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/sqrt_sqrt_tonepostode.ode################# diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #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(1.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $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(-2.0) # ELIMINATED in preodein.rb $array_given_rad_poles[1][2]=c(0.0) # ELIMINATED in preodein.rb $array_given_ord_poles[1][1]=c(0.5) # 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=(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(c(0.8) * (c(x) + c(2.0)) * sqrt(sqrt(c(0.1) * c(x) + c(0.2)))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.5e0+/-0.50e-31 y[1] (closed_form) 0.1414213562373095048801688724210188e1+/-0.114e-28 y[1] (numeric) 0.1414213562373095048801688724210188e1+/-0.114e-28 absolute error 0.0e0+/-0.228e-28 relative error 0.0e0+/-0.1612203461105328355633925145624489e-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 0.249999999999999999999999999999992e1+/-0.554e-28 Order of pole (given) 0.5e0+/-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) 0.1485274318892231580371045534202014e1+/-0.123e-28 y[1] (numeric) 0.1485274318892231580371132417211806e1+/-0.118e-28 absolute error 0.86883009792e-22+/-0.241e-28 relative error 0.5849627148794999850289786103450915e-20+/-0.162e-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 0.2599999999999999999999999999999914e1+/-0.556e-28 Order of pole (given) 0.5e0+/-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) 0.1557021796359320774105394949967925e1+/-0.131e-28 y[1] (numeric) 0.1557021796359320774105563005371407e1+/-0.122e-28 absolute error 0.168055403482e-21+/-0.253e-28 relative error 0.1079338798435273251257846083355026e-19+/-0.162e-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 0.2699999999999999999999999999999907e1+/-0.556e-28 Order of pole (given) 0.5e0+/-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) 0.1629436821628730086855230062024189e1+/-0.14e-28 y[1] (numeric) 0.1629436821628730086855474147682195e1+/-0.128e-28 absolute error 0.244085658006e-21+/-0.268e-28 relative error 0.149797558743038720051599863892941e-19+/-0.164e-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 0.2799999999999999999999999999999878e1+/-0.11e-27 Order of pole (given) 0.5e0+/-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) 0.170250142607637055975498194753671e1+/-0.147e-28 y[1] (numeric) 0.1702501426076370559755297415314164e1+/-0.134e-28 absolute error 0.315467777454e-21+/-0.281e-28 relative error 0.1852966303711329711496198104567019e-19+/-0.165e-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 0.2899999999999999999999999999999864e1+/-0.111e-27 Order of pole (given) 0.5e0+/-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) 0.1776198730781484601360295918793726e1+/-0.156e-28 y[1] (numeric) 0.1776198730781484601360678552027561e1+/-0.14e-28 absolute error 0.382633233835e-21+/-0.296e-28 relative error 0.2154225353300700794069118157724556e-19+/-0.166e-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 0.2999999999999999999999999999999852e1+/-0.111e-27 Order of pole (given) 0.5e0+/-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) 0.1850512846136166838304082278128402e1+/-0.163e-28 y[1] (numeric) 0.1850512846136166838304528238794415e1+/-0.146e-28 absolute error 0.445960666013e-21+/-0.309e-28 relative error 0.2409930127986718895729457767041729e-19+/-0.166e-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 0.3099999999999999999999999999999825e1+/-0.111e-27 Order of pole (given) 0.5e0+/-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) 0.1925428783660233506879799928073323e1+/-0.174e-28 y[1] (numeric) 0.1925428783660233506880305711888306e1+/-0.152e-28 absolute error 0.505783814983e-21+/-0.326e-28 relative error 0.2626863269497336091025931660957934e-19+/-0.169e-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 0.3200000000000000000000000000004673e1+/-0.109e-26 Order of pole (given) 0.5e0+/-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] 0.13e1+/-0.5e-31 y[1] (closed_form) 0.2000932378200508917630518331999959e1+/-0.182e-28 y[1] (numeric) 0.2000932378200508917631080730060612e1+/-0.159e-28 absolute error 0.562398060653e-21+/-0.341e-28 relative error 0.2810679994887080385092074667068728e-19+/-0.17e-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 0.3300000000000000000000000000004697e1+/-0.11e-26 Order of pole (given) 0.5e0+/-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] 0.14e1+/-0.5e-31 y[1] (closed_form) 0.2077010219012498527666458498953477e1+/-0.19e-28 y[1] (numeric) 0.2077010219012498527667074564794572e1+/-0.167e-28 absolute error 0.616065841095e-21+/-0.357e-28 relative error 0.296611848827544352395518729523625e-19+/-0.171e-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 0.3400000000000000000000000000004536e1+/-0.11e-26 Order of pole (given) 0.5e0+/-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 Finished! diff ( y , x , 1 ) = sqrt ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 20 Total Elapsed Time 52 Seconds Elapsed Time(since restart) 51 Seconds Time to Timeout 19 Minutes 8 Seconds Percent Done 0.105e3+/-0.257e-28%