##############ECHO OF PROBLEM################# ##############temp/lin_tanpostode.ode################# diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.0 x_end=0.1 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=10 ## Not Given = 0 ## No Pole = 3 ## Pole = 4 $glob_type_given_pole=4 ## Real Part $array_given_rad_poles[1][1]=0.8561944 ## Imag Part $array_given_rad_poles[1][2]=0.0 ## Order $array_given_ord_poles[1][1]=0.0 ## Not Used $array_given_ord_poles[1][2]=0.0 # ELIMINATED in preodein.rb #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 def exact_soln_y (x) return(ln(1.0 + expt(tan(2.0 * x + 3.0),2))/4.0) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 0.1 estimated_steps 100000.00000000001 step_error 9.999999999999999e-16 est_needed_step_err 9.999999999999999e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2085397146312388e-154 estimated_step_error 1.2085397146312388e-154 best_h 2.0e-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 8.110367360568399e-147 estimated_step_error 8.110367360568399e-147 best_h 4.0e-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 5.442768188776129e-139 estimated_step_error 5.442768188776129e-139 best_h 8.0e-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 3.652570220384114e-131 estimated_step_error 3.652570220384114e-131 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 2.4511853878456752e-123 estimated_step_error 2.4511853878456752e-123 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 1.6449452285447578e-115 estimated_step_error 1.6449452285447578e-115 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 1.1038806498009374e-107 estimated_step_error 1.1038806498009374e-107 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 7.407703503913967e-100 estimated_step_error 7.407703503913967e-100 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 4.9708040990768724e-92 estimated_step_error 4.9708040990768724e-92 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 3.3352844883807333e-84 estimated_step_error 3.3352844883807333e-84 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 2.237512695438289e-76 estimated_step_error 2.237512695438289e-76 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 1.5005519309269499e-68 estimated_step_error 1.5005519309269499e-68 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 1.0056406715755743e-60 estimated_step_error 1.0056406715755743e-60 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 6.7305278901435035e-53 estimated_step_error 6.7305278901435035e-53 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 4.492543764483644e-45 estimated_step_error 4.492543764483644e-45 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 2.9829210005009946e-37 estimated_step_error 2.9829210005009946e-37 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 1.9603828810934143e-29 estimated_step_error 1.9603828810934143e-29 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 1.264004407267119e-21 estimated_step_error 1.264004407267119e-21 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (analytic) 0.005028957536846423 y[1] (numeric) 0.005028957536846423 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.1 Radius of convergence (given) for eq 1 0.8561944 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.708891310928051 Order of pole (ratio test) 7.677003326668911 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ; Iterations 2 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 212.66739327841535%