##############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=-1.0 x_end=-0.9 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_min_h=0.0001 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=-0.714601837 # 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=16 $glob_max_minutes=3.0 $glob_subiter_method=3 $glob_max_iter=100000000 #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 16 estimated_h 0.0001 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 999.9999999999998 step_error 1.05409255338946e-19 est_needed_step_err 1.05409255338946e-19 opt_iter 1 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2853981633974064 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.30781323519300713 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.0001 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 999.9999999999998 step_error 1.05409255338946e-19 est_needed_step_err 1.05409255338946e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.769104887809524e-92 estimated_step_error 2.769104887809524e-92 Double H and LOOP opt_iter 2 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2853981633974064 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.30781323519300713 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.0002 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 499.9999999999999 step_error 1.4907119849998597e-19 est_needed_step_err 1.4907119849998597e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8586284465478633e-84 estimated_step_error 1.8586284465478633e-84 Double H and LOOP opt_iter 3 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2853981633974064 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.30781323519300713 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.0004 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 249.99999999999994 step_error 2.10818510677892e-19 est_needed_step_err 2.10818510677892e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2477255746731428e-76 estimated_step_error 1.2477255746731428e-76 Double H and LOOP opt_iter 4 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2853981633974064 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.30781323519300713 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.0008 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 124.99999999999997 step_error 2.9814239699997195e-19 est_needed_step_err 2.9814239699997195e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.379002748596237e-69 estimated_step_error 8.379002748596237e-69 Double H and LOOP opt_iter 5 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2853981633974064 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.30781323519300713 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.0016 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 62.499999999999986 step_error 4.21637021355784e-19 est_needed_step_err 4.21637021355784e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.630663247984856e-61 estimated_step_error 5.630663247984856e-61 Double H and LOOP opt_iter 6 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2853981633974064 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.30781323519300713 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.0032 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 31.249999999999993 step_error 5.962847939999439e-19 est_needed_step_err 5.962847939999439e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.7889293265320974e-53 estimated_step_error 3.7889293265320974e-53 Double H and LOOP opt_iter 7 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2853981633974064 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.30781323519300713 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.0064 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.09999999999999998 estimated_steps 15.624999999999996 step_error 8.43274042711568e-19 est_needed_step_err 8.43274042711568e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.556584513439701e-45 estimated_step_error 2.556584513439701e-45 Double H and LOOP opt_iter 8 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22296731515422372 Order of pole (three term test) 3.424745396688914e-12 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (closed_form) 0.30781323519300713 y[1] (numeric) 0.30781323519300713 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.285398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.28539816339740925 Order of pole (three term test) 3.0509814708959652e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.99 y[1] (closed_form) 0.32373717200885144 y[1] (numeric) 0.32373717200885144 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.275398163 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2753981633974338 Order of pole (three term test) 1.2693816208823706e-12 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.98 y[1] (closed_form) 0.3403917067162167 y[1] (numeric) 0.3403917067162167 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.26539816299999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2653981633974419 Order of pole (three term test) 5.052507217269007e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.97 y[1] (closed_form) 0.3578272075077493 y[1] (numeric) 0.3578272075077493 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.25539816299999996 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.2553981633974472 Order of pole (three term test) 1.1512220214195557e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.96 y[1] (closed_form) 0.3761001320103593 y[1] (numeric) 0.37610013201035924 absolute error 5.551115123125783e-17 relative error 1.4759673423812792e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.24539816299999995 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.24539816339744644 Order of pole (three term test) 2.199900769962678e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.95 y[1] (closed_form) 0.3952740386271159 y[1] (numeric) 0.3952740386271158 absolute error 1.1102230246251565e-16 relative error 2.808742583958295e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.23539816299999994 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.23539816339744807 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.94 y[1] (closed_form) 0.415420817612529 y[1] (numeric) 0.4154208176125289 absolute error 1.1102230246251565e-16 relative error 2.6725262133124078e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.22539816299999993 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.22539816339744617 Order of pole (three term test) 1.8798742221740117e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9299999999999999 y[1] (closed_form) 0.43662220175978633 y[1] (numeric) 0.4366222017597863 absolute error 5.551115123125783e-17 relative error 1.2713771999573683e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.21539816299999992 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.21539816339745202 Order of pole (three term test) 4.662012618636208e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9199999999999999 y[1] (closed_form) 0.4589716365264023 y[1] (numeric) 0.4589716365264022 absolute error 1.1102230246251565e-16 relative error 2.418936021902284e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.2053981629999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.20539816339744565 Order of pole (three term test) 1.675070860488659e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9099999999999999 y[1] (closed_form) 0.4825766173484501 y[1] (numeric) 0.48257661734844987 absolute error 2.220446049250313e-16 relative error 4.6012300833196277e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.009999999999999998 Radius of convergence (given) for eq 1 0.1953981629999999 Order of pole (given) 0.0 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.19539816339744423 Order of pole (three term test) 3.372590117321175e-13 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( 2.0 * x + 3.0 ) ; Iterations 10 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 110.00000000000013%