##############ECHO OF PROBLEM################# ##############temp/nonlinear2postode.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(0.2) $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=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.5) # 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=true $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(2.0)/(c(1.0) - c(2.0)*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) 2.0 y[1] (numeric) 2.0 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 14 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.5 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.5000000000000001 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.500000000000002 Order of pole (three term test) 1.0000000000000115 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.010000000000000002 y[1] (closed_form) 2.0408163265306123 y[1] (numeric) 2.0408163265306127 absolute error 4.440892098500626e-16 relative error 2.1760371282653068e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.49 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.48999999999999977 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4900000000000042 Order of pole (three term test) 1.0000000000001021 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.02000000000000001 y[1] (closed_form) 2.0833333333333335 y[1] (numeric) 2.0833333333333335 absolute error 0.0 relative error 0.0% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.48 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4799999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.48000000000000004 Order of pole (three term test) 1.0000000000000255 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.03000000000000002 y[1] (closed_form) 2.127659574468085 y[1] (numeric) 2.1276595744680855 absolute error 4.440892098500626e-16 relative error 2.0872192862952943e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.47 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.46999999999999975 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4700000000000009 Order of pole (three term test) 1.0000000000000906 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.04000000000000003 y[1] (closed_form) 2.173913043478261 y[1] (numeric) 2.173913043478262 absolute error 8.881784197001252e-16 relative error 4.0856207306205754e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.45999999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4599999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.45999999999999863 Order of pole (three term test) 0.9999999999999305 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.05000000000000004 y[1] (closed_form) 2.2222222222222223 y[1] (numeric) 2.2222222222222237 absolute error 1.3322676295501878e-15 relative error 5.995204332975845e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.44999999999999996 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4499999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.45000000000000234 Order of pole (three term test) 1.0000000000000486 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.060000000000000046 y[1] (closed_form) 2.272727272727273 y[1] (numeric) 2.2727272727272743 absolute error 1.3322676295501878e-15 relative error 5.861977570020827e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.43999999999999995 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4399999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.44000000000000344 Order of pole (three term test) 1.0000000000001033 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.07000000000000005 y[1] (closed_form) 2.3255813953488373 y[1] (numeric) 2.325581395348839 absolute error 1.7763568394002505e-15 relative error 7.638334409421077e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.42999999999999994 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4299999999999995 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.43000000000000266 Order of pole (three term test) 1.0000000000001013 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.08000000000000006 y[1] (closed_form) 2.3809523809523814 y[1] (numeric) 2.380952380952383 absolute error 1.7763568394002505e-15 relative error 7.460698725481051e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.41999999999999993 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4199999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.42000000000000004 Order of pole (three term test) 1.0000000000000377 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.09000000000000007 y[1] (closed_form) 2.439024390243903 y[1] (numeric) 2.4390243902439037 absolute error 8.881784197001252e-16 relative error 3.641531520770513e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.4099999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.4099999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.41000000000000364 Order of pole (three term test) 1.0000000000001326 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.10000000000000007 y[1] (closed_form) 2.5000000000000004 y[1] (numeric) 2.5000000000000018 absolute error 1.3322676295501878e-15 relative error 5.329070518200751e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.3999999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3999999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.4000000000000045 Order of pole (three term test) 1.0000000000001397 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.11000000000000008 y[1] (closed_form) 2.5641025641025648 y[1] (numeric) 2.5641025641025657 absolute error 8.881784197001252e-16 relative error 3.463895836830488e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.3899999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.38999999999999974 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.39000000000000107 Order of pole (three term test) 1.0000000000000409 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.12000000000000009 y[1] (closed_form) 2.6315789473684217 y[1] (numeric) 2.6315789473684226 absolute error 8.881784197001252e-16 relative error 3.375077994860475e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.3799999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.37999999999999984 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.38000000000000217 Order of pole (three term test) 1.000000000000107 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1300000000000001 y[1] (closed_form) 2.7027027027027035 y[1] (numeric) 2.7027027027027044 absolute error 8.881784197001252e-16 relative error 3.286260152890462e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.3699999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.36999999999999966 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.37000000000000255 Order of pole (three term test) 1.000000000000119 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1400000000000001 y[1] (closed_form) 2.7777777777777786 y[1] (numeric) 2.7777777777777803 absolute error 1.7763568394002505e-15 relative error 6.3948846218409e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.3599999999999999 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3599999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.3599999999999998 Order of pole (three term test) 1.0000000000000058 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.1500000000000001 y[1] (closed_form) 2.857142857142858 y[1] (numeric) 2.85714285714286 absolute error 1.7763568394002505e-15 relative error 6.217248937900874e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.34999999999999987 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3499999999999996 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.34999999999999976 Order of pole (three term test) 0.9999999999999937 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.16000000000000011 y[1] (closed_form) 2.9411764705882364 y[1] (numeric) 2.941176470588238 absolute error 1.7763568394002505e-15 relative error 6.039613253960849e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.33999999999999986 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3399999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.3400000000000026 Order of pole (three term test) 1.0000000000001248 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.17000000000000012 y[1] (closed_form) 3.0303030303030316 y[1] (numeric) 3.0303030303030334 absolute error 1.7763568394002505e-15 relative error 5.861977570020824e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.32999999999999985 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3299999999999998 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.3299999999999983 Order of pole (three term test) 0.9999999999999291 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.18000000000000013 y[1] (closed_form) 3.1250000000000018 y[1] (numeric) 3.125000000000003 absolute error 1.3322676295501878e-15 relative error 4.2632564145605986e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.31999999999999984 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.3199999999999997 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.32000000000000034 Order of pole (three term test) 1.0000000000000366 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.19000000000000014 y[1] (closed_form) 3.225806451612905 y[1] (numeric) 3.225806451612906 absolute error 1.3322676295501878e-15 relative error 4.1300296516055804e-14% Desired digits 8 Estimated correct digits 13 Correct digits 16 h 0.001 Radius of convergence (given) for eq 1 0.30999999999999983 Order of pole (given) 0.0 Radius of convergence (ratio test) for eq 1 0.30999999999999966 Order of pole (ratio test) 1.0 Radius of convergence (three term test) for eq 1 0.3099999999999989 Order of pole (three term test) 0.9999999999999407 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y * y ; Iterations 200 Total Elapsed Time 0 Seconds Elapsed Time(since restart) 0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 100.50000000000007%