -2.918174357160249 absolute error = 1.332267629550188e-15 relative error = 4.565414764478475e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.588 Order of pole (three term test) = 32.65 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.927886070813708 y[1] (closed_form) = -2.875466334834123 y[1] (numeric) = -2.875466334834123 absolute error = 8.881784197001252e-16 relative error = 3.088815226040063e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.544 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.013579588111094 y[1] (closed_form) = -2.846364957606071 y[1] (numeric) = -2.846364957606072 absolute error = 8.881784197001252e-16 relative error = 3.120395426899598e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.51 Order of pole (three term test) = 32.71 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.099273105408479 y[1] (closed_form) = -2.81681525193458 y[1] (numeric) = -2.816815251934581 absolute error = 8.881784197001252e-16 relative error = 3.15312983018722e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.472 Order of pole (three term test) = 32.73 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.227813381354557 y[1] (closed_form) = -2.771755642323635 y[1] (numeric) = -2.771755642323637 absolute error = 1.332267629550188e-15 relative error = 4.806583990330811e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.407 Order of pole (three term test) = 32.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.313506898651942 y[1] (closed_form) = -2.741297464480224 y[1] (numeric) = -2.741297464480226 absolute error = 1.332267629550188e-15 relative error = 4.859989281764423e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.359 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.399200415949328 y[1] (closed_form) = -2.710562741670376 y[1] (numeric) = -2.710562741670378 absolute error = 1.77635683940025e-15 relative error = 6.553461434748328e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.308 Order of pole (three term test) = 32.81 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.527740691895406 y[1] (closed_form) = -2.664053097621197 y[1] (numeric) = -2.664053097621199 absolute error = 2.220446049250313e-15 relative error = 8.33484156615725e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.224 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.613434209192791 y[1] (closed_form) = -2.632849966370867 y[1] (numeric) = -2.63284996637087 absolute error = 2.664535259100376e-15 relative error = 1.012034598679842e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.164 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.699127726490177 y[1] (closed_form) = -2.601550252294622 y[1] (numeric) = -2.601550252294625 absolute error = 2.664535259100376e-15 relative error = 1.02421056704563e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.102 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.827668002436255 y[1] (closed_form) = -2.554535049858655 y[1] (numeric) = -2.554535049858658 absolute error = 3.108624468950438e-15 relative error = 1.216904214769902e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.002 Order of pole (three term test) = 32.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.91336151973364 y[1] (closed_form) = -2.523225633897487 y[1] (numeric) = -2.523225633897491 absolute error = 3.552713678800501e-15 relative error = 1.408004750376929e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9322 Order of pole (three term test) = 32.91 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.999055037031026 y[1] (closed_form) = -2.492006319910137 y[1] (numeric) = -2.49200631991014 absolute error = 3.108624468950438e-15 relative error = 1.247438437099364e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.127595312977102 y[1] (closed_form) = -2.445465316952039 y[1] (numeric) = -2.445465316952042 absolute error = 3.108624468950438e-15 relative error = 1.271179127915395e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7474 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.213288830274487 y[1] (closed_form) = -2.414709939241533 y[1] (numeric) = -2.414709939241536 absolute error = 2.664535259100376e-15 relative error = 1.103459763758339e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6699 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.298982347571871 y[1] (closed_form) = -2.384236560569036 y[1] (numeric) = -2.384236560569039 absolute error = 3.108624468950438e-15 relative error = 1.303823840453363e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5906 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.427522623517948 y[1] (closed_form) = -2.339176869923475 y[1] (numeric) = -2.339176869923477 absolute error = 2.220446049250313e-15 relative error = 9.49242478326555e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0428467586486925 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4687 Order of pole (three term test) = 32.98 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 4.51311482637623 y[1] (closed_form) = -2.309686801096416 y[1] (numeric) = -2.309686801096419 absolute error = 2.664535259100376e-15 relative error = 1.153634881506667e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.04274544420958998 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.386 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 4.617971519132454 y[1] (closed_form) = -2.274214301975827 y[1] (numeric) = -2.27421430197583 absolute error = 3.108624468950438e-15 relative error = 1.366900413144742e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.03142124076823374 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2833 Order of pole (three term test) = 32.99 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 4.715571275804436 y[1] (closed_form) = -2.241929821390594 y[1] (numeric) = -2.241929821390596 absolute error = 2.664535259100376e-15 relative error = 1.188500743278242e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.02072723398331002 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1867 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 4.803143097960214 y[1] (closed_form) = -2.213634344745304 y[1] (numeric) = -2.213634344745306 absolute error = 2.220446049250313e-15 relative error = 1.003077158845669e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.01104780650437759 SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09945 Order of pole (three term test) = 33 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 4.900059289839392 y[1] (closed_form) = -2.183136042713046 y[1] (numeric) = -2.183136042713048 absolute error = 1.77635683940025e-15 relative error = 8.136720775278488e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 0.0005229160258382037 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( 0.3 * x + 0.1 ) - ( 0.1 * x + 0.2 ) ; Iterations = 341 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 100 %