##############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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=4 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.8561944 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=0.0 # ELIMINATED in preodein.rb $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=0.01 $glob_look_poles=true $glob_max_iter=1000000000 $glob_max_minutes=10.0 $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 estimated_h 1.0e-06 estimated_answer 1.0 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 3.6525702203841134e-131 estimated_step_error 3.6525702203841134e-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 2.4511853878456722e-123 estimated_step_error 2.4511853878456722e-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 1.6449452285447416e-115 estimated_step_error 1.6449452285447416e-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 1.1038806498008498e-107 estimated_step_error 1.1038806498008498e-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 7.407703503909264e-100 estimated_step_error 7.407703503909264e-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 4.970804099051622e-92 estimated_step_error 4.970804099051622e-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 3.335284488245168e-84 estimated_step_error 3.335284488245168e-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 2.237512694710478e-76 estimated_step_error 2.237512694710478e-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 1.5005519270195447e-68 estimated_step_error 1.5005519270195447e-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 1.0056406505978523e-60 estimated_step_error 1.0056406505978523e-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 6.730526763910631e-53 estimated_step_error 6.730526763910631e-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 4.492537718066949e-45 estimated_step_error 4.492537718066949e-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 2.9828885390485384e-37 estimated_step_error 2.9828885390485384e-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 1.960208604997565e-29 estimated_step_error 1.960208604997565e-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 1.2630687696019344e-21 estimated_step_error 1.2630687696019344e-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 0.01 Radius of convergence (given) for eq 1 0.8561944 Order of pole (given) 0.0 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] 0.01 y[1] (analytic) 0.0037053373194089675 y[1] (numeric) 0.003705337319408919 absolute error 4.85722573273506e-17 relative error 1.3108727530128966e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 0.8461944 Order of pole (given) 0.0 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] 0.02 y[1] (analytic) 0.002584717588216024 y[1] (numeric) 0.0025847175882160248 absolute error 8.673617379884035e-19 relative error 3.3557311713387537e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 0.8361944 Order of pole (given) 0.0 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] 0.03 y[1] (analytic) 0.001666190250721918 y[1] (numeric) 0.0016661902507218978 absolute error 2.0166160408230382e-17 relative error 1.2103155926817418e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 0.8261944 Order of pole (given) 0.0 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] 0.04 y[1] (analytic) 0.0009490140104840613 y[1] (numeric) 0.0009490140104840653 absolute error 4.0115480381963664e-18 relative error 4.227069351853094e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.8161944 Order of pole (given) 0.0 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] 0.05 y[1] (analytic) 0.00043261196250556685 y[1] (numeric) 0.0004326119625055726 absolute error 5.7462715141731735e-18 relative error 1.3282738371108337e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 0.8061944 Order of pole (given) 0.0 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] 0.060000000000000005 y[1] (analytic) 0.00011656973098206591 y[1] (numeric) 0.00011656973098202953 absolute error 3.6374982886888674e-17 relative error 3.120448385737882e-11% Correct digits 13 h 0.01 Radius of convergence (given) for eq 1 0.7961944 Order of pole (given) 0.0 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] 0.07 y[1] (analytic) 6.341366323577824e-07 y[1] (numeric) 6.341366323363122e-07 absolute error 2.1470167630528378e-17 relative error 3.3857321174933834e-09% Correct digits 11 h 0.01 Radius of convergence (given) for eq 1 0.7861944000000001 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.0007965773181296943 Order of pole (three term test) 21.999479738464455 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08 y[1] (analytic) 8.47123844836277e-05 y[1] (numeric) 8.471238448363442e-05 absolute error 6.7220534694101275e-18 relative error 7.935148456019786e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 0.7761944000000001 Order of pole (given) 0.0 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] 0.09 y[1] (analytic) 0.00036887176656518166 y[1] (numeric) 0.00036887176656517803 absolute error 3.63207727782644e-18 relative error 9.84644965280809e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 0.7661944 Order of pole (given) 0.0 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] 0.09999999999999999 y[1] (analytic) 0.0008533398774849093 y[1] (numeric) 0.0008533398774848628 absolute error 4.651227319962814e-17 relative error 5.4506152152078086e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 0.7561944 Order of pole (given) 0.0 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 Finished! diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; Iterations 11 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 10 Minutes 0.0 Seconds Percent Done 119.99999999999997%