##############ECHO OF PROBLEM################# ##############temp/lin_tanhpostode.ode################# diff ( y , x , 1 ) = tanh ( 3.0 * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=1.1 x_end=2.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # 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=3 #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(cosh(3.0*x + 1.0))/3.0) 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 1.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.8999999999999999 estimated_steps 900000.0 step_error 2.6352313834736493e-21 est_needed_step_err 2.6352313834736493e-21 opt_iter 1 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 1.0e-06 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 900000.0 step_error 3.1684589540230578e-21 est_needed_step_err 3.1684589540230578e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.5657189754166274e-225 estimated_step_error 4.5657189754166274e-225 Double H and LOOP opt_iter 2 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 450000.0 step_error 4.480877624601879e-21 est_needed_step_err 4.480877624601879e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.1375372641333543e-214 estimated_step_error 3.1375372641333543e-214 Double H and LOOP opt_iter 3 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 225000.0 step_error 6.3369179080461156e-21 est_needed_step_err 6.3369179080461156e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.1560979189874398e-203 estimated_step_error 2.1560979189874398e-203 Double H and LOOP opt_iter 4 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 112500.0 step_error 8.961755249203758e-21 est_needed_step_err 8.961755249203758e-21 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.4816574605549526e-192 estimated_step_error 1.4816574605549526e-192 Double H and LOOP opt_iter 5 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 56250.0 step_error 1.2673835816092231e-20 est_needed_step_err 1.2673835816092231e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0181848524648812e-181 estimated_step_error 1.0181848524648812e-181 Double H and LOOP opt_iter 6 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 28125.0 step_error 1.7923510498407515e-20 est_needed_step_err 1.7923510498407515e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.996880023136947e-171 estimated_step_error 6.996880023136947e-171 Double H and LOOP opt_iter 7 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 14062.5 step_error 2.5347671632184462e-20 est_needed_step_err 2.5347671632184462e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.808173978498614e-160 estimated_step_error 4.808173978498614e-160 Double H and LOOP opt_iter 8 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 7031.25 step_error 3.584702099681503e-20 est_needed_step_err 3.584702099681503e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.3040896560800915e-149 estimated_step_error 3.3040896560800915e-149 Double H and LOOP opt_iter 9 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 3515.625 step_error 5.0695343264368924e-20 est_needed_step_err 5.0695343264368924e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.2704674438501384e-138 estimated_step_error 2.2704674438501384e-138 Double H and LOOP opt_iter 10 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 1757.8125 step_error 7.169404199363006e-20 est_needed_step_err 7.169404199363006e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.5601356024714655e-127 estimated_step_error 1.5601356024714655e-127 Double H and LOOP opt_iter 11 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 878.90625 step_error 1.0139068652873785e-19 est_needed_step_err 1.0139068652873785e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.0719552273199641e-116 estimated_step_error 1.0719552273199641e-116 Double H and LOOP opt_iter 12 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 439.453125 step_error 1.4338808398726012e-19 est_needed_step_err 1.4338808398726012e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 7.364197404526034e-106 estimated_step_error 7.364197404526034e-106 Double H and LOOP opt_iter 13 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 219.7265625 step_error 2.027813730574757e-19 est_needed_step_err 2.027813730574757e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.057585278815116e-95 estimated_step_error 5.057585278815116e-95 Double H and LOOP opt_iter 14 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 109.86328125 step_error 2.8677616797452024e-19 est_needed_step_err 2.8677616797452024e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 3.4713571657706074e-84 estimated_step_error 3.4713571657706074e-84 Double H and LOOP opt_iter 15 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.016384 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 54.931640625 step_error 4.055627461149514e-19 est_needed_step_err 4.055627461149514e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.3797591457882807e-73 estimated_step_error 2.3797591457882807e-73 Double H and LOOP opt_iter 16 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.032768 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 27.4658203125 step_error 5.735523359490405e-19 est_needed_step_err 5.735523359490405e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.6275190003286523e-62 estimated_step_error 1.6275190003286523e-62 Double H and LOOP opt_iter 17 NO POLE (given) for Equation 1 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 min_size 1.2023456360961104 $glob_desired_digits_correct 16 estimated_h 0.065536 estimated_answer 1.2023456360961104 desired_abs_gbl_error 1.2023456360961103e-16 range 0.8999999999999999 estimated_steps 13.73291015625 step_error 8.111254922299028e-19 est_needed_step_err 8.111254922299028e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.107781922059004e-51 estimated_step_error 1.107781922059004e-51 Double H and LOOP opt_iter 18 SETTING H FOR MAX H SETTING H FOR DISPLAY INTERVAL NO POLE (given) for Equation 1 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 START of Soultion TOP MAIN SOLVE Loop x[1] 1.1 y[1] (closed_form) 1.2023456360961104 y[1] (numeric) 1.2023456360961104 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.1900000000000002 y[1] (closed_form) 1.2923200336715641 y[1] (numeric) 1.2923200336715646 absolute error 4.440892098500626e-16 relative error 3.4363717831439683e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.2800000000000002 y[1] (closed_form) 1.382305112996481 y[1] (numeric) 1.382305112996481 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.3700000000000003 y[1] (closed_form) 1.4722964176911344 y[1] (numeric) 1.4722964176911344 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.4600000000000004 y[1] (closed_form) 1.5622913504125326 y[1] (numeric) 1.5622913504125326 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.5500000000000005 y[1] (closed_form) 1.652288397429258 y[1] (numeric) 1.6522883974292577 absolute error 2.220446049250313e-16 relative error 1.343861067296141e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.6400000000000006 y[1] (closed_form) 1.742286676571351 y[1] (numeric) 1.7422866765713505 absolute error 4.440892098500626e-16 relative error 2.5488871367827168e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.7300000000000006 y[1] (closed_form) 1.832285673740316 y[1] (numeric) 1.8322856737403155 absolute error 4.440892098500626e-16 relative error 2.4236898002019853e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.8200000000000007 y[1] (closed_form) 1.9222850893408916 y[1] (numeric) 1.922285089340891 absolute error 6.661338147750939e-16 relative error 3.4653226957271787e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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] 1.9100000000000008 y[1] (closed_form) 2.0122847487826756 y[1] (numeric) 2.012284748782675 absolute error 4.440892098500626e-16 relative error 2.2068905015491113e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.09 NO POLE (given) for Equation 1 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 ) = tanh ( 3.0 * x + 1.0 ) ; Iterations 10 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 110.00000000000009%