Initializing... Initialized Initializing(2)... PI = 0.314159265358979323846264338327950271e1+/-0.313e-33 E = 0.271828182845904523536028747135266232e1+/-0.256e-32 LOG_E_10 = 0.230258509299404568401799145468436324e1+/-0.5e-32 Initialized(2) ##############ECHO OF PROBLEM################# ##############temp/arctan_tan_m0d5_0d5postode.ode################# diff ( y , x , 1 ) = arctan ( tan ( x ) ) ; ! #BEGIN FIRST INPUT BLOCK max_terms=30 # Digits:=32; ELIMINATED in preodein.rb ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-0.5) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_display_interval=0.001 # 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=0 #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(x)*c(x)/c(2.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -0.5e0+/-0.50e-32 y[1] (closed_form) 0.125e0+/-0.253e-32 y[1] (numeric) 0.125e0+/-0.265e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.518e-32 relative error 0.0e0+/-0.414400000000000000000000000000016774e-29% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.49e0+/-0.100e-31 y[1] (closed_form) 0.12005e0+/-0.493e-32 y[1] (numeric) 0.120049998199234532193478784327127378e0+/-0.707e-32 absolute error 0.1800765467806521215672872622e-8+/-0.12e-31 relative error 0.150001288447023841372167648646397334e-5+/-0.999e-29% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.48e0+/-0.150e-31 y[1] (closed_form) 0.1152e0+/-0.722e-32 y[1] (numeric) 0.115199996441310012913072466049316414e0+/-0.104e-31 absolute error 0.3558689987086927533950683586e-8+/-0.176e-31 relative error 0.308914061379073570655441283506944444e-5+/-0.152e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.47e0+/-0.200e-31 y[1] (closed_form) 0.11045e0+/-0.942e-32 y[1] (numeric) 0.110449994725776709554489705213702041e0+/-0.124e-31 absolute error 0.5274223290445510294786297959e-8+/-0.218e-31 relative error 0.477521348161657790383548932458125848e-5+/-0.197e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.46e0+/-0.250e-31 y[1] (closed_form) 0.1058e0+/-0.115e-31 y[1] (numeric) 0.105799993052200281907697781941511607e0+/-0.144e-31 absolute error 0.6947799718092302218058488393e-8+/-0.259e-31 relative error 0.656691844810236504542390207277882797e-5+/-0.244e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.45e0+/-0.300e-31 y[1] (closed_form) 0.10125e0+/-0.135e-31 y[1] (numeric) 0.101249991420161296305530871451171055e0+/-0.164e-31 absolute error 0.8579838703694469128548828945e-8+/-0.299e-31 relative error 0.84739147690809571639988434024691358e-5+/-0.295e-28% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.44e0+/-0.350e-31 y[1] (closed_form) 0.968e-1+/-0.154e-31 y[1] (numeric) 0.967999898292547628967011861176876764e-1+/-0.184e-31 absolute error 0.101707452371032988138823123236e-7+/-0.338e-31 relative error 0.105069682201480359647544548797520661e-4+/-0.349e-28% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.43e0+/-0.400e-31 y[1] (closed_form) 0.9245e-1+/-0.172e-31 y[1] (numeric) 0.924499882790896948672277806785102327e-1+/-0.204e-31 absolute error 0.117209103051327722193214897673e-7+/-0.376e-31 relative error 0.126781074149624361485359543183342347e-4+/-0.406e-28% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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] -0.42e0+/-0.450e-31 y[1] (closed_form) 0.882e-1+/-0.189e-31 y[1] (numeric) 0.881999867692886885077654823065085959e-1+/-0.224e-31 absolute error 0.132307113114922345176934914041e-7+/-0.413e-31 relative error 0.150008064756147783647318496645124716e-4+/-0.468e-28% Desired digits 8 Estimated correct digits 13 Correct digits 5 h 0.1e-2+/-0.5e-33 NO INFO (given) for Equation 1 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 Finished! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = arctan ( tan ( x ) ) ; Iterations 86 Total Elapsed Time 3 Minutes 2 Seconds Elapsed Time(since restart) 3 Minutes 2 Seconds Expected Time Remaining 31 Minutes 49 Seconds Optimized Time Remaining 31 Minutes 49 Seconds Expected Total Time 34 Minutes 51 Seconds Time to Timeout 0.0 Seconds Percent Done 0.87e1+/-0.539e-29%