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/sing4postode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=32; ELIMINATED in preodein.rb max_terms=30 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(-2.0) x_end=c(-1.0) $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_h=c(0.1) $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 # 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) # ELIMINATED in preodein.rb #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=true $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(1.0) / (c(x) * c( x) + c(1.0))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] -0.2e1+/-0.50e-32 y[1] (closed_form) 0.2e0+/-0.92e-33 y[1] (numeric) 0.2e0+/-0.112e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.204e-32 relative error 0.0e0+/-0.102000000000000000000000000000000938e-29% Desired digits 8 Estimated correct digits 13 Correct digits 34 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.223606797749978969640917366873127562e1+/-0.474e-30 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.199e1+/-0.100e-31 y[1] (closed_form) 0.201608838531481220136690792524344267e0+/-0.173e-32 y[1] (numeric) 0.201608838531481220136690753887383252e0+/-0.532e-32 absolute error 0.38636961015e-25+/-0.705e-32 relative error 0.1916431903305015e-22+/-0.349e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.222712819568160467398137696074714236e1+/-0.919e-30 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.198e1+/-0.150e-31 y[1] (closed_form) 0.203235509308186326314933745223965531e0+/-0.257e-32 y[1] (numeric) 0.203235509308186326314933667419918528e0+/-0.952e-32 absolute error 0.77804047003e-25+/-0.12e-31 relative error 0.3828270328735612e-22+/-0.59e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.221819746641276281122341406138612488e1+/-0.135e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.197e1+/-0.200e-31 y[1] (closed_form) 0.204880247495338974369481038333094306e0+/-0.343e-32 y[1] (numeric) 0.204880247495338974369480920826277716e0+/-0.108e-31 absolute error 0.11750681659e-24+/-0.142e-31 relative error 0.573539021094131000000000000000000001e-22+/-0.693e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.220927589947475777011918715085558777e1+/-0.18e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.196e1+/-0.250e-31 y[1] (closed_form) 0.206543291473892927957699933906146728e0+/-0.43e-32 y[1] (numeric) 0.206543291473892927957699776155377846e0+/-0.118e-31 absolute error 0.157750768882e-24+/-0.161e-31 relative error 0.763766122619091200000000000000000001e-22+/-0.779e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.220036360631601067207892577167362564e1+/-0.224e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.195e1+/-0.300e-31 y[1] (closed_form) 0.208224882873503383654346694429984383e0+/-0.517e-32 y[1] (numeric) 0.20822488287350338365434649588864921e0+/-0.128e-31 absolute error 0.198541335173e-24+/-0.179e-31 relative error 0.9534947621683325e-22+/-0.859e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.219146070008111256569497704240974414e1+/-0.267e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.194e1+/-0.350e-31 y[1] (closed_form) 0.209925266605088588462507347384331178e0+/-0.605e-32 y[1] (numeric) 0.209925266605088588462507107500461021e0+/-0.148e-31 absolute error 0.239883870157e-24+/-0.208e-31 relative error 0.11427108038798852e-21+/-0.99e-29% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.218256729564061781302134118564251455e1+/-0.309e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.193e1+/-0.400e-31 y[1] (closed_form) 0.211644690892928950877267243751190501e0+/-0.7e-32 y[1] (numeric) 0.211644690892928950877266961967547827e0+/-0.167e-31 absolute error 0.281783642674e-24+/-0.237e-31 relative error 0.13313995332703826e-21+/-0.111e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.217368350962139840216588403665937828e1+/-0.356e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.192e1+/-0.450e-31 y[1] (closed_form) 0.21338340730624786616592693752133834e0+/-0.793e-32 y[1] (numeric) 0.213383407306247866165926613275512423e0+/-0.19e-31 absolute error 0.324245825917e-24+/-0.269e-31 relative error 0.15195456385774288e-21+/-0.126e-28% Desired digits 8 Estimated correct digits 13 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.216480946043756931841210013272585378e1+/-0.398e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.191e1+/-0.500e-31 y[1] (closed_form) 0.215141670790215356812461005572169273e0+/-0.894e-32 y[1] (numeric) 0.21514167079021535681246063829668218e0+/-0.213e-31 absolute error 0.367275487093e-24+/-0.302e-31 relative error 0.17071331915569733e-21+/-0.14e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.215594526832199522791789143721391139e1+/-0.444e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.19e1+/-0.550e-31 