##############ECHO OF PROBLEM################# ##############temp/sub_lin_sinpostode.ode################# diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x); ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=0.1; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.1; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(cos(x) + (0.05 * x * x) + x) ; } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 4.9 estimated_steps = 4900000.000000001 step_error = 2.040816326530612e-17 est_needed_step_err = 2.040816326530612e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.467208605532302e-183 estimated_step_error = 2.467208605532302e-183 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.655715664606566e-175 estimated_step_error = 1.655715664606566e-175 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.111131969458436e-167 estimated_step_error = 1.111131969458436e-167 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.456680367024186e-160 estimated_step_error = 7.456680367024186e-160 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.004093412037817e-152 estimated_step_error = 5.004093412037817e-152 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.358190142481624e-144 estimated_step_error = 3.358190142481624e-144 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.25364312158092e-136 estimated_step_error = 2.25364312158092e-136 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.512394117654307e-128 estimated_step_error = 1.512394117654307e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.014950270158055e-120 estimated_step_error = 1.014950270158055e-120 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.811212724408108e-113 estimated_step_error = 6.811212724408108e-113 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.570923134360025e-105 estimated_step_error = 4.570923134360025e-105 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.067488750234022e-97 estimated_step_error = 3.067488750234022e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.05854901161809e-89 estimated_step_error = 2.05854901161809e-89 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.381458319740244e-81 estimated_step_error = 1.381458319740244e-81 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.270668118428105e-74 estimated_step_error = 9.270668118428105e-74 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.221249002016115e-66 estimated_step_error = 6.221249002016115e-66 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.174750875079241e-58 estimated_step_error = 4.174750875079241e-58 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.801274754399603e-50 estimated_step_error = 2.801274754399603e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y[1] (analytic) = 1.095504165278026 y[1] (numeric) = 1.095504165278026 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 0.2 y[1] (analytic) = 1.182066577841242 y[1] (numeric) = 1.182066577841242 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 0.3 y[1] (analytic) = 1.259836489125606 y[1] (numeric) = 1.259836489125606 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 0.4 y[1] (analytic) = 1.329060994002885 y[1] (numeric) = 1.329060994002885 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 0.5 y[1] (analytic) = 1.390082561890373 y[1] (numeric) = 1.390082561890373 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 0.6 y[1] (analytic) = 1.443335614909678 y[1] (numeric) = 1.443335614909678 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 0.7 y[1] (analytic) = 1.489342187284488 y[1] (numeric) = 1.489342187284489 absolute error = 2.220446049250313e-16 relative error = 1.490890453656486e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) = 110.9 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999999 y[1] (analytic) = 1.528706709347165 y[1] (numeric) = 1.528706709347166 absolute error = 2.220446049250313e-16 relative error = 1.452499708200113e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) = 123 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.8999999999999999 y[1] (analytic) = 1.562109968270665 y[1] (numeric) = 1.562109968270665 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) = 97.47 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999999 y[1] (analytic) = 1.59030230586814 y[1] (numeric) = 1.59030230586814 absolute error = 2.220446049250313e-16 relative error = 1.396241482551445e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 1.1 