##############ECHO OF PROBLEM################# ##############temp/add_lin_fullpostode.ode################# diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-5.0); x_end=c(5.0); array_y_init[0 + 1] = exact_soln_y(x_start); 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] = -5 y[1] (closed_form) = -0.3165571430008035 y[1] (numeric) = -0.3165571430008035 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5583 Order of pole (three term test) = 32.97 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (closed_form) = -0.4443324033252436 y[1] (numeric) = -0.4443324033252436 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6515 Order of pole (three term test) = 32.96 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.800000000000001 y[1] (closed_form) = -0.5705093593615311 y[1] (numeric) = -0.5705093593615319 absolute error = 7.771561172376096e-16 relative error = 1.362214492164232e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7423 Order of pole (three term test) = 32.95 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.700000000000001 y[1] (closed_form) = -0.6950001084422313 y[1] (numeric) = -0.6950001084422326 absolute error = 1.332267629550188e-15 relative error = 1.916931541976769e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8304 Order of pole (three term test) = 32.93 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.600000000000001 y[1] (closed_form) = -0.8177173654398506 y[1] (numeric) = -0.8177173654398521 absolute error = 1.443289932012704e-15 relative error = 1.76502296883026e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9156 Order of pole (three term test) = 32.92 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.500000000000002 y[1] (closed_form) = -0.9385745413175604 y[1] (numeric) = -0.9385745413175626 absolute error = 2.220446049250313e-15 relative error = 2.36576420039401e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9975 Order of pole (three term test) = 32.9 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.400000000000002 y[1] (closed_form) = -1.057485821053488 y[1] (numeric) = -1.05748582105349 absolute error = 1.998401444325282e-15 relative error = 1.889766656478131e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.076 Order of pole (three term test) = 32.88 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.300000000000002 y[1] (closed_form) = -1.174366240868441 y[1] (numeric) = -1.174366240868443 absolute error = 2.442490654175344e-15 relative error = 2.079837251085427e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 32.86 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.200000000000003 y[1] (closed_form) = -1.289131764687574 y[1] (numeric) = -1.289131764687577 absolute error = 2.886579864025407e-15 relative error = 2.239165881328647e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 32.84 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.100000000000003 y[1] (closed_form) = -1.401699359767188 y[1] (numeric) = -1.401699359767191 absolute error = 3.33066907387547e-15 relative error = 2.376165081810888e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.286 Order of pole (three term test) = 32.82 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.000000000000004 y[1] (closed_form) = -1.511987071418588 y[1] (numeric) = -1.511987071418592 absolute error = 3.996802888650564e-15 relative error = 2.643410756747181e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.347 Order of pole (three term test) = 32.79 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.900000000000004 y[1] (closed_form) = -1.619914096761777 y[1] (numeric) = -1.619914096761781 absolute error = 4.218847493575595e-15 relative error = 2.604364948739634e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.404 Order of pole (three term test) = 32.77 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.800000000000004 y[1] (closed_form) = -1.725400857442591 y[1] (numeric) = -1.725400857442596 absolute error = 4.884981308350689e-15 relative error = 2.831215301232239e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.455 Order of pole (three term test) = 32.74 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.700000000000005 y[1] (closed_form) = -1.828369071247847 y[1] (numeric) = -1.828369071247853 absolute error = 5.551115123125783e-15 relative error = 3.036102070648784e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.501 Order of pole (three term test) = 32.72 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.600000000000005 y[1] (closed_form) = -1.928741822554053 y[1] (numeric) = -1.928741822554059 absolute error = 5.995204332975845e-15 relative error = 3.108349838672008e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.542 Order of pole (three term test) = 32.69 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.500000000000005 y[1] (closed_form) = -2.026443631546273 y[1] (numeric) = -2.02644363154628 absolute error = 6.661338147750939e-15 relative error = 3.287206238580651e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.577 Order of pole (three term test) = 32.66 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.400000000000006 y[1] (closed_form) = -2.121400522144871 y[1] (numeric) = -2.121400522144878 absolute error = 6.661338147750939e-15 relative error = 3.140066233704846e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.607 Order of pole (three term test) = 32.63 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.300000000000006 y[1] (closed_form) = -2.213540088578984 y[1] (numeric) = -2.213540088578991 