Initializing... Initialized Initializing(2)... PI = 0.3141592653589793238462643383279486e1+/-0.313e-31 E = 0.2718281828459045235360287471352649e1+/-0.256e-30 LOG_E_10 = 0.2302585092994045684017991454684277e1+/-0.5e-30 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/tanpostode.ode################# diff ( y , x , 1 ) = tan ( x ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(1.5) $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(1.570796327) # 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 #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(20.0) $glob_subiter_method=3 $glob_max_iter=1000 $glob_upper_ratio_limit=c(1.11) $glob_lower_ratio_limit=c(0.99) # ELIMINATED in preodein.rb # ELIMINATED in preodein.rb #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return($glob__m1 * ln(cos(c(x)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1e0+/-0.50e-31 y[1] (closed_form) 0.500835562323530907913299772126732e-2+/-0.106e-30 y[1] (numeric) 0.500835562323530907913299772126732e-2+/-0.106e-30 absolute error 0.0e0+/-0.212e-30 relative error 0.0e0+/-0.4232926252610068304940021216230055e-26% Desired digits 8 Estimated correct digits 14 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1470796327000000000000000000000949e1+/-0.102e-28 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.2e0+/-0.5e-31 y[1] (closed_form) 0.201347730524083489257559281056834e-1+/-0.186e-30 y[1] (numeric) 0.2013477305240834892468951168424442e-1+/-0.114e-30 absolute error 0.106641642143898e-20+/-0.300e-30 relative error 0.5296391564301363757647720343988445e-17+/-0.148e-26% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1370796327000000000000000000001071e1+/-0.102e-28 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.3e0+/-0.5e-31 y[1] (closed_form) 0.45691655926058019453301984654094e-1+/-0.292e-30 y[1] (numeric) 0.4569165592605801945022290143952605e-1+/-0.128e-30 absolute error 0.307908321456795e-20+/-0.420e-30 relative error 0.6738830432302069960711781470246706e-17+/-0.919e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1270796327000000000000000000001191e1+/-0.102e-28 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.4e0+/-0.5e-31 y[1] (closed_form) 0.822290190750554293994091739943397e-1+/-0.427e-30 y[1] (numeric) 0.8222901907505542939319418060692192e-1+/-0.148e-30 absolute error 0.621499338741778e-20+/-0.575e-30 relative error 0.7558150951241407062013269087365632e-17+/-0.699e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.117079632700000000000000000000128e1+/-0.102e-28 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.5e0+/-0.5e-31 y[1] (closed_form) 0.130584240443722716787612591825988e0+/-0.607e-30 y[1] (numeric) 0.1305842404437227167768385751463548e0+/-0.197e-30 absolute error 0.107740166796332e-19+/-0.804e-30 relative error 0.8250625529561071265766271738162062e-17+/-0.615e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1070796327000000000000000000001493e1+/-0.102e-28 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.6e0+/-0.5e-31 y[1] (closed_form) 0.191965169419437719670525662506479e0+/-0.837e-30 y[1] (numeric) 0.1919651694194377196532809957826208e0+/-0.255e-30 absolute error 0.172446667238582e-19+/-0.109e-29 relative error 0.8983226892676117701607562056242239e-17+/-0.567e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.9707963270000000000000000000000057e0+/-0.994e-30 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.7e0+/-0.5e-31 y[1] (closed_form) 0.268085757567931100529413292614205e0+/-0.115e-29 y[1] (numeric) 0.2680857575679311005029854907572035e0+/-0.371e-30 absolute error 0.264278018570015e-19+/-0.152e-29 relative error 0.9857965636352343504639358814624877e-17+/-0.566e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.87079632700000000000000000000002e0+/-0.99e-30 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.8e0+/-0.5e-31 