y[1] (analytic) = 1.614096121425577 y[1] (numeric) = 1.614096121425578 absolute error = 2.220446049250313e-16 relative error = 1.375659119538188e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 1.2 y[1] (analytic) = 1.634357754476674 y[1] (numeric) = 1.634357754476674 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 1.3 y[1] (analytic) = 1.651998828624587 y[1] (numeric) = 1.651998828624587 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 1.4 y[1] (analytic) = 1.667967142900241 y[1] (numeric) = 1.667967142900241 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 1.5 y[1] (analytic) = 1.683237201667703 y[1] (numeric) = 1.683237201667703 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 1.6 y[1] (analytic) = 1.698800477698711 y[1] (numeric) = 1.698800477698711 absolute error = 2.220446049250313e-16 relative error = 1.307067003099888e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02919 Order of pole (three term test) = 27 Derivative of radius w.r.t nth term = 3.177e+53 Derivative of order w.r.t nth term = 9.28e+51 Derivative of radius w.r.t (n-1)th term = 4.024e+52 Derivative of order w.r.t (n-1)th term = -1.345e+53 Derivative of radius w.r.t (n-2)th term = -3.862e+45 Derivative of order w.r.t (n-2)th term = -8.69e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.05832 Guess error in order = 0.002556 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 1.715655505704475 y[1] (numeric) = 1.715655505704475 absolute error = 2.220446049250313e-16 relative error = 1.294226050548862e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1278 Order of pole (three term test) = 26.98 Derivative of radius w.r.t nth term = 1.38e+54 Derivative of order w.r.t nth term = 1.793e+53 Derivative of radius w.r.t (n-1)th term = 3.867e+52 Derivative of order w.r.t (n-1)th term = -5.926e+53 Derivative of radius w.r.t (n-2)th term = -3.318e+47 Derivative of order w.r.t (n-2)th term = -8.622e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.2513 Guess error in order = 0.04898 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 1.734797905306913 y[1] (numeric) = 1.734797905306913 absolute error = 4.440892098500626e-16 relative error = 2.559890166408151e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2213 Order of pole (three term test) = 26.95 Derivative of radius w.r.t nth term = 2.346e+54 Derivative of order w.r.t nth term = 5.474e+53 Derivative of radius w.r.t (n-1)th term = 3.522e+52 Derivative of order w.r.t (n-1)th term = -1.042e+54 Derivative of radius w.r.t (n-2)th term = -1.819e+48 Derivative of order w.r.t (n-2)th term = -8.467e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.4197 Guess error in order = 0.1469 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.900000000000001 y[1] (analytic) = 1.757210433136497 y[1] (numeric) = 1.757210433136496 absolute error = 4.440892098500626e-16 relative error = 2.527239774335932e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3059 Order of pole (three term test) = 26.9 Derivative of radius w.r.t nth term = 3.152e+54 Derivative of order w.r.t nth term = 1.077e+54 Derivative of radius w.r.t (n-1)th term = 3.019e+52 Derivative of order w.r.t (n-1)th term = -1.475e+54 Derivative of radius w.r.t (n-2)th term = -5.241e+48 Derivative of order w.r.t (n-2)th term = -8.227e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.5479 Guess error in order = 0.2808 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 1.783853163452858 y[1] (numeric) = 1.783853163452857 absolute error = 4.440892098500626e-16 relative error = 2.489494196879275e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3784 Order of pole (three term test) = 26.83 Derivative of radius w.r.t nth term = 3.747e+54 Derivative of order w.r.t nth term = 1.715e+54 Derivative of radius w.r.t (n-1)th term = 2.397e+52 Derivative of order w.r.t (n-1)th term = -1.887e+54 Derivative of radius w.r.t (n-2)th term = -1.118e+49 Derivative of order w.r.t (n-2)th term = -7.905e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.6257 Guess error in order = 0.4296 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.100000000000001 y[1] (analytic) = 1.815653895400143 y[1] (numeric) = 1.815653895400142 absolute error = 2.220446049250313e-16 relative error = 1.22294565879306e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4358 Order of pole (three term test) = 26.75 Derivative of radius w.r.t nth term = 4.096e+54 Derivative of order w.r.t nth term = 2.396e+54 