absolute error = 6.661338147750939e-15 relative error = 3.009359614547251e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 32.6 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.200000000000006 y[1] (closed_form) = -2.302791560546834 y[1] (numeric) = -2.302791560546841 absolute error = 6.661338147750939e-15 relative error = 2.892723015785718e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.648 Order of pole (three term test) = 32.57 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.100000000000007 y[1] (closed_form) = -2.389085866904218 y[1] (numeric) = -2.389085866904225 absolute error = 7.105427357601002e-15 relative error = 2.974119706634164e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 32.54 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.000000000000007 y[1] (closed_form) = -2.472355697823879 y[1] (numeric) = -2.472355697823887 absolute error = 7.549516567451064e-15 relative error = 3.053572175757723e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 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] = -2.900000000000007 y[1] (closed_form) = -2.552535565369806 y[1] (numeric) = -2.552535565369813 absolute error = 7.549516567451064e-15 relative error = 2.957653820724455e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 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) = 32.48 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.800000000000008 y[1] (closed_form) = -2.629561862431954 y[1] (numeric) = -2.629561862431962 absolute error = 7.993605777301127e-15 relative error = 3.0399002554396e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 32.45 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.700000000000008 y[1] (closed_form) = -2.703372919968355 y[1] (numeric) = -2.703372919968363 absolute error = 7.993605777301127e-15 relative error = 2.956900884172021e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.648 Order of pole (three term test) = 32.42 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.600000000000009 y[1] (closed_form) = -2.773909062503087 y[1] (numeric) = -2.773909062503096 absolute error = 8.881784197001252e-15 relative error = 3.201901719512972e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 32.4 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.500000000000009 y[1] (closed_form) = -2.84111266183018 y[1] (numeric) = -2.841112661830189 absolute error = 8.881784197001252e-15 relative error = 3.126164025920679e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.606 Order of pole (three term test) = 32.37 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.400000000000009 y[1] (closed_form) = -2.904928188875108 y[1] (numeric) = -2.904928188875116 absolute error = 8.881784197001252e-15 relative error = 3.057488385088307e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.576 Order of pole (three term test) = 32.34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.30000000000001 y[1] (closed_form) = -2.965302263667206 y[1] (numeric) = -2.965302263667215 absolute error = 9.325873406851315e-15 relative error = 3.144999253910107e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 32.31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.20000000000001 y[1] (closed_form) = -3.022183703378049 y[1] (numeric) = -3.022183703378058 absolute error = 9.325873406851315e-15 relative error = 3.085806265326397e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 32.28 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.10000000000001 y[1] (closed_form) = -3.075523568382532 y[1] (numeric) = -3.075523568382541 absolute error = 9.769962616701378e-15 relative error = 3.176682733678273e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.454 Order of pole (three term test) = 32.26 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.000000000000011 y[1] (closed_form) = -3.125275206301238 y[1] (numeric) = -3.125275206301248 absolute error = 1.021405182655144e-14 relative error = 3.268208766369656e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.402 Order of pole (three term test) = 32.23 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000011 y[1] (closed_form) = -3.171394293984425 y[1] (numeric) = -3.171394293984435 absolute error = 1.021405182655144e-14 relative error = 3.220681782118891e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.346 Order of pole (three term test) = 32.21 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.80000000000001 y[1] (closed_form) = -3.213838877399874 y[1] (numeric) = -3.213838877399884 absolute error = 9.769962616701378e-15 relative error = 3.039966528939893e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.285 Order of pole (three term test) = 32.18 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.70000000000001 y[1] (closed_form) = -3.25256940938868 y[1] (numeric) = -3.252569409388689 absolute error = 9.325873406851315e-15 relative error = 2.867232711447074e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.219 Order of pole (three term test) = 32.16 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.60000000000001 y[1] (closed_form) = -3.287548785255031 y[1] (numeric) = -3.287548785255041 absolute error = 9.325873406851315e-15 relative error = 2.83672548029667e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.148 Order of pole (three term test) = 32.14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.50000000000001 y[1] (closed_form) = -3.318742376157927 y[1] (numeric) = -3.318742376157937 absolute error = 9.769962616701378e-15 relative error = 