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/arctan_sqrtpostode.ode################# diff ( y , x , 1 ) = arctan ( 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(-1.0) x_end=c(0.5) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true # ELIMINATED in preodein.rb $glob_max_h=c(0.01) # 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=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(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) + c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(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] -0.1e1+/-0.50e-30 y[1] (closed_form) 0.206773400697984684905726871527388e0+/-0.957e-28 y[1] (numeric) 0.206773400697984684905726871527388e0+/-0.957e-28 absolute error 0.0e0+/-0.1914e-27 relative error 0.0e0+/-0.925650975192697879647217532122499e-25% Desired digits 8 Estimated correct digits 14 Correct digits 32 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1e1+/-0.1e-31 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-30 y[1] (closed_form) 0.238106170530110074698485774717516e0+/-0.877e-28 y[1] (numeric) 0.2381067032031969942834742895644337e0+/-0.961e-28 absolute error 0.5326730869195849885148469177e-6+/-0.183e-27 relative error 0.2237124244758810273652129342732336e-3+/-0.768e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1100000000000000000000000000001404e1+/-0.995e-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-30 y[1] (closed_form) 0.270797914082765104709323776926169e0+/-0.814e-28 y[1] (numeric) 0.2707989462281871125779014313545801e0+/-0.963e-28 absolute error 0.10321454220078685776544284111e-5+/-0.177e-27 relative error 0.3811496944147101642639780246547151e-3+/-0.653e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1200000000000000000000000000001352e1+/-0.996e-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-30 y[1] (closed_form) 0.304779043584311802286308316398321e0+/-0.753e-28 y[1] (numeric) 0.3047805459914502695230623944950275e0+/-0.965e-28 absolute error 0.15024071384672367540780967065e-5+/-0.171e-27 relative error 0.4929496204195620965451478567550015e-3+/-0.561e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1300000000000000000000000000001151e1+/-0.994e-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-30 y[1] (closed_form) 0.339987926301144167889213235272975e0+/-0.352e-28 y[1] (numeric) 0.3399898730085733925496568314171621e0+/-0.967e-28 absolute error 0.19467074292246604435961441871e-5+/-0.131e-27 relative error 0.5725813414622156692002233395070458e-3+/-0.385e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1400000000000000000000000000000957e1+/-0.994e-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] -0.5e0+/-0.5e-30 y[1] (closed_form) 0.376369458122609650831026937945771e0+/-0.326e-28 y[1] (numeric) 0.3763718258590384722440878680199694e0+/-0.967e-28 absolute error 0.23677364288214130609300741984e-5+/-0.129e-27 relative error 0.6290989817909393157971542331055587e-3+/-0.342e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.15000000000000000000000000000009e1+/-0.997e-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] -0.4e0+/-0.5e-30 y[1] (closed_form) 0.413873974503432681121619835001001e0+/-0.307e-28 y[1] (numeric) 0.413876742256501676494718558763583e0+/-0.967e-28 absolute error 0.2767753068995373098723762582e-5+/-0.127e-27 relative error 0.6687429602975476017454842493639908e-3+/-0.306e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1600000000000000000000000000000853e1+/-0.1e-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] -0.3e0+/-0.5e-30 y[1] (closed_form) 0.452456402261009952947412880618459e0+/-0.284e-28 y[1] (numeric) 0.4524595509383792379611369819242889e0+/-0.967e-28 absolute error 0.31486773692850137241013058299e-5+/-0.125e-27 relative error 0.6959073522996866052314819567028185e-3+/-0.276e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.170000000000000000000000000000078e1+/-0.994e-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] -0.2e0+/-0.5e-30 y[1] (closed_form) 0.492075587517373132711533547980268e0+/-0.268e-28 y[1] (numeric) 0.4920790996759653532678051125215435e0+/-0.967e-28 absolute error 0.35121585922205562715645412755e-5+/-0.123e-27 relative error 0.713743717695923419137104651278057e-3+/-0.249e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1800000000000000000000000000000723e1+/-0.999e-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] -0.1e0+/-0.5e-30 y[1] (closed_form) 0.532693755173357074932223040806965e0+/-0.249e-28 y[1] (numeric) 0.5326976147999404742036429884335233e0+/-0.967e-28 absolute error 0.38596265833992714199476265583e-5+/-0.121e-27 relative error 0.7245488699493416611480589001266731e-3+/-0.227e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.190000000000000000000000000000063e1+/-0.997e-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] 0.0e0+/-0.50000000000000000000000000000000000000000000000000000000000000000000001e-30 y[1] (closed_form) 0.574276068408002141840802853496008e0+/-0.121e-28 y[1] (numeric) 0.574280260739126838794714309561769e0+/-0.967e-28 absolute error 0.4192331124696953911456065761e-5+/-0.108e-27 relative error 0.7300201689265686039986292319987143e-3+/-0.188e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.1999999999999999999999999999999974e1+/-0.503e-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] 0.1e0+/-0.2e-100 y[1] (closed_form) 0.616790265476396654280917881518398e0+/-0.129e-28 y[1] (numeric) 0.6167947768489648010921963601585714e0+/-0.967e-28 absolute error 0.45113725681468112784786401734e-5+/-0.109e-27 relative error 0.7314273296227066670158622928782465e-3+/-0.176e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.209999999999999999999999999999996e1+/-0.503e-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] 0.2e0+/-0.4e-100 y[1] (closed_form) 0.660206357103098901411535658366096e0+/-0.134e-28 y[1] (numeric) 0.660211174829111475472524137319289e0+/-0.967e-28 absolute error 0.4817726012574060988478953193e-5+/-0.11e-27 relative error 0.7297303276075115158954473258194803e-3+/-0.166e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2199999999999999999999999999999949e1+/-0.503e-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] 0.3e0+/-0.6e-100 y[1] (closed_form) 0.704496371989249160166141136097063e0+/-0.144e-28 y[1] (numeric) 0.7045014842498701248160881880674577e0+/-0.967e-28 absolute error 0.51122606209646499470519703947e-5+/-0.111e-27 relative error 0.7256617385451439455104183973584623e-3+/-0.157e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2299999999999999999999999999999943e1+/-0.503e-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] 0.4e0+/-0.8e-100 y[1] (closed_form) 0.749634140965318634069301778444741e0+/-0.152e-28 y[1] (numeric) 0.7496395367205466474119905413058429e0+/-0.967e-28 absolute error 0.53957552280133426887628611019e-5+/-0.111e-27 relative error 0.7197851502687861185130313974455544e-3+/-0.148e-25% Desired digits 8 Estimated correct digits 13 Correct digits 6 h 0.5e-1+/-0.1e-100 Radius of convergence (given) for eq 1 0.2399999999999999999999999999999937e1+/-0.503e-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 Finished! diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations 30 Total Elapsed Time 2 Minutes 58 Seconds Elapsed Time(since restart) 2 Minutes 55 Seconds Time to Timeout 17 Minutes 2 Seconds Percent Done 0.1033333333333333333333333333333333e3+/-0.763e-28%