Derivative of radius w.r.t (n-1)th term = 1.707e+52 Derivative of order w.r.t (n-1)th term = -2.273e+54 Derivative of radius w.r.t (n-2)th term = -1.996e+49 Derivative of order w.r.t (n-2)th term = -7.505e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.6494 Guess error in order = 0.5697 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.200000000000001 y[1] (analytic) = 1.853498882744655 y[1] (numeric) = 1.853498882744654 absolute error = 4.440892098500626e-16 relative error = 2.395950782513863e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) = 88.04 Radius of convergence (three term test) for eq 1 = 0.4758 Order of pole (three term test) = 26.65 Derivative of radius w.r.t nth term = 4.189e+54 Derivative of order w.r.t nth term = 3.049e+54 Derivative of radius w.r.t (n-1)th term = 1.002e+52 Derivative of order w.r.t (n-1)th term = -2.627e+54 Derivative of radius w.r.t (n-2)th term = -3.161e+49 Derivative of order w.r.t (n-2)th term = -7.029e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.622 Guess error in order = 0.6792 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.300000000000001 y[1] (analytic) = 1.898223978720176 y[1] (numeric) = 1.898223978720176 absolute error = 4.440892098500626e-16 relative error = 2.339498472406176e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) = 111.8 Radius of convergence (three term test) for eq 1 = 0.4968 Order of pole (three term test) = 26.56 Derivative of radius w.r.t nth term = 4.034e+54 Derivative of order w.r.t nth term = 3.605e+54 Derivative of radius w.r.t (n-1)th term = 3.373e+51 Derivative of order w.r.t (n-1)th term = -2.947e+54 Derivative of radius w.r.t (n-2)th term = -4.588e+49 Derivative of order w.r.t (n-2)th term = -6.483e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.5526 Guess error in order = 0.7406 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.400000000000001 y[1] (analytic) = 1.950606284458755 y[1] (numeric) = 1.950606284458755 absolute error = 4.440892098500626e-16 relative error = 2.276672711393865e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) = 122 Radius of convergence (three term test) for eq 1 = 0.4981 Order of pole (three term test) = 26.46 Derivative of radius w.r.t nth term = 3.663e+54 Derivative of order w.r.t nth term = 3.999e+54 Derivative of radius w.r.t (n-1)th term = -2.384e+51 Derivative of order w.r.t (n-1)th term = -3.231e+54 Derivative of radius w.r.t (n-2)th term = -6.219e+49 Derivative of order w.r.t (n-2)th term = -5.872e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.4545 Guess error in order = 0.7443 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.500000000000001 y[1] (analytic) = 2.011356384453067 y[1] (numeric) = 2.011356384453066 absolute error = 4.440892098500626e-16 relative error = 2.207909116866032e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) = 96.52 Radius of convergence (three term test) for eq 1 = 0.4795 Order of pole (three term test) = 26.36 Derivative of radius w.r.t nth term = 3.125e+54 Derivative of order w.r.t nth term = 4.183e+54 Derivative of radius w.r.t (n-1)th term = -6.846e+51 Derivative of order w.r.t (n-1)th term = -3.478e+54 Derivative of radius w.r.t (n-2)th term = -7.976e+49 Derivative of order w.r.t (n-2)th term = -5.203e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.3435 Guess error in order = 0.6897 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.600000000000001 y[1] (analytic) = 2.081111246631053 y[1] (numeric) = 2.081111246631053 absolute error = 4.440892098500626e-16 relative error = 2.133904232985928e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4417 Order of pole (three term test) = 26.27 Derivative of radius w.r.t nth term = 2.48e+54 Derivative of order w.r.t nth term = 4.122e+54 Derivative of radius w.r.t (n-1)th term = -9.74e+51 Derivative of order w.r.t (n-1)th term = -3.688e+54 Derivative of radius w.r.t (n-2)th term = -9.759e+49 Derivative of order w.r.t (n-2)th term = -4.482e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.2348 Guess error in order = 0.5854 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.700000000000001 y[1] (analytic) = 2.16042785798294 y[1] (numeric) = 2.160427857982939 absolute error = 4.440892098500626e-16 relative error = 2.05556139358748e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3864 Order of pole (three term test) = 26.18 Derivative of radius w.r.t nth term = 1.798e+54 Derivative of order w.r.t nth term = 3.804e+54 