##############ECHO OF PROBLEM################# ##############temp/sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) ; ! // BEGIN FIRST INPUT BLOCK Digits=16; max_terms=40; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(0.0); x_end=c(1.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; glob_type_given_pole=3; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=true; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(2.0) - cos(c(x))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y[1] (closed_form) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 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 SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = 0.00999999400000118 y[1] (closed_form) = 1.000049999523336 y[1] (numeric) = 1.000049999523335 absolute error = 8.881784197001252e-16 relative error = 8.881340134227958e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.01999998733333588 y[1] (closed_form) = 1.000199993080106 y[1] (numeric) = 1.000199993080105 absolute error = 1.110223024625157e-15 relative error = 1.110001032099826e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.02999998066667069 y[1] (closed_form) = 1.0004499656711 y[1] (numeric) = 1.000449965671099 absolute error = 8.881784197001252e-16 relative error = 8.877789496492581e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.03999997400000518 y[1] (closed_form) = 1.0007998922993 y[1] (numeric) = 1.000799892299299 absolute error = 1.110223024625157e-15 relative error = 1.109335675560937e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.04999996733333964 y[1] (closed_form) = 1.001249737972382 y[1] (numeric) = 1.001249737972381 absolute error = 4.440892098500626e-16 relative error = 4.435349074341653e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.0599999606666741 y[1] (closed_form) = 1.001799457706213 y[1] (numeric) = 1.001799457706212 absolute error = 1.110223024625157e-15 relative error = 1.108228813746014e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.06999995400000855 y[1] (closed_form) = 1.002448996529351 y[1] (numeric) = 1.00244899652935 absolute error = 1.110223024625157e-15 relative error = 1.107510734679707e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.07999994733334301 y[1] (closed_form) = 1.003198289488542 y[1] (numeric) = 1.003198289488541 absolute error = 8.881784197001252e-16 relative error = 8.853468242583853e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.08999994066667746 y[1] (closed_form) = 1.004047261655215 y[1] (numeric) = 1.004047261655215 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.09999993400001192 y[1] (closed_form) = 1.004995828132972 y[1] (numeric) = 1.004995828132973 absolute error = 1.110223024625157e-15 relative error = 1.104704112740119e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1099999273333464 y[1] (closed_form) = 1.006043894066084 y[1] (numeric) = 1.006043894066084 absolute error = 4.440892098500626e-16 relative error = 4.414213062366559e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1199999206666808 y[1] (closed_form) = 1.00719135464897 y[1] (numeric) = 1.007191354648972 absolute error = 1.554312234475219e-15 relative error = 1.543214432193904e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1299999140000153 y[1] (closed_form) = 1.008438095136681 y[1] (numeric) = 1.008438095136682 absolute error = 1.110223024625157e-15 relative error = 1.100933245163333e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1399999073333497 y[1] (closed_form) = 1.009783990856374 y[1] (numeric) = 1.009783990856374 absolute error = 4.440892098500626e-16 relative error = 4.397863442788799e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1499999006666842 y[1] (closed_form) = 1.011228907219778 y[1] (numeric) = 1.011228907219778 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1599998940000187 y[1] (closed_form) = 1.012772699736652 y[1] (numeric) = 1.012772699736652 absolute error = 6.661338147750939e-16 relative error = 6.577327913245556e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1699998873333531 y[1] (closed_form) = 1.014415214029238 y[1] (numeric) = 1.014415214029238 absolute error = 4.440892098500626e-16 relative error = 4.377785385198916e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1799998806666876 y[1] (closed_form) = 1.016156285847694 y[1] (numeric) = 1.016156285847695 absolute error = 1.554312234475219e-15 relative error = 1.529599586326022e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.189999874000022 