##############ECHO OF PROBLEM################# ##############temp/lin_tanpostode.ode################# diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=c(-1.0); x_end=c(-0.9); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_min_h=c(0.0001); glob_type_given_pole=1; array_given_rad_poles[1][1]=c(-0.714601837); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(0.0); array_given_ord_poles[1][2]=c(0.0); /* 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=false; 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(ln(c(1.0) + expt(tan(c(2.0) * c(x) + c(3.0)),c(2)))/c(4.0)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = 0.3078132351930071 y[1] (numeric) = 0.3078132351930071 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (closed_form) = 0.3237371720088514 y[1] (numeric) = 0.3237371720088514 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (closed_form) = 0.3403917067162167 y[1] (numeric) = 0.3403917067162167 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (closed_form) = 0.3578272075077493 y[1] (numeric) = 0.3578272075077493 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (closed_form) = 0.3761001320103593 y[1] (numeric) = 0.3761001320103592 absolute error = 1.110223024625157e-16 relative error = 2.951934684762558e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (closed_form) = 0.3952740386271159 y[1] (numeric) = 0.3952740386271157 absolute error = 1.665334536937735e-16 relative error = 4.213113875937443e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (closed_form) = 0.415420817612529 y[1] (numeric) = 0.4154208176125289 absolute error = 1.665334536937735e-16 relative error = 4.008789319968611e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (closed_form) = 0.4366222017597863 y[1] (numeric) = 0.4366222017597862 absolute error = 1.110223024625157e-16 relative error = 2.542754399914737e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (closed_form) = 0.4589716365264023 y[1] (numeric) = 0.4589716365264022 absolute error = 1.665334536937735e-16 relative error = 3.628404032853425e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (closed_form) = 0.4825766173484501 y[1] (numeric) = 0.4825766173484499 absolute error = 2.220446049250313e-16 relative error = 4.601230083319628e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = 0.001 Finished! diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; Iterations = 100 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 101 %