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/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(0.5) $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) # 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=3 #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_y1 (x) x = c(x) return(c(1.0) + cos(c(x))) end def exact_soln_y2 (x) x = c(x) return(c(1.0) - sin(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 y2[1] (closed_form) 0.900166583353171847693185801589378e0+/-0.106e-30 y2[1] (numeric) 0.900166583353171847693185801589378e0+/-0.196e-30 absolute error 0.0e0+/-0.302e-30 relative error 0.0e0+/-0.3354934581941853261182246997145766e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 y1[1] (closed_form) 0.1995004165278025766095561987803869e1+/-0.606e-31 y1[1] (numeric) 0.1995004165278025766095561987803869e1+/-0.16e-30 absolute error 0.0e0+/-0.2206e-30 relative error 0.0e0+/-0.110576210235258814328038380553607637112e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.2e0+/-0.5e-31 y2[1] (closed_form) 0.8013306692049387845405873728816113e0+/-0.112e-30 y2[1] (numeric) 0.8013306692049387845364757906449852e0+/-0.589e-30 absolute error 0.41115822366261e-20+/-0.701e-30 relative error 0.5130943310463224906729495269434834e-18+/-0.874e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 y1[1] (closed_form) 0.1980066577841241631124196516748168e1+/-0.682e-31 y1[1] (numeric) 0.198006657784124163112352244320057e1+/-0.691e-30 absolute error 0.674073547598e-21+/-0.759e-30 relative error 0.3404297386469224420313413754458896e-19+/-0.383e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.3e0+/-0.5e-31 y2[1] (closed_form) 0.7044797933386604248946792543149737e0+/-0.117e-30 y2[1] (numeric) 0.7044797933386604248866317615429778e0+/-0.1e-29 absolute error 0.80474927719959e-20+/-0.111e-29 relative error 0.114233124187385686484343634818268e-17+/-0.157e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 y1[1] (closed_form) 0.1955336489125606019642310227568049e1+/-0.778e-31 y1[1] (numeric) 0.1955336489125606019640147868987908e1+/-0.124e-29 absolute error 0.2162358580141e-20+/-0.131e-29 relative error 0.1105875429710806869238451637649381e-18+/-0.669e-28% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.4e0+/-0.5e-31 y2[1] (closed_form) 0.6105816576913495083336882432042957e0+/-0.121e-30 y2[1] (numeric) 0.610581657691349508322001123429632e0+/-0.125e-29 absolute error 0.116871197746637e-19+/-0.137e-29 relative error 0.1914096112689249348984068049923578e-17+/-0.224e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 y1[1] (closed_form) 0.19210609940028850827985267320518e1+/-0.89e-31 y1[1] (numeric) 0.19210609940028850827940942853124e1+/-0.207e-29 absolute error 0.44324467394e-20+/-0.215e-29 relative error 0.2307290998691394633786666688579692e-18+/-0.111e-27% Desired digits 8 Estimated correct digits 13 Correct digits 32 h 0.5e-1+/-0.1e-100 NO POLE (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 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 1 ) = m1 * y1 + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations 8 Total Elapsed Time 1 Minutes 17 Seconds Elapsed Time(since restart) 1 Minutes 17 Seconds Time to Timeout 18 Minutes 43 Seconds Percent Done 0.1125e3+/-0.586e-28%