y[1] (closed_form) = 1.017995741086521 y[1] (numeric) = 1.017995741086523 absolute error = 2.220446049250313e-15 relative error = 2.181193849475637e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.1999998673333565 y[1] (closed_form) = 1.019933395801974 y[1] (numeric) = 1.019933395801975 absolute error = 1.332267629550188e-15 relative error = 1.306230029366403e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2099998606666909 y[1] (closed_form) = 1.021969056230454 y[1] (numeric) = 1.021969056230455 absolute error = 1.77635683940025e-15 relative error = 1.73817086590896e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2199998540000254 y[1] (closed_form) = 1.024102518807886 y[1] (numeric) = 1.024102518807887 absolute error = 1.110223024625157e-15 relative error = 1.084093637341621e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2299998473333598 y[1] (closed_form) = 1.026333570190074 y[1] (numeric) = 1.026333570190074 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2399998406666943 y[1] (closed_form) = 1.028661987274037 y[1] (numeric) = 1.028661987274038 absolute error = 2.220446049250313e-16 relative error = 2.158576944341565e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2499998340000288 y[1] (closed_form) = 1.031087537220318 y[1] (numeric) = 1.031087537220319 absolute error = 2.220446049250313e-16 relative error = 2.153499066855521e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.259999827333366 y[1] (closed_form) = 1.033609977476268 y[1] (numeric) = 1.033609977476267 absolute error = 6.661338147750939e-16 relative error = 6.444730887772305e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2699998206667032 y[1] (closed_form) = 1.036229055800297 y[1] (numeric) = 1.036229055800295 absolute error = 2.220446049250313e-15 relative error = 2.142813924027082e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2799998140000404 y[1] (closed_form) = 1.038944510287106 y[1] (numeric) = 1.038944510287104 absolute error = 2.442490654175344e-15 relative error = 2.35093465530741e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2899998073333777 y[1] (closed_form) = 1.041756069393871 y[1] (numeric) = 1.041756069393867 absolute error = 3.774758283725532e-15 relative error = 3.623456963319459e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.2999998006667149 y[1] (closed_form) = 1.044663451967399 y[1] (numeric) = 1.044663451967395 absolute error = 4.440892098500626e-15 relative error = 4.251026577159524e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3099997940000521 y[1] (closed_form) = 1.047666367272244 y[1] (numeric) = 1.047666367272238 absolute error = 5.329070518200751e-15 relative error = 5.086610284222242e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3199997873333894 y[1] (closed_form) = 1.050764515019776 y[1] (numeric) = 1.050764515019771 absolute error = 4.884981308350689e-15 relative error = 4.648978185429824e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3299997806667266 y[1] (closed_form) = 1.053957585398217 y[1] (numeric) = 1.053957585398213 absolute error = 4.884981308350689e-15 relative error = 4.634893639012042e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3399997740000638 y[1] (closed_form) = 1.057245259103616 y[1] (numeric) = 1.057245259103611 absolute error = 5.329070518200751e-15 relative error = 5.040524393288834e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.349999767333401 y[1] (closed_form) = 1.06062720737178 y[1] (numeric) = 1.060627207371774 absolute error = 5.551115123125783e-15 relative error = 5.233804191089319e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3599997606667383 y[1] (closed_form) = 1.064103092011151 y[1] (numeric) = 1.064103092011144 absolute error = 6.439293542825908e-15 relative error = 6.051381291126284e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3699997540000755 y[1] (closed_form) = 1.067672565436625 y[1] (numeric) = 1.067672565436617 absolute error = 7.327471962526033e-15 relative error = 6.863032918270652e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3799997473334127 y[1] (closed_form) = 1.07133527070431 y[1] (numeric) = 1.071335270704302 absolute error = 8.659739592076221e-15 relative error = 8.083127503478152e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.38999974066675 y[1] (closed_form) = 1.075090841547221 y[1] (numeric) = 1.07509084154721 absolute error = 1.021405182655144e-14 relative error = 9.500640719673374e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.3999997340000872 