2.943874971100336e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.074 Order of pole (three term test) = 32.12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.40000000000001 y[1] (closed_form) = -3.346118060274801 y[1] (numeric) = -3.34611806027481 absolute error = 9.325873406851315e-15 relative error = 2.787072434044788e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9953 Order of pole (three term test) = 32.1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.30000000000001 y[1] (closed_form) = -3.369646251708989 y[1] (numeric) = -3.369646251708998 absolute error = 9.769962616701378e-15 relative error = 2.899403049132036e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9134 Order of pole (three term test) = 32.08 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.20000000000001 y[1] (closed_form) = -3.389299927115043 y[1] (numeric) = -3.389299927115053 absolute error = 9.769962616701378e-15 relative error = 2.882590159265582e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8281 Order of pole (three term test) = 32.07 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.10000000000001 y[1] (closed_form) = -3.405054650017915 y[1] (numeric) = -3.405054650017925 absolute error = 1.021405182655144e-14 relative error = 2.999673390410254e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7399 Order of pole (three term test) = 32.05 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.00000000000001 y[1] (closed_form) = -3.416888592804138 y[1] (numeric) = -3.416888592804148 absolute error = 1.021405182655144e-14 relative error = 2.989284417426403e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.649 Order of pole (three term test) = 32.04 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000000097 y[1] (closed_form) = -3.424782556365201 y[1] (numeric) = -3.424782556365212 absolute error = 1.06581410364015e-14 relative error = 3.112063572209159e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.05 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5558 Order of pole (three term test) = 32.03 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8000000000000096 y[1] (closed_form) = -3.428719987375457 y[1] (numeric) = -3.428719987375467 absolute error = 1.021405182655144e-14 relative error = 2.9789693717071e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 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 = 0.4606 Order of pole (three term test) = 32.02 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = -0.6747516313754328 y[1] (closed_form) = -3.428049484131495 y[1] (numeric) = -3.428049484131506 absolute error = 1.021405182655144e-14 relative error = 2.979552037924912e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.03757339450744566 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 = 0.339 Order of pole (three term test) = 32.01 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE SETTING H FOR POLE TOP MAIN SOLVE Loop x[1] = -0.5827043126874106 y[1] (closed_form) = -3.423573446926334 y[1] (numeric) = -3.423573446926345 absolute error = 1.06581410364015e-14 relative error = 3.113162665159214e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.02756648499843092 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 = 0.2484 Order of pole (three term test) = 32.01 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] = -0.4971490526634457 y[1] (closed_form) = -3.416380756455143 y[1] (numeric) = -3.416380756455153 absolute error = 1.06581410364015e-14 relative error = 3.119716974246294e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.01816159510686725 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 = 0.1636 Order of pole (three term test) = 32 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 TOP MAIN SOLVE Loop x[1] = -0.3968497257890957 y[1] (closed_form) = -3.404223661741713 y[1] (numeric) = -3.404223661741724 absolute error = 1.110223024625157e-14 relative error = 3.261310462947461e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.00705503402472647 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 = 0.0635 Order of pole (three term test) = 32 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 TOP MAIN SOLVE Loop x[1] = -0.2998868762687706 y[1] (closed_form) = -3.388646303243484 y[1] (numeric) = -3.388646303243494 absolute error = 1.021405182655144e-14 relative error = 3.014198270493718e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0004743833017077799 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] = -0.1997919996084264 y[1] (closed_form) = -3.368621255687971 y[1] (numeric) = -3.368621255687982 absolute error = 1.154631945610163e-14 relative error = 3.42760986756985e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0004743833017077799 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] = -0.09969712294808289 y[1] (closed_form) = -3.344591251807823 y[1] (numeric) = -3.344591251807838 absolute error = 1.465494392505207e-14 relative error = 4.381684583170142e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0004743833017077799 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] = 0.0003977537122584533 y[1] (closed_form) = -3.316561259549271 y[1] (numeric) = -3.316561259549283 absolute error = 1.243449787580175e-14 relative error = 3.749213990846542e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = 0.0004743833017077799 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! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; Iterations = 1000 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 20 Minutes 0.0 Seconds Percent Done = 50.76 %