##############ECHO OF PROBLEM################# ##############temp/expt_sin_linpostode.ode################# diff ( y , x , 1 ) = expt ( sin ( x ) , ( 0.2 * x + 0.3 ) ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=0.1 x_end=0.2 $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=0 #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(0.0) 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 0.1 estimated_steps 100000.00000000001 step_error 1.0540925533894597e-20 est_needed_step_err 1.0540925533894597e-20 opt_iter 1 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10000519490154472 Order of pole (three term test) 0.9993522061449652 NO COMPLEX POLE (six term test) for Equation 1 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 0.1 estimated_steps 100000.00000000001 step_error 1.0540925533894597e-20 est_needed_step_err 1.0540925533894597e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1483916146355002e-137 estimated_step_error 1.1483916146355002e-137 Double H and LOOP opt_iter 2 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 2.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 50000.00000000001 step_error 1.4907119849998598e-20 est_needed_step_err 1.4907119849998598e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.598389669015201e-130 estimated_step_error 6.598389669015201e-130 Double H and LOOP opt_iter 3 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 4.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 25000.000000000004 step_error 2.1081851067789195e-20 est_needed_step_err 2.1081851067789195e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.428063340634194e-122 estimated_step_error 4.428063340634194e-122 Double H and LOOP opt_iter 4 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 8.0e-06 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 12500.000000000002 step_error 2.9814239699997196e-20 est_needed_step_err 2.9814239699997196e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.9715679659092402e-114 estimated_step_error 2.9715679659092402e-114 Double H and LOOP opt_iter 5 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 1.6e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 6250.000000000001 step_error 4.216370213557839e-20 est_needed_step_err 4.216370213557839e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.9941116366743738e-106 estimated_step_error 1.9941116366743738e-106 Double H and LOOP opt_iter 6 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 3.2e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 3125.0000000000005 step_error 5.962847939999439e-20 est_needed_step_err 5.962847939999439e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.3381265330448507e-98 estimated_step_error 1.3381265330448507e-98 Double H and LOOP opt_iter 7 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 6.4e-05 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 1562.5000000000002 step_error 8.432740427115678e-20 est_needed_step_err 8.432740427115678e-20 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.97868490503329e-91 estimated_step_error 8.97868490503329e-91 Double H and LOOP opt_iter 8 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000128 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 781.2500000000001 step_error 1.1925695879998878e-19 est_needed_step_err 1.1925695879998878e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 6.0237088099936546e-83 estimated_step_error 6.0237088099936546e-83 Double H and LOOP opt_iter 9 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000256 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 390.62500000000006 step_error 1.6865480854231356e-19 est_needed_step_err 1.6865480854231356e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 4.040049393720842e-75 estimated_step_error 4.040049393720842e-75 Double H and LOOP opt_iter 10 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.000512 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 195.31250000000003 step_error 2.3851391759997757e-19 est_needed_step_err 2.3851391759997757e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 2.708024923037729e-67 estimated_step_error 2.708024923037729e-67 Double H and LOOP opt_iter 11 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.001024 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 97.65625000000001 step_error 3.373096170846271e-19 est_needed_step_err 3.373096170846271e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.8130365732724793e-59 estimated_step_error 1.8130365732724793e-59 Double H and LOOP opt_iter 12 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.002048 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 48.82812500000001 step_error 4.770278351999551e-19 est_needed_step_err 4.770278351999551e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.2109933937763048e-51 estimated_step_error 1.2109933937763048e-51 Double H and LOOP opt_iter 13 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.004096 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 24.414062500000004 step_error 6.746192341692542e-19 est_needed_step_err 6.746192341692542e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 8.051208448329741e-44 estimated_step_error 8.051208448329741e-44 Double H and LOOP opt_iter 14 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10003684493636435 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.0 min_size 1.0 $glob_desired_digits_correct 16 estimated_h 0.008192 estimated_answer 1.0 desired_abs_gbl_error 1.0e-16 range 0.1 estimated_steps 12.207031250000002 step_error 9.540556703999103e-19 est_needed_step_err 9.540556703999103e-19 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 5.304345214403527e-36 estimated_step_error 5.304345214403527e-36 Double H and LOOP opt_iter 15 SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.06105764461448019 Order of pole (three term test) 0.9858878039792649 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.0 y[1] (numeric) 0.0 absolute error 0.0 relative error -1.0% Desired digits 16 Estimated correct digits -16 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.11221152892289604 y[1] (closed_form) 0.0 y[1] (numeric) 0.005986330755261182 absolute error 0.005986330755261182 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.12442305784579208 y[1] (closed_form) 0.0 y[1] (numeric) 0.012102063891150589 absolute error 0.012102063891150589 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.1305288223072401 y[1] (closed_form) 0.0 y[1] (numeric) 0.01522258671886632 absolute error 0.01522258671886632 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.14274035123013618 y[1] (closed_form) 0.0 y[1] (numeric) 0.02158167232923096 absolute error 0.02158167232923096 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.15495188015303224 y[1] (closed_form) 0.0 y[1] (numeric) 0.028089768835726472 absolute error 0.028089768835726472 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.16105764461448027 y[1] (closed_form) 0.0 y[1] (numeric) 0.031396904069864305 absolute error 0.031396904069864305 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.17326917353737634 y[1] (closed_form) 0.0 y[1] (numeric) 0.03811244261055112 absolute error 0.03811244261055112 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.1854807024602724 y[1] (closed_form) 0.0 y[1] (numeric) 0.04495720968034473 absolute error 0.04495720968034473 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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] 0.19158646692172043 y[1] (closed_form) 0.0 y[1] (numeric) 0.048426084387712856 absolute error 0.048426084387712856 relative error -1.0% Desired digits 16 Estimated correct digits 13 Correct digits -16 h 0.006105764461448019 NO INFO (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 ) = expt ( sin ( x ) , ( 0.2 * x + 0.3 ) ) ; Iterations 17 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 109.90376030606451%