y[1] (closed_form) = 1.078938902411902 y[1] (numeric) = 1.078938902411891 absolute error = 1.110223024625157e-14 relative error = 1.028995267612763e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4099997273334244 y[1] (closed_form) = 1.082879068495989 y[1] (numeric) = 1.082879068495976 absolute error = 1.243449787580175e-14 relative error = 1.148281302830244e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4199997206667617 y[1] (closed_form) = 1.08691094578668 y[1] (numeric) = 1.086910945786665 absolute error = 1.4210854715202e-14 relative error = 1.307453455160168e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4299997140000989 y[1] (closed_form) = 1.091034131100144 y[1] (numeric) = 1.091034131100128 absolute error = 1.576516694967722e-14 relative error = 1.444974680469476e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4399997073334361 y[1] (closed_form) = 1.095248212121836 y[1] (numeric) = 1.095248212121818 absolute error = 1.731947918415244e-14 relative error = 1.581329144614556e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4499997006667734 y[1] (closed_form) = 1.099552767447727 y[1] (numeric) = 1.099552767447709 absolute error = 1.709743457922741e-14 relative error = 1.554944436083213e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4599996940001106 y[1] (closed_form) = 1.103947366626445 y[1] (numeric) = 1.103947366626427 absolute error = 1.798561299892754e-14 relative error = 1.629209285030482e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4699996873334478 y[1] (closed_form) = 1.108431570202321 y[1] (numeric) = 1.108431570202302 absolute error = 1.887379141862766e-14 relative error = 1.702747551225254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4799996806667851 y[1] (closed_form) = 1.113004929759332 y[1] (numeric) = 1.113004929759313 absolute error = 1.976196983832779e-14 relative error = 1.77555097106362e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4899996740001223 y[1] (closed_form) = 1.117666987965944 y[1] (numeric) = 1.117666987965923 absolute error = 2.087219286295294e-14 relative error = 1.867478693357358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.4999996673334595 y[1] (closed_form) = 1.122417278620841 y[1] (numeric) = 1.122417278620819 absolute error = 2.19824158875781e-14 relative error = 1.958488728415584e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5099996606667913 y[1] (closed_form) = 1.127255326699547 y[1] (numeric) = 1.127255326699527 absolute error = 2.042810365310288e-14 relative error = 1.812198458437418e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5199996540001229 y[1] (closed_form) = 1.132180648401935 y[1] (numeric) = 1.132180648401917 absolute error = 1.887379141862766e-14 relative error = 1.66703003140602e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5299996473334546 y[1] (closed_form) = 1.137192751200596 y[1] (numeric) = 1.137192751200578 absolute error = 1.77635683940025e-14 relative error = 1.562054310955513e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5399996406667863 y[1] (closed_form) = 1.142291133890093 y[1] (numeric) = 1.142291133890076 absolute error = 1.687538997430238e-14 relative error = 1.477328281174076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.549999634000118 y[1] (closed_form) = 1.147475286637087 y[1] (numeric) = 1.147475286637071 absolute error = 1.598721155460225e-14 relative error = 1.39325105653962e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5599996273334497 y[1] (closed_form) = 1.152744691031315 y[1] (numeric) = 1.1527446910313 absolute error = 1.4210854715202e-14 relative error = 1.232784225836522e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5699996206667813 y[1] (closed_form) = 1.15809882013743 y[1] (numeric) = 1.158098820137419 absolute error = 1.110223024625157e-14 relative error = 9.58660008386338e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.579999614000113 y[1] (closed_form) = 1.163537138547698 y[1] (numeric) = 1.163537138547689 absolute error = 8.659739592076221e-15 relative error = 7.442598353916855e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5899996073334447 y[1] (closed_form) = 1.169059102435534 y[1] (numeric) = 1.169059102435527 absolute error = 6.661338147750939e-15 relative error = 5.698033686982278e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.5999996006667764 y[1] (closed_form) = 1.174664159609888 y[1] (numeric) = 1.174664159609884 absolute error = 4.218847493575595e-15 relative error = 