##############ECHO OF PROBLEM################# ##############temp/lin_coshpostode.ode################# diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits = 32; max_terms = 30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start = 0.1; x_end = 2.0 ; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.00001 ; glob_look_poles = true; glob_max_iter = 100; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_h = 0.005 ; glob_display_interval = 0.1; glob_look_poles = true; glob_max_iter = 10000; glob_max_minutes = 10; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(sinh(2.0*x+3.0)/2); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 6.122941998282747 y[1] (numeric) = 6.122941998282747 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000000000000001 y[1] (analytic) = 7.482681694359174 y[1] (numeric) = 7.482681694365717 absolute error = 6.543210417930823e-12 relative error = 8.744472483526096e-11 % Correct digits = 12 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3000000000000002 y[1] (analytic) = 9.142727680307679 y[1] (numeric) = 9.142727680322221 absolute error = 1.454125708733045e-11 relative error = 1.590472514964057e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4000000000000002 y[1] (analytic) = 11.16970343036117 y[1] (numeric) = 11.16970343038548 absolute error = 2.430589063351363e-11 relative error = 2.176055146410248e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5000000000000003 y[1] (analytic) = 13.64495859856389 y[1] (numeric) = 13.64495859860013 absolute error = 3.623945588060451e-11 relative error = 2.655886100264068e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6000000000000004 y[1] (analytic) = 16.66783386602618 y[1] (numeric) = 16.66783386607701 absolute error = 5.082512188891997e-11 relative error = 3.049293765311407e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7000000000000005 y[1] (analytic) = 20.35964783126629 y[1] (numeric) = 20.35964783133492 absolute error = 6.863487556074688e-11 relative error = 3.371122925581472e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8000000000000006 y[1] (analytic) = 24.86856595154733 y[1] (numeric) = 24.86856595163772 absolute error = 9.038814141604234e-11 relative error = 3.634634244377021e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9000000000000007 y[1] (analytic) = 30.37554694292151 y[1] (numeric) = 30.37554694303848 absolute error = 1.169624397334701e-10 relative error = 3.850545965583877e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.000000000000001 y[1] (analytic) = 37.10160528889445 y[1] (numeric) = 37.10160528904386 absolute error = 1.494129264756339e-10 relative error = 4.027128349628509e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.104999999999998 y[1] (analytic) = 45.77214913000751 y[1] (numeric) = 45.77214913019897 absolute error = 1.91455740150559e-10 relative error = 4.182799885728843e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.204999999999996 y[1] (analytic) = 55.90677901008328 y[1] (numeric) = 55.90677901032387 absolute error = 2.405968757557275e-10 relative error = 4.303536709069463e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.304999999999994 y[1] (analytic) = 68.285144233849 y[1] (numeric) = 68.28514423414961 absolute error = 3.006164206453832e-10 relative error = 4.402369271065659e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.404999999999992 y[1] (analytic) = 83.40403206112258 y[1] (numeric) = 83.40403206149651 absolute error = 3.739302201211103e-10 relative error = 4.483359028099215e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.50499999999999 y[1] (analytic) = 101.8702165464282 y[1] (numeric) = 101.8702165468917 absolute error = 4.634728156815981e-10 relative error = 4.549640036058688e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.604999999999988 y[1] (analytic) = 124.4248105123328 y[1] (numeric) = 124.4248105129056 absolute error = 5.727969210056472e-10 relative error = 4.603558716682735e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.704999999999986 y[1] (analytic) = 151.9730090092387 y[1] (numeric) = 151.973009009945 absolute error = 7.063647444738308e-10 relative error = 4.647961826108805e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.804999999999984 y[1] (analytic) = 185.6204179711123 y[1] (numeric) = 185.6204179719818 absolute error = 8.695053566043498e-10 relative error = 4.684319570596318e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 1.904999999999981 y[1] (analytic) = 226.7174260636597 y[1] (numeric) = 226.7174260647284 absolute error = 1.068741539711482e-09 relative error = 4.713980562797106e-10 % Correct digits = 11 h = 0.005 TOP MAIN SOLVE Loop NO POLE x[1] = 2.004999999999979 y[1] (analytic) = 276.9134005230174 y[1] (numeric) = 276.9134005243295 absolute error = 1.312059794145171e-09 relative error = 4.738159264474131e-10 % Correct digits = 11 h = 0.005 Finished! diff ( y , x , 1 ) = cosh (2.0 * x + 3.0) ; Iterations = 381 Total Elapsed Time = 20 Seconds Elapsed Time(since restart) = 19 Seconds Time to Timeout = 9 Minutes 40 Seconds Percent Done = 100.5 %