y[1] (closed_form) 0.216919739696312364425162689804772234e0+/-0.994e-32 y[1] (numeric) 0.2169197396963123644251622789271957e0+/-0.239e-31 absolute error 0.410877576534e-24+/-0.338e-31 relative error 0.189414562782174e-21+/-0.155e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.21470910553583888469209698781039017e1+/-0.487e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.189e1+/-0.600e-31 y[1] (closed_form) 0.218717875811990113952013298046849368e0+/-0.109e-31 y[1] (numeric) 0.218717875811990113952012842989933162e0+/-0.26e-31 absolute error 0.455056916206e-24+/-0.369e-31 relative error 0.20805657265854526e-21+/-0.168e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.213824694551401148494001290233335519e1+/-0.53e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.188e1+/-0.650e-31 y[1] (closed_form) 0.220536344389555398729710656316160903e0+/-0.119e-31 y[1] (numeric) 0.220536344389555398729710156497973317e0+/-0.284e-31 absolute error 0.499818187586e-24+/-0.403e-31 relative error 0.22663755897899584e-21+/-0.182e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.212941306467298636229910190786718586e1+/-0.574e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.187e1+/-0.700e-31 y[1] (closed_form) 0.222375414174208899464075251840156552e0+/-0.13e-31 y[1] (numeric) 0.222375414174208899464074706674237649e0+/-0.313e-31 absolute error 0.545165918903e-24+/-0.443e-31 relative error 0.24515566207149007e-21+/-0.199e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.212058954067023540999612411914172825e1+/-0.617e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.186e1+/-0.750e-31 y[1] (closed_form) 0.224235357431159745268633958202529374e0+/-0.141e-31 y[1] (numeric) 0.224235357431159745268633367098057672e0+/-0.339e-31 absolute error 0.591104471702e-24+/-0.480e-31 relative error 0.26360895020022392e-21+/-0.214e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.211177650332605036303259103948044862e1+/-0.66e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.185e1+/-0.800e-31 y[1] (closed_form) 0.226116449971735443753533069530808366e0+/-0.152e-31 y[1] (numeric) 0.226116449971735443753532431892781677e0+/-0.371e-31 absolute error 0.637638026689e-24+/-0.523e-31 relative error 0.28199541730321025e-21+/-0.231e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.210297408448130905634316452001556162e1+/-0.704e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.184e1+/-0.850e-31 y[1] (closed_form) 0.228018971178402043049981758482305727e0+/-0.163e-31 y[1] (numeric) 0.228018971178402043049981073711736894e0+/-0.391e-31 absolute error 0.684770568833e-24+/-0.554e-31 relative error 0.300312980667400480000000000000000001e-21+/-0.242e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.209418241803334792489860544610516233e1+/-0.745e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.183e1+/-0.900e-31 y[1] (closed_form) 0.229943204028604934581158453861896111e0+/-0.175e-31 y[1] (numeric) 0.229943204028604934581157721356024397e0+/-0.411e-31 absolute error 0.732505871714e-24+/-0.586e-31 relative error 0.31855947854970146e-21+/-0.254e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.208540163997250179586490683127336155e1+/-0.79e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.182e1+/-0.950e-31 y[1] (closed_form) 0.231889435117336054169372043409702253e0+/-0.186e-31 y[1] (numeric) 0.23188943511733605416937126256222121e0+/-0.437e-31 absolute error 0.780847481043e-24+/-0.623e-31 relative error 0.336732667724983320000000000000000001e-21+/-0.268e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.207663188841932214030996545658502087e1+/-0.832e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.181e1+/-0.1e-30 y[1] (closed_form) 0.23385795467832838333995930871588597e0+/-0.199e-31 y[1] (numeric) 0.233857954678328383339958478917188621e0+/-0.458e-31 absolute error 0.829798697349e-24+/-0.657e-31 relative error 0.354830220973405890000000000000000001e-21+/-0.28e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.20678733036624850242483916802727363e1+/-0.876e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.18e1+/-0.1e-30 y[1] (closed_form) 0.235849056603773584905660377358490566e0+/-0.201e-31 y[1] (numeric) 0.235849056603773584905659497995932776e0+/-0.482e-31 absolute error 0.87936255779e-24+/-0.683e-31 relative error 0.37284972450296e-21+/-0.289e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.205912602819740006315947389283950958e1+/-0.875e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.179e1+/-0.1e-30 y[1] (closed_form) 0.237863038462453319378701743536071929e0+/-0.203e-31 y[1] (numeric) 0.237863038462453319378700813994254905e0+/-0.502e-31 