3.591535043494214e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6099995940001081 y[1] (closed_form) = 1.180351749570461 y[1] (numeric) = 1.180351749570459 absolute error = 2.220446049250313e-15 relative error = 1.881173175757438e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6199995873334397 y[1] (closed_form) = 1.186121303563754 y[1] (numeric) = 1.186121303563754 absolute error = 2.220446049250313e-16 relative error = 1.872022737117093e-14 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 16 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6299995806667714 y[1] (closed_form) = 1.191972244639946 y[1] (numeric) = 1.191972244639947 absolute error = 1.77635683940025e-15 relative error = 1.490266948234879e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6399995740001031 y[1] (closed_form) = 1.197903987710584 y[1] (numeric) = 1.197903987710585 absolute error = 1.554312234475219e-15 relative error = 1.29752655506707e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6499995673334348 y[1] (closed_form) = 1.203915939607095 y[1] (numeric) = 1.203915939607099 absolute error = 3.774758283725532e-15 relative error = 3.135400204899228e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6599995606667665 y[1] (closed_form) = 1.210007499140102 y[1] (numeric) = 1.210007499140108 absolute error = 5.329070518200751e-15 relative error = 4.404163215507244e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6699995540000981 y[1] (closed_form) = 1.21617805715954 y[1] (numeric) = 1.216178057159546 absolute error = 6.439293542825908e-15 relative error = 5.294696368610106e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6799995473334298 y[1] (closed_form) = 1.22242699661557 y[1] (numeric) = 1.222426996615579 absolute error = 8.659739592076221e-15 relative error = 7.08405460289384e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6899995406667615 y[1] (closed_form) = 1.228753692620289 y[1] (numeric) = 1.228753692620299 absolute error = 9.992007221626409e-15 relative error = 8.13182274172351e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.6999995340000932 y[1] (closed_form) = 1.235157512510213 y[1] (numeric) = 1.235157512510224 absolute error = 1.154631945610163e-14 relative error = 9.348054267699045e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7099995273334249 y[1] (closed_form) = 1.24163781590954 y[1] (numeric) = 1.241637815909555 absolute error = 1.443289932012704e-14 relative error = 1.162408162444252e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7199995206667565 y[1] (closed_form) = 1.248193954794198 y[1] (numeric) = 1.248193954794214 absolute error = 1.554312234475219e-14 relative error = 1.245248968323592e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7299995140000882 y[1] (closed_form) = 1.254825273556634 y[1] (numeric) = 1.254825273556653 absolute error = 1.887379141862766e-14 relative error = 1.504097169252292e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7399995073334199 y[1] (closed_form) = 1.261531109071382 y[1] (numeric) = 1.261531109071404 absolute error = 2.131628207280301e-14 relative error = 1.689715134214486e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7499995006667516 y[1] (closed_form) = 1.268310790761374 y[1] (numeric) = 1.268310790761398 absolute error = 2.353672812205332e-14 relative error = 1.855753991332368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7599994940000833 y[1] (closed_form) = 1.275163640664994 y[1] (numeric) = 1.275163640665019 absolute error = 2.55351295663786e-14 relative error = 2.002498248229703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7699994873334149 y[1] (closed_form) = 1.282088973503875 y[1] (numeric) = 1.282088973503903 absolute error = 2.797762022055394e-14 relative error = 2.182190222266144e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7799994806667466 y[1] (closed_form) = 1.28908609675143 y[1] (numeric) = 1.28908609675146 absolute error = 2.997602166487923e-14 relative error = 2.325370023027981e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.7899994740000783 y[1] (closed_form) = 1.296154310702096 y[1] (numeric) = 1.296154310702126 absolute error = 3.086420008457935e-14 relative error = 2.381213396409642e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.79999946733341 y[1] (closed_form) = 1.303292908541311 y[1] (numeric) = 1.303292908541344 absolute error = 3.308464613382966e-14 relative error = 2.53854263435371e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8099994606667417 y[1] (closed_form) = 