##############ECHO OF PROBLEM################# ##############temp/pos_hpostode.ode################# diff ( y , x , 1 ) = 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 = 0.2 ; glob_display_interval = 0.01; array_y_init[0 + 1] = exact_soln_y(x_start); glob_h = 0.0001; glob_look_poles = true; glob_max_iter = 10000000; // END SECOND INPUT BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(2.0 - cos(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.004995834721974 y[1] (numeric) = 1.004995834721974 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1100000000000003 y[1] (analytic) = 1.006043902043303 y[1] (numeric) = 1.006043902043304 absolute error = 4.440892098500626e-16 relative error = 4.41421302736496e-14 % Correct digits = 15 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1200000000000006 y[1] (analytic) = 1.007191364146134 y[1] (numeric) = 1.007191364146133 absolute error = 8.881784197001252e-16 relative error = 8.818368100813651e-14 % Correct digits = 15 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1300000000000002 y[1] (analytic) = 1.008438106285212 y[1] (numeric) = 1.008438106285211 absolute error = 6.661338147750939e-16 relative error = 6.605599397953476e-14 % Correct digits = 15 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1400999999999991 y[1] (analytic) = 1.009797963049884 y[1] (numeric) = 1.009797963049883 absolute error = 1.332267629550188e-15 relative error = 1.319340777363376e-13 % Correct digits = 14 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.150099999999998 y[1] (analytic) = 1.011243870821035 y[1] (numeric) = 1.011243870821035 absolute error = 2.220446049250313e-16 relative error = 2.195757238506197e-14 % Correct digits = 15 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1600999999999969 y[1] (analytic) = 1.012788653381144 y[1] (numeric) = 1.012788653381144 absolute error = 4.440892098500626e-16 relative error = 4.384816203928561e-14 % Correct digits = 15 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1700999999999958 y[1] (analytic) = 1.014432156253241 y[1] (numeric) = 1.014432156253242 absolute error = 8.881784197001252e-16 relative error = 8.755424541948392e-14 % Correct digits = 15 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1800999999999947 y[1] (analytic) = 1.016174215088409 y[1] (numeric) = 1.016174215088411 absolute error = 1.77635683940025e-15 relative error = 1.748082969459823e-13 % Correct digits = 14 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1900999999999936 y[1] (analytic) = 1.018014655682216 y[1] (numeric) = 1.018014655682218 absolute error = 2.664535259100376e-15 relative error = 2.617383987772509e-13 % Correct digits = 14 h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2000999999999925 y[1] (analytic) = 1.019953293992136 y[1] (numeric) = 1.01995329399214 absolute error = 3.774758283725532e-15 relative error = 3.70091288097221e-13 % Correct digits = 14 h = 0.0001 Finished! diff ( y , x , 1 ) = sin(x); Iterations = 1001 Total Elapsed Time = 49 Seconds Elapsed Time(since restart) = 48 Seconds Time to Timeout = 14 Minutes 11 Seconds Percent Done = 100.2 %