##############ECHO OF PROBLEM################# ##############temp/sing5postode.ode################# diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=-1.0 x_end=-0.7 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=100 $glob_max_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 # ELIMINATED in preodein.rb $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=0.0 # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=0.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=4.0 # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=0.0 #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(1.0/x/x/x) 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 0.30000000000000004 estimated_steps 300000.00000000006 step_error 3.3333333333333326e-16 est_needed_step_err 3.3333333333333326e-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 6.562503088236751e-96 estimated_step_error 6.562503088236751e-96 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 4.3008040478155865e-91 estimated_step_error 4.3008040478155865e-91 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 2.818577593557857e-86 estimated_step_error 2.818577593557857e-86 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 1.8471864887776104e-81 estimated_step_error 1.8471864887776104e-81 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 1.210576694767835e-76 estimated_step_error 1.210576694767835e-76 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 7.93369516334265e-72 estimated_step_error 7.93369516334265e-72 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 5.199504761864271e-67 estimated_step_error 5.199504761864271e-67 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 3.407650074260886e-62 estimated_step_error 3.407650074260886e-62 best_h 0.0001 START of Soultion TOP MAIN SOLVE Loop x[1] -1.0 y[1] (analytic) -1.0 y[1] (numeric) -1.0 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.0001 Radius of convergence (given) for eq 1 1.0 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 1.0000000000000009 Order of pole (three term test) 3.5911013752493536e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9899000000000011 y[1] (analytic) -1.0309225213378324 y[1] (numeric) -1.030922521337836 absolute error 3.552713678800501e-15 relative error 3.4461500309355254e-13% Correct digits 15 h 0.0001 Radius of convergence (given) for eq 1 0.9899000000000011 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9899000000000007 Order of pole (three term test) 2.5950757615887004e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9799000000000022 y[1] (analytic) -1.0628077851634612 y[1] (numeric) -1.0628077851634687 absolute error 7.549516567451064e-15 relative error 7.103369652387275e-13% Correct digits 15 h 0.0001 Radius of convergence (given) for eq 1 0.9799000000000022 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9799000000000062 Order of pole (three term test) 7.50073637788974e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9699000000000033 y[1] (analytic) -1.0960216223446904 y[1] (numeric) -1.096021622344703 absolute error 1.2656542480726785e-14 relative error 1.1547712401559172e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.9699000000000033 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9699000000000073 Order of pole (three term test) 5.401947451317328e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9599000000000044 y[1] (analytic) -1.1306339576048192 y[1] (numeric) -1.1306339576048359 absolute error 1.6653345369377348e-14 relative error 1.472921033139361e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.9599000000000044 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9599000000000042 Order of pole (three term test) 3.877210589004117e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9499000000000055 y[1] (analytic) -1.1667191788509423 y[1] (numeric) -1.1667191788509623 absolute error 1.9984014443252818e-14 relative error 1.7128384280898099e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.9499000000000055 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9499000000000032 Order of pole (three term test) 2.7731927882882102e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9399000000000066 y[1] (analytic) -1.2043564730987109 y[1] (numeric) -1.2043564730987353 absolute error 2.4424906541753444e-14 relative error 2.0280462709608022e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.9399000000000066 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9399000000000125 Order of pole (three term test) 7.906065993161129e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9299000000000077 y[1] (analytic) -1.2436301916061556 y[1] (numeric) -1.2436301916061845 absolute error 2.886579864025407e-14 relative error 2.321091819343315e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.9299000000000077 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.929900000000015 Order of pole (three term test) 8.421681906105711e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9199000000000088 y[1] (analytic) -1.2846302471051385 y[1] (numeric) -1.284630247105172 absolute error 3.352873534367973e-14 relative error 2.6099911176181127e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.9199000000000088 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.919900000000009 Order of pole (three term test) 3.972349492991375e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.9099000000000099 y[1] (analytic) -1.3274525463399303 y[1] (numeric) -1.3274525463399682 absolute error 3.7969627442180354e-14 relative error 2.860337836321962e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.9099000000000099 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.9099000000000127 Order of pole (three term test) 5.5998310530579814e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.899900000000011 y[1] (analytic) -1.372199461482977 y[1] (numeric) -1.3721994614830197 absolute error 4.285460875053104e-14 relative error 3.1230597266243485e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.899900000000011 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8999000000000108 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8899000000000121 y[1] (analytic) -1.4189803444035745 y[1] (numeric) -1.4189803444036222 absolute error 4.773959005888173e-14 relative error 3.3643587980034794e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8899000000000121 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8899000000000178 Order of pole (three term test) 8.24930792428963e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8799000000000132 y[1] (analytic) -1.467912088222083 y[1] (numeric) -1.4679120882221364 absolute error 5.3290705182007514e-14 relative error 3.6303744351988103e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8799000000000132 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8799000000000119 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8699000000000143 