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/sing2postode.ode################# diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=20 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-2.0) x_end=c(-1.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.001) $glob_min_h=c(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 # ELIMINATED in preodein.rb $glob_type_given_pole=2 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(1.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][2]=c(0.0) #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK $glob_desired_digits_correct=8 $glob_max_minutes=(5.0) $glob_subiter_method=3 $glob_max_iter=1000 $glob_upper_ratio_limit=c(1.1) $glob_lower_ratio_limit=c(0.9) # ELIMINATED in preodein.rb #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK def exact_soln_y (x) x = c(x) return(arctan(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0e0+/-0.50e-31 min_size 0.1e1+/-0.50e-31 $glob_desired_digits_correct 8 estimated_h 0.1e-2+/-0.5e-31 estimated_answer 0.1e1+/-0.50e-31 desired_abs_gbl_error 0.9999999999999999999999999999751083e-8+/-0.815e-35 range 0.5e0+/-0.100e-29 estimated_steps 0.5e3+/-0.26e-25 step_error 0.2236067977499789696409173668675892e-10+/-0.116e-34 est_needed_step_err 0.2236067977499789696409173668675892e-10+/-0.116e-34 opt_iter 1 SETTING H FOR MIN H SETTING H FOR DISPLAY INTERVAL START of Soultion TOP MAIN SOLVE Loop x[1] -0.2e1+/-0.50e-30 y[1] (closed_form) -0.110714871779409050301706546017855e1+/-0.155e-30 y[1] (numeric) -0.110714871779409050301706546017855e1+/-0.265e-30 absolute error 0.0e0+/-0.420e-30 relative error 0.0e0+/-0.3793528306087171484487898049737062e-28% Desired digits 8 Estimated correct digits 26 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.223606797749978969640917366873123e1+/-0.474e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2236067977499758929478286194599976e1+/-0.118e-18 Order of pole (six term test) -0.78150454903318718062e-13+/-0.143e-23 TOP MAIN SOLVE Loop x[1] -0.195e1+/-0.5e-30 y[1] (closed_form) -0.109694499030013626798639002132514e1+/-0.16e-30 y[1] (numeric) -0.109694499030013626798675668828305e1+/-0.489e-30 absolute error 0.36666695791e-21+/-0.649e-30 relative error 0.3342619376106324798617706692998352e-19+/-0.591e-28% Desired digits 8 Estimated correct digits 25 Correct digits 22 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2191460700081112565694977042409691e1+/-0.471e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2191460700081085635622508883947098e1+/-0.9e-19 Order of pole (six term test) -0.66735457233492523343e-13+/-0.111e-23 TOP MAIN SOLVE Loop x[1] -0.19e1+/-0.5e-30 y[1] (closed_form) -0.108631839775787341806397958192569e1+/-0.164e-30 y[1] (numeric) -0.108631839775787341806473775031978e1+/-0.711e-30 absolute error 0.75816839409e-21+/-0.875e-30 relative error 0.6979246560261111507129929580425298e-19+/-0.805e-28% Desired digits 8 Estimated correct digits 25 Correct digits 22 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2147091055358388846920969878103863e1+/-0.47e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2147091055358365995021902260717601e1+/-0.785e-19 Order of pole (six term test) -0.54521688654523582181e-13+/-0.956e-24 TOP MAIN SOLVE Loop x[1] -0.185e1+/-0.5e-30 y[1] (closed_form) -0.107524465330906808242086208732186e1+/-0.168e-30 y[1] (numeric) -0.107524465330906808242203831680734e1+/-0.932e-30 absolute error 0.117622948548e-20+/-0.11e-29 relative error 0.1093918004484050068583283279051911e-18+/-0.102e-27% Desired digits 8 Estimated correct digits 25 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2102974084481309056343164520015523e1+/-0.466e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2102974084481290394463480812402391e1+/-0.62e-19 Order of pole (six term test) -0.41871601243536963978e-13+/-0.72e-24 TOP MAIN SOLVE Loop x[1] -0.18e1+/-0.5e-30 