##############ECHO OF PROBLEM################# ##############temp/mult_sin_sinpostode.ode################# diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; ! #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 # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb $glob_type_given_pole=3 # 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(-(sin(x) * cos(x))/2.0 + x/2.0) 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 POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 8.264789130434852e-177 estimated_step_error 8.264789130434852e-177 Double H and LOOP opt_iter 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 5.54640711081085e-169 estimated_step_error 5.54640711081085e-169 Double H and LOOP opt_iter 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 3.722132165016696e-161 estimated_step_error 3.722132165016696e-161 Double H and LOOP opt_iter 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 2.497882438065287e-153 estimated_step_error 2.497882438065287e-153 Double H and LOOP opt_iter 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 1.676302978444555e-145 estimated_step_error 1.676302978444555e-145 Double H and LOOP opt_iter 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 1.1249511746391186e-137 estimated_step_error 1.1249511746391186e-137 Double H and LOOP opt_iter 7 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 7.549463677467823e-130 estimated_step_error 7.549463677467823e-130 Double H and LOOP opt_iter 8 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 5.066418554253187e-122 estimated_step_error 5.066418554253187e-122 Double H and LOOP opt_iter 9 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 3.400095450684846e-114 estimated_step_error 3.400095450684846e-114 Double H and LOOP opt_iter 10 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 2.2818721527065832e-106 estimated_step_error 2.2818721527065832e-106 Double H and LOOP opt_iter 11 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 1.5314817170988626e-98 estimated_step_error 1.5314817170988626e-98 Double H and LOOP opt_iter 12 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 1.0279522306717597e-90 estimated_step_error 1.0279522306717597e-90 Double H and LOOP opt_iter 13 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 6.901050895634196e-83 estimated_step_error 6.901050895634196e-83 Double H and LOOP opt_iter 14 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716264 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 min_size 0.00033266730123469174 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 4.634679859924864e-75 estimated_step_error 4.634679859924864e-75 Double H and LOOP opt_iter 15 SETTING H FOR DISPLAY INTERVAL SETTING H FOR POLE NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.05942052342356118 Order of pole (three term test) 22.960530497001436 NO COMPLEX POLE (six term test) for Equation 1 START of Soultion TOP MAIN SOLVE Loop x[1] 0.1 y[1] (closed_form) 0.00033266730123469174 y[1] (numeric) 0.00033266730123469174 absolute error 0.0 relative error 0.0% Desired digits 16 Estimated correct digits 14 Correct digits 16 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.09735458557716259 Order of pole (three term test) 22.96053049700144 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11188410468471224 y[1] (closed_form) 0.0004656896105969255 y[1] (numeric) 0.00046568961059692256 absolute error 2.927345865710862e-18 relative error 6.286045037505907e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.10818647294857461 Order of pole (three term test) 22.950757970848876 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12376820936942448 y[1] (closed_form) 0.0006300505828308947 y[1] (numeric) 0.0006300505828308899 absolute error 4.7704895589362195e-18 relative error 7.571597723950708e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11877393617801985 Order of pole (three term test) 22.939967053697337 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1297102617117806 y[1] (closed_form) 0.0007250037547591043 y[1] (numeric) 0.0007250037547590992 absolute error 5.095750210681871e-18 relative error 7.028584579365422e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.12396851064916607 Order of pole (three term test) 22.93419722876788 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14159436639649284 y[1] (closed_form) 0.0009424863558749469 y[1] (numeric) 0.000942486355874944 absolute error 2.927345865710862e-18 relative error 3.1059822218787374e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.13414467485567436 Order of pole (three term test) 22.921925141264968 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.15347847108120508 y[1] (closed_form) 0.0011994299577946094 y[1] (numeric) 0.0011994299577945992 absolute error 1.0191500421363742e-17 relative error 8.496953369501328e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14401776792808088 Order of pole (three term test) 22.908699804360186 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1594205234235612 y[1] (closed_form) 0.0013437041559696133 y[1] (numeric) 0.0013437041559696172 absolute error 3.903127820947816e-18 relative error 2.9047523620490175e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.14883366398500286 Order of pole (three term test) 22.90173892250963 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17130462810827343 y[1] (closed_form) 0.0016658534052585439 y[1] (numeric) 0.0016658534052585495 absolute error 5.637851296924623e-18 relative error 3.3843622008562134e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.15821055415022972 Order of pole (three term test) 22.88714039084279 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18318873279298567 y[1] (closed_form) 0.0020354467054271713 y[1] (numeric) 0.002035446705427169 absolute error 2.168404344971009e-18 relative error 1.06532111068756e-13% Desired digits 16 Estimated correct digits 13 Correct digits 15 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.16723000148647518 Order of pole (three term test) 22.871667198460305 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1950728374776979 y[1] (closed_form) 0.0024556319451742026 y[1] (numeric) 0.002455631945174201 absolute error 1.734723475976807e-18 relative error 7.064264982323097e-14% Desired digits 16 Estimated correct digits 13 Correct digits 16 h 0.005942052342356119 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.17587162848612606 Order of pole (three term test) 22.85535430372313 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sin ( x ) * sin ( x ) ; Iterations 17 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 106.95694216241013%