y[1] (closed_form) 0.361390746811343700739551877017128e0+/-0.156e-29 y[1] (numeric) 0.3613907468113437006998736547467181e0+/-0.529e-30 absolute error 0.396782222704099e-19+/-0.208e-29 relative error 0.1097931328361405615210094660888409e-16+/-0.575e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.7707963270000000000000000000000219e0+/-0.996e-30 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.9e0+/-0.5e-31 y[1] (closed_form) 0.475442443585814285009717936105181e0+/-0.214e-29 y[1] (numeric) 0.47544244358581428495031087704593e0+/-0.739e-30 absolute error 0.59407059059251e-19+/-0.287e-29 relative error 0.1249511057767572032020190139511782e-16+/-0.603e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.6707963270000000000000000000000239e0+/-0.993e-30 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.1e1+/-0.5e-31 y[1] (closed_form) 0.615626470386014262147037516408842e0+/-0.3e-29 y[1] (numeric) 0.6156264703860142620568181963714099e0+/-0.985e-30 absolute error 0.902193200374321e-19+/-0.398e-29 relative error 0.1465487992757396760068504575248264e-16+/-0.646e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.570796327000000000000000000000255e0+/-0.1e-29 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.11e1+/-0.5e-31 y[1] (closed_form) 0.790548077254231578323607612842124e0+/-0.43e-29 y[1] (numeric) 0.7905480772542315781818107350501681e0+/-0.118e-29 absolute error 0.1417968777919559e-18+/-0.548e-29 relative error 0.1793652807106323295610002617973171e-16+/-0.693e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.4707963270000000000000000000003343e0+/-0.999e-30 Order of pole (given) 0.0e0+/-0.50e-31 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] 0.12e1+/-0.5e-31 y[1] (closed_form) 0.101512328314065961666425318875818e1+/-0.645e-29 y[1] (numeric) 0.1015123283140659616426838720235525e1+/-0.148e-29 absolute error 0.237414468522655e-18+/-0.793e-29 relative error 0.2338774732741086032826810492129447e-16+/-0.781e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.3707963270000000000000000000004337e0+/-0.998e-30 Order of pole (given) 0.0e0+/-0.50e-31 Radius of convergence (ratio test) for eq 1 0.3817021011123935984689874698274566e0+/-0.177e-28 Order of pole (ratio test) 0.9999999999999999999999999999999032e0+/-0.5e-31 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.13e1+/-0.5e-31 y[1] (closed_form) 0.131864009162916856660279594824668e1+/-0.102e-28 y[1] (numeric) 0.1318640091629168566157480847586493e1+/-0.187e-29 absolute error 0.445315100660187e-18+/-0.12e-28 relative error 0.3377078427139311363991840586393108e-16+/-0.91e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2707963270000000000000000000000202e0+/-0.365e-30 Order of pole (given) 0.0e0+/-0.50e-31 Radius of convergence (ratio test) for eq 1 0.2787609246418053578219286462971959e0+/-0.291e-28 Order of pole (ratio test) 0.9999999999999999999999999923139154e0+/-0.5e-31 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 0.14e1+/-0.5e-31 y[1] (closed_form) 0.177215013766969902721411068686746e1+/-0.19e-28 y[1] (numeric) 0.177215013766969902617056345969422e1+/-0.299e-29 absolute error 0.104354722717324e-17+/-0.219e-28 relative error 0.5888593776515231269148773770175187e-16+/-0.123e-26% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1707963270000000000000000000000932e0+/-0.309e-30 Order of pole (given) 0.0e0+/-0.50e-31 Radius of convergence (ratio test) for eq 1 0.1758197481712171171748698227677438e0+/-0.203e-28 Order of pole (ratio test) 0.9999999999999999998940135846185299e0+/-0.5e-31 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 SETTING H FOR POLE Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations 32 Total Elapsed Time 1 Minutes 2 Seconds Elapsed Time(since restart) 1 Minutes 2 Seconds Time to Timeout 18 Minutes 58 Seconds Percent Done 0.1016055568626384369649338795669505e3+/-0.707e-25%