y[1] (closed_form) -0.106369782240255966094389111605256e1+/-0.173e-30 y[1] (numeric) -0.106369782240255966094551377003183e1+/-0.113e-29 absolute error 0.162265397927e-20+/-0.13e-29 relative error 0.1525483972134993888707987424158553e-18+/-0.122e-27% Desired digits 8 Estimated correct digits 25 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2059126028197400063159473892839475e1+/-0.465e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2059126028197385576780407710089293e1+/-0.489e-19 Order of pole (six term test) -0.29154527104168288196e-13+/-0.109e-23 TOP MAIN SOLVE Loop x[1] -0.175e1+/-0.5e-30 y[1] (closed_form) -0.105165021254837366745986731208632e1+/-0.179e-30 y[1] (numeric) -0.105165021254837366746196662505031e1+/-0.133e-29 absolute error 0.209931296399e-20+/-0.15e-29 relative error 0.1996208377025774698627899287002245e-18+/-0.142e-27% Desired digits 8 Estimated correct digits 24 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2015564437074637413091653307575905e1+/-0.463e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.2015564437074626965728588882967662e1+/-0.352e-19 Order of pole (six term test) -0.16745960179799389279e-13+/-0.417e-23 TOP MAIN SOLVE Loop x[1] -0.17e1+/-0.5e-30 y[1] (closed_form) -0.10390722595360910276212503379073e1+/-0.184e-30 y[1] (numeric) -0.103907225953609102762385846594405e1+/-0.153e-29 absolute error 0.260812803675e-20+/-0.171e-29 relative error 0.2510054534527210667453617820143011e-18+/-0.164e-27% Desired digits 8 Estimated correct digits 24 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1972308292331601996806399908324762e1+/-0.459e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1972308292331595335970262325892324e1+/-0.279e-19 Order of pole (six term test) -0.5025486998377683152e-14+/-0.469e-23 TOP MAIN SOLVE Loop x[1] -0.165e1+/-0.5e-30 y[1] (closed_form) -0.102593241134335292660599590143871e1+/-0.19e-30 y[1] (numeric) -0.102593241134335292660914694871005e1+/-0.173e-29 absolute error 0.315104727134e-20+/-0.192e-29 relative error 0.307139850198711222465653568233417e-18+/-0.187e-27% Desired digits 8 Estimated correct digits 24 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.192937813815747378494842310871409e1+/-0.457e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1929378138157470550033849352496543e1+/-0.158e-19 Order of pole (six term test) 0.5627382224852441733e-14+/-0.118e-23 TOP MAIN SOLVE Loop x[1] -0.16e1+/-0.5e-30 y[1] (closed_form) -0.101219701145133418325981347523811e1+/-0.196e-30 y[1] (numeric) -0.101219701145133418326354348725801e1+/-0.193e-29 absolute error 0.37300120199e-20+/-0.212e-29 relative error 0.3685065237005332444117509164414363e-18+/-0.209e-27% Desired digits 8 Estimated correct digits 24 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1886796226411320762264132075525196e1+/-0.454e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1886796226411320494867041180421482e1+/-0.156e-19 Order of pole (six term test) 0.14840518242103001595e-13+/-0.881e-24 TOP MAIN SOLVE Loop x[1] -0.155e1+/-0.5e-30 y[1] (closed_form) -0.997830183906190454944961879442731e0+/-0.202e-30 y[1] (numeric) -0.997830183906190454949308791584282e0+/-0.211e-29 absolute error 0.4346912141551e-20+/-0.231e-29 relative error 0.4356364651682724187934773842561365e-18+/-0.231e-27% Desired digits 8 Estimated correct digits 24 Correct digits 21 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.184458667456967171922534287275171e1+/-0.45e-28 Order of pole (given) 0.1e1+/-0.50e-31 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 0.1844586674569673876577702536787811e1+/-0.125e-19 Order of pole (six term test) 0.22260970197710740712e-13+/-0.582e-24 Finished! diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; Iterations 10 Total Elapsed Time 53 Seconds Elapsed Time(since restart) 50 Seconds Time to Timeout 4 Minutes 7 Seconds Percent Done 0.11e3+/-0.424e-27%