Derivative of radius w.r.t (n-1)th term = -1.094e+52 Derivative of order w.r.t (n-1)th term = -3.86e+54 Derivative of radius w.r.t (n-2)th term = -1.146e+50 Derivative of order w.r.t (n-2)th term = -3.716e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.1411 Guess error in order = 0.4479 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.800000000000001 y[1] (analytic) = 2.249777659331343 y[1] (numeric) = 2.249777659331342 absolute error = 4.440892098500626e-16 relative error = 1.973924881012689e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3156 Order of pole (three term test) = 26.11 Derivative of radius w.r.t nth term = 1.151e+54 Derivative of order w.r.t nth term = 3.238e+54 Derivative of radius w.r.t (n-1)th term = -1.048e+52 Derivative of order w.r.t (n-1)th term = -3.995e+54 Derivative of radius w.r.t (n-2)th term = -1.297e+50 Derivative of order w.r.t (n-2)th term = -2.912e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.07084 Guess error in order = 0.2989 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.900000000000001 y[1] (analytic) = 2.349541834850411 y[1] (numeric) = 2.34954183485041 absolute error = 8.881784197001252e-16 relative error = 3.780219643361546e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2323 Order of pole (three term test) = 26.06 Derivative of radius w.r.t nth term = 6.052e+53 Derivative of order w.r.t nth term = 2.456e+54 Derivative of radius w.r.t (n-1)th term = -8.544e+51 Derivative of order w.r.t (n-1)th term = -4.095e+54 Derivative of radius w.r.t (n-2)th term = -1.42e+50 Derivative of order w.r.t (n-2)th term = -2.08e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.02659 Guess error in order = 0.1619 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.000000000000001 y[1] (analytic) = 2.460007503399556 y[1] (numeric) = 2.460007503399555 absolute error = 8.881784197001252e-16 relative error = 3.610470368373777e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1397 Order of pole (three term test) = 26.02 Derivative of radius w.r.t nth term = 2.147e+53 Derivative of order w.r.t nth term = 1.506e+54 Derivative of radius w.r.t (n-1)th term = -5.465e+51 Derivative of order w.r.t (n-1)th term = -4.16e+54 Derivative of radius w.r.t (n-2)th term = -1.505e+50 Derivative of order w.r.t (n-2)th term = -1.227e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.005565 Guess error in order = 0.05855 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 2.581364849726723 y[1] (numeric) = 2.581364849726722 absolute error = 8.881784197001252e-16 relative error = 3.440731827560729e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04154 Order of pole (three term test) = 26 Derivative of radius w.r.t nth term = 1.881e+52 Derivative of order w.r.t nth term = 4.52e+53 Derivative of radius w.r.t (n-1)th term = -1.671e+51 Derivative of order w.r.t (n-1)th term = -4.191e+54 Derivative of radius w.r.t (n-2)th term = -1.547e+50 Derivative of order w.r.t (n-2)th term = -3.615e+155 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.0001437 Guess error in order = 0.005178 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000002 y[1] (analytic) = 2.713705224205249 y[1] (numeric) = 2.713705224205248 absolute error = 8.881784197001252e-16 relative error = 3.272936248852313e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 3.300000000000002 y[1] (analytic) = 2.857020230091138 y[1] (numeric) = 2.857020230091137 absolute error = 8.881784197001252e-16 relative error = 3.108757895185757e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 3.400000000000002 y[1] (analytic) = 3.011201807420542 y[1] (numeric) = 3.011201807420541 absolute error = 8.881784197001252e-16 relative error = 2.949581185529898e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 3.500000000000002 y[1] (analytic) = 3.176043312709207 y[1] (numeric) = 3.176043312709206 absolute error = 1.332267629550188e-15 relative error = 4.194740116480798e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 3.600000000000002 y[1] (analytic) = 3.351241583665856 y[1] (numeric) = 3.351241583665855 absolute error = 1.332267629550188e-15 relative error = 3.975444909861875e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 3.700000000000002 y[1] (analytic) = 3.536399968289595 y[1] (numeric) = 3.536399968289594 absolute error = 1.332267629550188e-15 relative error = 3.767299065423723e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 3.800000000000002 y[1] (analytic) = 