##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb x_start=c(0.0) x_end=c(0.5) $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=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(1.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(3.0) $glob_subiter_method=3 $glob_max_iter=100000 $glob_upper_ratio_limit=c(1.000001) $glob_lower_ratio_limit=c(0.999999) $glob_look_poles=false $glob_h=c(0.001) $glob_display_interval=c(0.01) #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(c(1.0)/(c(1.0) - c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.0 y[1] (closed_form) 1.0 y[1] (numeric) 1.0 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.010000000000000002 y[1] (closed_form) 1.0101010101010102 y[1] (numeric) 1.0101010101010106 absolute error 4.440892098500626e-16 relative error 4.39648317751562e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.02000000000000001 y[1] (closed_form) 1.0204081632653061 y[1] (numeric) 1.0204081632653066 absolute error 4.440892098500626e-16 relative error 4.3520742565306136e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.03000000000000002 y[1] (closed_form) 1.0309278350515465 y[1] (numeric) 1.0309278350515472 absolute error 6.661338147750939e-16 relative error 6.46149800331841e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.04000000000000003 y[1] (closed_form) 1.0416666666666667 y[1] (numeric) 1.0416666666666676 absolute error 8.881784197001252e-16 relative error 8.526512829121202e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.05000000000000004 y[1] (closed_form) 1.0526315789473684 y[1] (numeric) 1.0526315789473697 absolute error 1.3322676295501878e-15 relative error 1.2656542480726785e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.060000000000000046 y[1] (closed_form) 1.0638297872340425 y[1] (numeric) 1.0638297872340436 absolute error 1.1102230246251565e-15 relative error 1.0436096431476471e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.07000000000000005 y[1] (closed_form) 1.0752688172043012 y[1] (numeric) 1.075268817204302 absolute error 6.661338147750939e-16 relative error 6.195044477408372e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.08000000000000006 y[1] (closed_form) 1.0869565217391306 y[1] (numeric) 1.086956521739131 absolute error 4.440892098500626e-16 relative error 4.0856207306205754e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.09000000000000007 y[1] (closed_form) 1.098901098901099 y[1] (numeric) 1.0989010989010994 absolute error 4.440892098500626e-16 relative error 4.041211809635569e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.10000000000000007 y[1] (closed_form) 1.1111111111111112 y[1] (numeric) 1.1111111111111116 absolute error 4.440892098500626e-16 relative error 3.9968028886505635e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.11000000000000008 y[1] (closed_form) 1.1235955056179776 y[1] (numeric) 1.1235955056179783 absolute error 6.661338147750939e-16 relative error 5.928590951498336e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.12000000000000009 y[1] (closed_form) 1.1363636363636365 y[1] (numeric) 1.136363636363637 absolute error 4.440892098500626e-16 relative error 3.9079850466805504e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1300000000000001 y[1] (closed_form) 1.149425287356322 y[1] (numeric) 1.1494252873563229 absolute error 8.881784197001252e-16 relative error 7.727152251391088e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1400000000000001 y[1] (closed_form) 1.1627906976744187 y[1] (numeric) 1.1627906976744196 absolute error 8.881784197001252e-16 relative error 7.638334409421077e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.1500000000000001 y[1] (closed_form) 1.1764705882352944 y[1] (numeric) 1.1764705882352953 absolute error 8.881784197001252e-16 relative error 7.549516567451063e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.16000000000000011 y[1] (closed_form) 1.1904761904761907 y[1] (numeric) 1.1904761904761911 absolute error 4.440892098500626e-16 relative error 3.7303493627405253e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.17000000000000012 y[1] (closed_form) 1.204819277108434 y[1] (numeric) 1.2048192771084343 absolute error 2.220446049250313e-16 relative error 1.8429702208777592e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.18000000000000013 y[1] (closed_form) 1.2195121951219514 y[1] (numeric) 1.2195121951219519 absolute error 4.440892098500626e-16 relative error 3.641531520770513e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.19000000000000014 y[1] (closed_form) 1.234567901234568 y[1] (numeric) 1.2345679012345685 absolute error 4.440892098500626e-16 relative error 3.5971225997855066e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.20000000000000015 y[1] (closed_form) 1.2500000000000002 y[1] (numeric) 1.2500000000000004 absolute error 2.220446049250313e-16 relative error 1.77635683940025e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.21000000000000016 y[1] (closed_form) 1.2658227848101269 y[1] (numeric) 1.2658227848101269 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.22000000000000017 y[1] (closed_form) 1.2820512820512824 y[1] (numeric) 1.2820512820512822 absolute error 2.220446049250313e-16 relative error 1.731947918415244e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.23000000000000018 y[1] (closed_form) 1.2987012987012991 y[1] (numeric) 1.2987012987012987 absolute error 4.440892098500626e-16 relative error 3.419486915845481e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.24000000000000019 y[1] (closed_form) 1.3157894736842108 y[1] (numeric) 1.3157894736842104 absolute error 4.440892098500626e-16 