absolute error 0.929541817024e-24+/-0.705e-31 relative error 0.390788675295059840000000000000000001e-21+/-0.296e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.205039020676553173981898184001804605e1+/-0.873e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.178e1+/-0.1e-30 y[1] (closed_form) 0.239900201516169273582189809039439593e0+/-0.206e-31 y[1] (numeric) 0.239900201516169273582188828700512426e0+/-0.525e-31 absolute error 0.980338927167e-24+/-0.731e-31 relative error 0.40864447840029228e-21+/-0.304e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.204166598639444449162812607659914941e1+/-0.873e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.177e1+/-0.1e-30 y[1] (closed_form) 0.241960850734351181978755837305523966e0+/-0.208e-31 y[1] (numeric) 0.241960850734351181978754805549507259e0+/-0.548e-31 absolute error 0.1031756016707e-23+/-0.756e-31 relative error 0.42641444414483603e-21+/-0.312e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.203295351643858300983593294896646624e1+/-0.872e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.176e1+/-0.1e-30 y[1] (closed_form) 0.244045294806716126513080827801639984e0+/-0.21e-31 y[1] (numeric) 0.24404529480671612651307974400677157e0+/-0.568e-31 absolute error 0.1083794868414e-23+/-0.778e-31 relative error 0.44409578528132064e-21+/-0.318e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.202425294862079921832343265297519857e1+/-0.87e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.175e1+/-0.1e-30 y[1] (closed_form) 0.246153846153846153846153846153846153e0+/-0.213e-31 y[1] (numeric) 0.246153846153846153846152709696950009e0+/-0.591e-31 absolute error 0.1136456896144e-23+/-0.804e-31 relative error 0.461685614058500000000000000000000001e-21+/-0.326e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.201556443707463741309165330757594241e1+/-0.87e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.174e1+/-0.1e-30 y[1] (closed_form) 0.24828682093554474128513258516237958e0+/-0.215e-31 y[1] (numeric) 0.24828682093554474128513139541925904e0+/-0.615e-31 absolute error 0.118974312054e-23+/-0.830e-31 relative error 0.479180939228690400000000000000000001e-21+/-0.334e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.200688813838738904436384927407121437e1+/-0.868e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.173e1+/-0.1e-30 y[1] (closed_form) 0.25044453905682586591199378897543139e0+/-0.218e-31 y[1] (numeric) 0.250444539056825865911992545321287863e0+/-0.641e-31 absolute error 0.1243654143527e-23+/-0.859e-31 relative error 0.496578662968895830000000000000000001e-21+/-0.342e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.199822421164392861031783283322807841e1+/-0.867e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.172e1+/-0.1e-30 y[1] (closed_form) 0.252627324171382376717865804365400161e0+/-0.22e-31 y[1] (numeric) 0.252627324171382376717864506175278537e0+/-0.665e-31 absolute error 0.1298190121624e-23+/-0.885e-31 relative error 0.513875577743644160000000000000000001e-21+/-0.35e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.198957281847134210389524848773230457e1+/-0.865e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.171e1+/-0.1e-30 y[1] (closed_form) 0.254835503682373028210290257638694222e0+/-0.223e-31 y[1] (numeric) 0.254835503682373028210288904287956273e0+/-0.685e-31 absolute error 0.1353350737949e-23+/-0.908e-31 relative error 0.531068363078567090000000000000000001e-21+/-0.356e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.198093412308435941082349750855533903e1+/-0.865e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.17e1+/-0.1e-30 y[1] (closed_form) 0.257069408740359897172236503856041131e0+/-0.225e-31 y[1] (numeric) 0.257069408740359897172235094720868191e0+/-0.705e-31 absolute error 0.140913517294e-23+/-0.930e-31 relative error 0.54815358227366e-21+/-0.361e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.197230829233160199680639990832478003e1+/-0.863e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.169e1+/-0.1e-30 y[1] (closed_form) 0.259329374238219963175228858172765229e0+/-0.228e-31 y[1] (numeric) 0.259329374238219963175227392630691566e0+/-0.728e-31 absolute error 0.1465542073663e-23+/-0.956e-31 relative error 0.56512767902518943e-21+/-0.368e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.196369549574265714360373892059428852e1+/-0.862e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.168e1+/-0.1e-30 y[1] (closed_form) 0.261615738802846379238174968606111343e0+/-0.231e-31 y[1] (numeric) 0.261615738802846379238173446036589611e0+/-0.751e-31 absolute error 0.1522569521732e-23+/-0.982e-31 relative error 0.581986973986839680000000000000000001e-21+/-0.375e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.195509590557598989617551156384415886e1+/-0.86e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.167e1+/-0.1e-30 