1.310501176416192 y[1] (numeric) = 1.310501176416226 absolute error = 3.397282455352979e-14 relative error = 2.592353609817793e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8199994540000733 y[1] (closed_form) = 1.317778393506919 y[1] (numeric) = 1.317778393506956 absolute error = 3.708144902248023e-14 relative error = 2.81393663799554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.829999447333405 y[1] (closed_form) = 1.325123832098818 y[1] (numeric) = 1.325123832098857 absolute error = 3.863576125695545e-14 relative error = 2.915634020087134e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8399994406667367 y[1] (closed_form) = 1.33253675765513 y[1] (numeric) = 1.332536757655172 absolute error = 4.196643033083092e-14 relative error = 3.149363804768838e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8499994340000684 y[1] (closed_form) = 1.340016428890466 y[1] (numeric) = 1.34001642889051 absolute error = 4.39648317751562e-14 relative error = 3.280917369913077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8599994273334001 y[1] (closed_form) = 1.347562097844931 y[1] (numeric) = 1.347562097844978 absolute error = 4.640732242933154e-14 relative error = 3.443798434487566e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8699994206667317 y[1] (closed_form) = 1.355173009958926 y[1] (numeric) = 1.355173009958974 absolute error = 4.862776847858186e-14 relative error = 3.588307036904146e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8799994140000634 y[1] (closed_form) = 1.362848404148595 y[1] (numeric) = 1.362848404148647 absolute error = 5.151434834260726e-14 relative error = 3.779903046134433e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8899994073333951 y[1] (closed_form) = 1.370587512881939 y[1] (numeric) = 1.370587512881994 absolute error = 5.46229728115577e-14 relative error = 3.985369215622123e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.8999994006667268 y[1] (closed_form) = 1.378389562255566 y[1] (numeric) = 1.378389562255624 absolute error = 5.750955267558311e-14 relative error = 4.17222781210529e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9099993940000585 y[1] (closed_form) = 1.386253772072081 y[1] (numeric) = 1.38625377207214 absolute error = 5.928590951498336e-14 relative error = 4.276699599263609e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9199993873333902 y[1] (closed_form) = 1.394179355918103 y[1] (numeric) = 1.394179355918165 absolute error = 6.106226635438361e-14 relative error = 4.379799922813554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9299993806667218 y[1] (closed_form) = 1.402165521242911 y[1] (numeric) = 1.402165521242974 absolute error = 6.306066779870889e-14 relative error = 4.497376867661852e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9399993740000535 y[1] (closed_form) = 1.41021146943769 y[1] (numeric) = 1.410211469437755 absolute error = 6.505906924303417e-14 relative error = 4.613426472057836e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9499993673333852 y[1] (closed_form) = 1.418316395915399 y[1] (numeric) = 1.418316395915466 absolute error = 6.705747068735946e-14 relative error = 4.727962736698093e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9599993606667169 y[1] (closed_form) = 1.426479490191226 y[1] (numeric) = 1.426479490191295 absolute error = 6.905587213168474e-14 relative error = 4.841000000808109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9699993540000486 y[1] (closed_form) = 1.434699935963633 y[1] (numeric) = 1.434699935963704 absolute error = 7.083222897108499e-14 relative error = 4.937076192417176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9799993473333802 y[1] (closed_form) = 1.44297691119599 y[1] (numeric) = 1.442976911196063 absolute error = 7.283063041541027e-14 relative error = 5.04724849374379e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9899993406667119 y[1] (closed_form) = 1.451309588198774 y[1] (numeric) = 1.45130958819885 absolute error = 7.549516567451064e-14 relative error = 5.201865011324563e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 TOP MAIN SOLVE Loop x[1] = 0.9999993340000436 y[1] (closed_form) = 1.459697133712341 y[1] (numeric) = 1.459697133712419 absolute error = 7.771561172376096e-14 relative error = 5.324091548094811e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = 9.999993333334665e-05 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 ( x ) ; Iterations = 9992 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 100 %