relative error 3.375077994860475e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.25000000000000017 y[1] (closed_form) 1.3333333333333337 y[1] (numeric) 1.333333333333333 absolute error 6.661338147750939e-16 relative error 4.996003610813203e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2600000000000002 y[1] (closed_form) 1.3513513513513518 y[1] (numeric) 1.3513513513513513 absolute error 4.440892098500626e-16 relative error 3.286260152890462e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2700000000000002 y[1] (closed_form) 1.3698630136986305 y[1] (numeric) 1.3698630136986298 absolute error 6.661338147750939e-16 relative error 4.8627768478581844e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2800000000000002 y[1] (closed_form) 1.3888888888888893 y[1] (numeric) 1.3888888888888882 absolute error 1.1102230246251565e-15 relative error 7.993605777301125e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.2900000000000002 y[1] (closed_form) 1.4084507042253527 y[1] (numeric) 1.4084507042253511 absolute error 1.5543122344752192e-15 relative error 1.1035616864774051e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3000000000000002 y[1] (closed_form) 1.428571428571429 y[1] (numeric) 1.4285714285714273 absolute error 1.7763568394002505e-15 relative error 1.2434497875801748e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3100000000000002 y[1] (closed_form) 1.4492753623188412 y[1] (numeric) 1.4492753623188397 absolute error 1.5543122344752192e-15 relative error 1.0724754417879007e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.32000000000000023 y[1] (closed_form) 1.4705882352941182 y[1] (numeric) 1.4705882352941169 absolute error 1.3322676295501878e-15 relative error 9.059419880941274e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.33000000000000024 y[1] (closed_form) 1.4925373134328366 y[1] (numeric) 1.4925373134328348 absolute error 1.7763568394002505e-15 relative error 1.1901590823981673e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.34000000000000025 y[1] (closed_form) 1.5151515151515158 y[1] (numeric) 1.5151515151515145 absolute error 1.3322676295501878e-15 relative error 8.792966355031236e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.35000000000000026 y[1] (closed_form) 1.5384615384615392 y[1] (numeric) 1.5384615384615379 absolute error 1.3322676295501878e-15 relative error 8.659739592076217e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.36000000000000026 y[1] (closed_form) 1.5625000000000009 y[1] (numeric) 1.5624999999999991 absolute error 1.7763568394002505e-15 relative error 1.1368683772161597e-13% Desired digits 8 Estimated correct digits 13 Correct digits 15 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3700000000000003 y[1] (closed_form) 1.587301587301588 y[1] (numeric) 1.5873015873015868 absolute error 1.3322676295501878e-15 relative error 8.39328606616618e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3800000000000003 y[1] (closed_form) 1.6129032258064524 y[1] (numeric) 1.612903225806451 absolute error 1.3322676295501878e-15 relative error 8.260059303211161e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.3900000000000003 y[1] (closed_form) 1.639344262295083 y[1] (numeric) 1.6393442622950818 absolute error 1.1102230246251565e-15 relative error 6.772360450213451e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4000000000000003 y[1] (closed_form) 1.6666666666666676 y[1] (numeric) 1.6666666666666663 absolute error 1.3322676295501878e-15 relative error 7.993605777301122e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4100000000000003 y[1] (closed_form) 1.6949152542372892 y[1] (numeric) 1.6949152542372878 absolute error 1.3322676295501878e-15 relative error 7.860379014346103e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4200000000000003 y[1] (closed_form) 1.7241379310344838 y[1] (numeric) 1.7241379310344827 absolute error 1.1102230246251565e-15 relative error 6.439293542825904e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4300000000000003 y[1] (closed_form) 1.754385964912282 y[1] (numeric) 1.7543859649122808 absolute error 1.1102230246251565e-15 relative error 6.328271240363387e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.44000000000000034 y[1] (closed_form) 1.785714285714287 y[1] (numeric) 1.7857142857142856 absolute error 1.3322676295501878e-15 relative error 7.460698725481047e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.45000000000000034 y[1] (closed_form) 1.8181818181818195 y[1] (numeric) 1.8181818181818183 absolute error 1.1102230246251565e-15 relative error 6.106226635438357e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.46000000000000035 y[1] (closed_form) 1.8518518518518532 y[1] (numeric) 1.8518518518518519 absolute error 1.3322676295501878e-15 relative error 7.194245199571009e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.47000000000000036 y[1] (closed_form) 1.8867924528301903 y[1] (numeric) 1.8867924528301885 absolute error 1.7763568394002505e-15 relative error 9.41469124882132e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.48000000000000037 y[1] (closed_form) 1.9230769230769247 y[1] (numeric) 1.9230769230769234 absolute error 1.3322676295501878e-15 relative error 6.92779167366097e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 TOP MAIN SOLVE Loop x[1] 0.4900000000000004 y[1] (closed_form) 1.960784313725492 y[1] (numeric) 1.9607843137254901 absolute error 1.7763568394002505e-15 relative error 9.05941988094127e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Finished! diff ( y , x , 1 ) = y * y ; Iterations 500 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.20000000000007%