y[1] (analytic) -1.5191197410976953 y[1] (numeric) -1.5191197410977533 absolute error 5.795364188543317e-14 relative error 3.814948902155445e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8699000000000143 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8699000000000164 Order of pole (three term test) 2.6572121295281233e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8599000000000154 y[1] (analytic) -1.5727371777797952 y[1] (numeric) -1.5727371777798593 absolute error 6.417089082333405e-14 relative error 4.080204355181769e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8599000000000154 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8599000000000144 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8499000000000165 y[1] (analytic) -1.6289078351112252 y[1] (numeric) -1.6289078351112942 absolute error 6.905587213168474e-14 relative error 4.23939713734445e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8499000000000165 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.849900000000021 Order of pole (three term test) 5.049381287280793e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8399000000000176 y[1] (analytic) -1.687785518417234 y[1] (numeric) -1.6877855184173105 absolute error 7.66053886991358e-14 relative error 4.538810640523481e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8399000000000176 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8399000000000212 Order of pole (three term test) 3.457404802224031e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8299000000000187 y[1] (analytic) -1.7495352865593767 y[1] (numeric) -1.7495352865594604 absolute error 8.37108160567368e-14 relative error 4.7847457950597775e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8299000000000187 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8299000000000163 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8199000000000198 y[1] (analytic) -1.814334424393878 y[1] (numeric) -1.8143344243939694 absolute error 9.14823772291129e-14 relative error 5.042200379330552e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8199000000000198 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8199000000000229 Order of pole (three term test) 6.395521850874748e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.8099000000000209 y[1] (analytic) -1.8823735124662702 y[1] (numeric) -1.8823735124663692 absolute error 9.903189379656396e-14 relative error 5.261011862986385e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.8099000000000209 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.8099000000000227 Order of pole (three term test) 4.318494678768259e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.799900000000022 y[1] (analytic) -1.9538576050184613 y[1] (numeric) -1.9538576050185685 absolute error 1.0724754417879012e-13 relative error 5.489015366489657e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.799900000000022 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7999000000000263 Order of pole (three term test) 5.803632643242212e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7899000000000231 y[1] (analytic) -2.0290075288041733 y[1] (numeric) -2.0290075288042893 absolute error 1.1590728377086634e-13 relative error 5.7125112709255484e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7899000000000231 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.789900000000024 Order of pole (three term test) 3.8802996087221157e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7799000000000242 y[1] (analytic) -2.1080613168313023 y[1] (numeric) -2.108061316831427 absolute error 1.247890679678676e-13 relative error 5.919612820154692e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7799000000000242 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7799000000000248 Order of pole (three term test) 2.5810895260538283e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7699000000000253 y[1] (analytic) -2.19127579300713 y[1] (numeric) -2.191275793007266 absolute error 1.3633538742396922e-13 relative error 6.221735660068309e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7699000000000253 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7699000000000263 Order of pole (three term test) 0.0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7599000000000264 y[1] (analytic) -2.278928325792075 y[1] (numeric) -2.2789283257922217 absolute error 1.4654943925052066e-13 relative error 6.4306295898790605e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7599000000000264 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.759900000000029 Order of pole (three term test) 4.4959744362535355e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7499000000000275 y[1] (analytic) -2.371318771413961 y[1] (numeric) -2.371318771414118 absolute error 1.567634910770721e-13 relative error 6.61081474860496e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7499000000000275 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7499000000000292 Order of pole (three term test) 2.942557269692317e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7399000000000286 y[1] (analytic) -2.4687716300095763 y[1] (numeric) -2.468771630009744 absolute error 1.6786572132332367e-13 relative error 6.799564580328255e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7399000000000286 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7399000000000326 Order of pole (three term test) 7.659747869432454e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7299000000000297 y[1] (analytic) -2.5716384413050815 y[1] (numeric) -2.571638441305262 absolute error 1.8074430840897548e-13 relative error 7.028371698987728e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7299000000000297 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7299000000000321 Order of pole (three term test) 2.477851307266149e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.7199000000000308 y[1] (analytic) -2.680300450194177 y[1] (numeric) -2.6803004501943684 absolute error 1.91402449445377e-13 relative error 7.141081867576102e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.7199000000000308 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7199000000000325 Order of pole (three term test) 3.1870373580993554e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] -0.709900000000032 y[1] (analytic) -2.7951715769090124 y[1] (numeric) -2.7951715769092145 absolute error 2.020605904817785e-13 relative error 7.228915468052354e-12% Correct digits 14 h 0.0001 Radius of convergence (given) for eq 1 0.709900000000032 Order of pole (given) 4.0 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.7099000000000312 Order of pole (three term test) 4.0739644357295166e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 3.0 / x / x / x / x ; Iterations 3001 Total Elapsed Time 1 Seconds Elapsed Time(since restart) 1 Seconds Time to Timeout 9 Minutes 59.0 Seconds Percent Done 100.06666666665562%