3.731032288085587 y[1] (numeric) = 3.731032288085586 absolute error = 1.332267629550188e-15 relative error = 3.570774859827819e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) = 100.5 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.900000000000002 y[1] (analytic) = 3.934567695799864 y[1] (numeric) = 3.934567695799863 absolute error = 1.77635683940025e-15 relative error = 4.514744634579561e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) = 126.8 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000002 y[1] (analytic) = 4.146356379136392 y[1] (numeric) = 4.146356379136391 absolute error = 8.881784197001252e-16 relative error = 2.142069659446678e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) = 107.6 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 4.365676053466735 y[1] (numeric) = 4.365676053466734 absolute error = 8.881784197001252e-16 relative error = 2.034457914015019e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 4.200000000000001 y[1] (analytic) = 4.591739178659303 y[1] (numeric) = 4.591739178659303 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (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] = 4.300000000000001 y[1] (analytic) = 4.823700827920026 y[1] (numeric) = 4.823700827920027 absolute error = 8.881784197001252e-16 relative error = 1.841280069773951e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 4.4 y[1] (analytic) = 5.060667130021582 y[1] (numeric) = 5.060667130021583 absolute error = 1.77635683940025e-15 relative error = 3.510123850790943e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 4.5 y[1] (analytic) = 5.301704200569221 y[1] (numeric) = 5.301704200569223 absolute error = 2.664535259100376e-15 relative error = 5.025808981976581e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 4.6 y[1] (analytic) = 5.545847473064945 y[1] (numeric) = 5.545847473064948 absolute error = 3.552713678800501e-15 relative error = 6.406078955570469e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 4.699999999999999 y[1] (analytic) = 5.792111336537108 y[1] (numeric) = 5.792111336537112 absolute error = 4.440892098500626e-15 relative error = 7.667138700333881e-14 % Correct digits = 16 h = 0.1 NO INFO (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] = 4.799999999999999 y[1] (analytic) = 6.039498983439444 y[1] (numeric) = 6.03949898343945 absolute error = 6.217248937900877e-15 relative error = 1.029431241722009e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08716 Order of pole (three term test) = 26.99 Derivative of radius w.r.t nth term = -9.455e+53 Derivative of order w.r.t nth term = -8.305e+52 Derivative of radius w.r.t (n-1)th term = -3.956e+52 Derivative of order w.r.t (n-1)th term = 4.028e+53 Derivative of radius w.r.t (n-2)th term = 1.039e+47 Derivative of order w.r.t (n-2)th term = 8.661e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.173 Guess error in order = 0.02279 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999999 y[1] (analytic) = 6.287012369422572 y[1] (numeric) = 6.287012369422579 absolute error = 6.217248937900877e-15 relative error = 9.88903563819757e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1832 Order of pole (three term test) = 26.97 Derivative of radius w.r.t nth term = -1.96e+54 Derivative of order w.r.t nth term = -3.721e+53 Derivative of radius w.r.t (n-1)th term = -3.686e+52 Derivative of order w.r.t (n-1)th term = 8.565e+53 Derivative of radius w.r.t (n-2)th term = 1.006e+48 Derivative of order w.r.t (n-2)th term = 8.541e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.3537 Guess error in order = 0.1007 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999998 y[1] (analytic) = 6.533662185463222 y[1] (numeric) = 6.533662185463229 absolute error = 7.105427357601002e-15 relative error = 1.087510672561233e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.272 Order of pole (three term test) = 26.92 Derivative of radius w.r.t nth term = -2.84e+54 Derivative of order w.r.t nth term = -8.402e+53 Derivative of radius w.r.t (n-1)th term = -3.245e+52 Derivative of order w.r.t (n-1)th term = 1.297e+54 Derivative of radius w.r.t (n-2)th term = 3.54e+48 Derivative of order w.r.t (n-2)th term = 8.337e+156 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 0.5002 Guess error in order = 0.222 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = (0.1 * x + 1.0) - sin(x); Iterations = 50 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 104.1 %