y[1] (closed_form) 0.263928844783446382855182242867322969e0+/-0.233e-31 y[1] (numeric) 0.263928844783446382855180662652323247e0+/-0.771e-31 absolute error 0.1580214999722e-23+/-0.1e-30 relative error 0.598727661244668580000000000000000001e-21+/-0.378e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.194650969686770376489485777942595163e1+/-0.86e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.166e1+/-0.1e-30 y[1] (closed_form) 0.266269038236233890723186707849611247e0+/-0.236e-31 y[1] (numeric) 0.266269038236233890723185069374255197e0+/-0.797e-31 absolute error 0.163847535605e-23+/-0.103e-30 relative error 0.615345804718138e-21+/-0.386e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.193793704748116108664506169810028465e1+/-0.858e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.165e1+/-0.1e-30 y[1] (closed_form) 0.268636668905305574210879785090664875e0+/-0.239e-31 y[1] (numeric) 0.268636668905305574210878087743896609e0+/-0.82e-31 absolute error 0.1697346768266e-23+/-0.105e-30 relative error 0.631837334487018500000000000000000001e-21+/-0.39e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.192937813815747378494842310871411376e1+/-0.856e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.164e1+/-0.1e-30 y[1] (closed_form) 0.271032090199479618386816999132697311e0+/-0.242e-31 y[1] (numeric) 0.271032090199479618386815242307992627e0+/-0.84e-31 absolute error 0.1756824704684e-23+/-0.108e-30 relative error 0.64819804304020864e-21+/-0.398e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.192083315256687508058967857792534712e1+/-0.854e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.163e1+/-0.1e-30 y[1] (closed_form) 0.273455659164866416910497962755339221e0+/-0.245e-31 y[1] (numeric) 0.273455659164866416910496145851454925e0+/-0.863e-31 absolute error 0.1816903884296e-23+/-0.11e-30 relative error 0.664423581448204240000000000000000001e-21+/-0.402e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.191230227736098248887607522383472621e1+/-0.854e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.162e1+/-0.1e-30 y[1] (closed_form) 0.275907736452930140161130118088511201e0+/-0.248e-31 y[1] (numeric) 0.275907736452930140161128240510276294e0+/-0.883e-31 absolute error 0.1877578234907e-23+/-0.113e-30 relative error 0.680509455459693080000000000000000002e-21+/-0.409e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.190378570222596219601951319990795457e1+/-0.852e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.161e1+/-0.1e-30 y[1] (closed_form) 0.278388686283789426797694941677570223e0+/-0.25e-31 y[1] (numeric) 0.278388686283789426797693002836720786e0+/-0.903e-31 absolute error 0.1938840849437e-23+/-0.115e-30 relative error 0.696451021526264770000000000000000001e-21+/-0.413e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.189528361993660463334663891293665903e1+/-0.85e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.16e1+/-0.1e-30 y[1] (closed_form) 0.28089887640449438202247191011235955e0+/-0.253e-31 y[1] (numeric) 0.280898876404494382022469909428419241e0+/-0.927e-31 absolute error 0.2000683940309e-23+/-0.118e-30 relative error 0.712243482750004000000000000000000001e-21+/-0.42e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.188679622641132076226413207552453532e1+/-0.849e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.159e1+/-0.1e-30 y[1] (closed_form) 0.283438678042005612085825231711119299e0+/-0.256e-31 y[1] (numeric) 0.283438678042005612085823168612327432e0+/-0.952e-31 absolute error 0.2063098791867e-23+/-0.12e-30 relative error 0.72788188475859627e-21+/-0.423e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.187832372076806824315940363406847991e1+/-0.849e-29 Order of pole (given) 0.1e1+/-0.50e-33 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] -0.158e1+/-0.1e-30 y[1] (closed_form) 0.286008465850589177439652213705525683e0+/-0.259e-31 y[1] (numeric) 0.286008465850589177439650087629814921e0+/-0.976e-31 absolute error 0.2126075710762e-23+/-0.123e-30 relative error 0.743361111510825680000000000000000001e-21+/-0.43e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 Radius of convergence (given) for eq 1 0.186986630538121628563563910617828699e1+/-0.847e-29 Order of pole (given) 0.1e1+/-0.50e-33 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! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; Iterations 422 Total Elapsed Time 3 Minutes 1 Seconds Elapsed Time(since restart) 3 Minutes 1 Seconds Expected Time Remaining 4 Minutes 6 Seconds Optimized Time Remaining 4 Minutes 6 Seconds Expected Total Time 7 Minutes 7 Seconds Time to Timeout 0.0 Seconds Percent Done 0.423e2+/-0.109e-28%