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/sqrt_tonepostode.ode################# diff ( y , x , 1 ) = sqrt ( 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(0.5) x_end=c(0.6) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.01) $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 $glob_type_given_pole=1 # ELIMINATED in preodein.rb $array_given_rad_poles[1][1]=c(0.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(1.5) # 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=(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=false $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)*expt(c(x),c(1.5))/c(3.0)) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.5e0+/-0.50e-33 y[1] (closed_form) 0.235702260395515841466948120701616602e0+/-0.743e-32 y[1] (numeric) 0.235702260395515841466948120701616602e0+/-0.765e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.1508e-31 relative error 0.0e0+/-0.639790215617588200077883978832507053e-29% Desired digits 8 Estimated correct digits 14 Correct digits 34 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.51e0+/-0.550e-32 y[1] (closed_form) 0.24280856657045689993197959358648728e0+/-0.773e-31 y[1] (numeric) 0.242808566570456899931979709871407214e0+/-0.131e-31 absolute error 0.116284919934e-24+/-0.904e-31 relative error 0.478916051342270330049326567038579155e-22+/-0.372e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.52e0+/-0.105e-31 y[1] (closed_form) 0.249984888432169924322932674544621244e0+/-0.746e-31 y[1] (numeric) 0.249984888432169924322932903740493277e0+/-0.179e-31 absolute error 0.229195872033e-24+/-0.925e-31 relative error 0.916838907625367332905438422742358602e-22+/-0.37e-28% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.53e0+/-0.155e-31 y[1] (closed_form) 0.257230549421244978912104688033955384e0+/-0.112e-30 y[1] (numeric) 0.257230549421244978912105026926875353e0+/-0.229e-31 absolute error 0.338892919969e-24+/-0.134e-30 relative error 0.131746762090074837812628357729059426e-21+/-0.52e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.54e0+/-0.205e-31 y[1] (closed_form) 0.26454489222058323460530668006823647e0+/-0.15e-30 y[1] (numeric) 0.26454489222058323460530712559393106e0+/-0.28e-31 absolute error 0.44552569459e-24+/-0.178e-30 relative error 0.168412132568604299686268551579457853e-21+/-0.672e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.55e0+/-0.255e-31 y[1] (closed_form) 0.271927277860174308119417906162693016e0+/-0.188e-30 y[1] (numeric) 0.271927277860174308119418455396944728e0+/-0.34e-31 absolute error 0.549234251712e-24+/-0.222e-30 relative error 0.201978358344181136915507494613752482e-21+/-0.816e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.56e0+/-0.305e-31 y[1] (closed_form) 0.279377084879120956790253238679635908e0+/-0.226e-30 y[1] (numeric) 0.279377084879120956790253888829481981e0+/-0.407e-31 absolute error 0.650149846073e-24+/-0.266e-30 relative error 0.232714091907109191761938639626841017e-21+/-0.952e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.57e0+/-0.355e-31 y[1] (closed_form) 0.286893708540288488494994022663952666e0+/-0.266e-30 y[1] (numeric) 0.286893708540288488494994771059582493e0+/-0.472e-31 absolute error 0.748395629827e-24+/-0.313e-30 relative error 0.260861638839982713893532700257798563e-21+/-0.109e-27% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.58e0+/-0.405e-31 y[1] (closed_form) 0.294476560093404453712241226383455367e0+/-0.305e-30 y[1] (numeric) 0.294476560093404453712242070470739755e0+/-0.545e-31 absolute error 0.844087284388e-24+/-0.359e-30 relative error 0.286639888798030504617013956258546758e-21+/-0.121e-27% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 TOP MAIN SOLVE Loop x[1] 0.59e0+/-0.455e-31 y[1] (closed_form) 0.302125066082831921580274356188100881e0+/-0.343e-30 y[1] (numeric) 0.302125066082831921580275293521694151e0+/-0.619e-31 absolute error 0.93733359327e-24+/-0.404e-30 relative error 0.310246880678552022919903784143467959e-21+/-0.133e-27% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 Finished! diff ( y , x , 1 ) = sqrt ( x ) ; Iterations 100 Total Elapsed Time 1 Minutes 14 Seconds Elapsed Time(since restart) 1 Minutes 14 Seconds Time to Timeout 1 Minutes 46 Seconds Percent Done 0.101e3+/-0.525e-28%