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/mtest3postode.ode################# diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; ! #BEGIN FIRST INPUT BLOCK # Digits:=16; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=c(0.1) x_end=c(0.5) $array_y1_init[0 + 1] = exact_soln_y1(x_start) $array_y2_init[0 + 1] = exact_soln_y2(x_start) # 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=3 #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_y1 (x) x = c(x) return(c(1.0) + cos(c(x))) end def exact_soln_y2 (x) x = c(x) return(c(1.0) - sin(c(x))) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] 0.1e0+/-0.50e-33 y2[1] (closed_form) 0.900166583353171847693185801589377974e0+/-0.106e-32 y2[1] (numeric) 0.900166583353171847693185801589377974e0+/-0.196e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.302e-32 relative error 0.0e0+/-0.335493458194185326118224699714498433e-30% Desired digits 8 Estimated correct digits 13 Correct digits 34 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.199500416527802576609556198780387028e1+/-0.606e-33 y1[1] (numeric) 0.199500416527802576609556198780387028e1+/-0.259e-32 $glob_prec 0.1e-15+/-0.50e-49% absolute error 0.0e0+/-0.3196e-32 relative error 0.0e0+/-0.16020016677782736654234390945118725466319e-30% Desired digits 8 Estimated correct digits 13 Correct digits 34 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.993346653975306045806982181437353022e-1+/-0.31e-29 Order of pole (three term test) 0.329900332889206208158581195308632656e2+/-0.129e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.99334665397530607501335785458613889e-1+/-0.31e-29 Order of pole (three term test) 0.320099667110793791847339230141150958e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.11e0+/-0.550e-32 y2[1] (closed_form) 0.890221699162825191335050509916545299e0+/-0.603e-32 y2[1] (numeric) 0.890221699162825191335050344243523041e0+/-0.163e-31 absolute error 0.165673022258e-24+/-0.223e-31 relative error 0.186103104893759421087338208503608175e-22+/-0.25e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.199395609795669685035783961141984805e1+/-0.116e-32 y1[1] (numeric) 0.199395609795669685035783959324771452e1+/-0.214e-31 absolute error 0.1817213353e-25+/-0.225e-31 relative error 0.911360764092141406588519398517211463e-24+/-0.112e-29% Desired digits 8 Estimated correct digits 13 Correct digits 25 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.109114811540434656523670875193145027e0+/-0.342e-29 Order of pole (three term test) 0.329879487246653027450601927170758925e2+/-0.13e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.10911481154043465971821686318814194e0+/-0.342e-29 Order of pole (three term test) 0.320120512753346972556541698087743814e2+/-0.127e-26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.12e0+/-0.105e-31 y2[1] (closed_form) 0.880287792711080640032649385729030291e0+/-0.109e-31 y2[1] (numeric) 0.880287792711080640032649054762989556e0+/-0.273e-31 absolute error 0.330966040735e-24+/-0.382e-31 relative error 0.375974815822109671298334649626509175e-22+/-0.433e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.199280863585386625224809816785763385e1+/-0.180e-32 y1[1] (numeric) 0.199280863585386625224809812820177876e1+/-0.385e-31 absolute error 0.3965585509e-25+/-0.403e-31 relative error 0.198994797475917730586493982377183211e-23+/-0.202e-29% Desired digits 8 Estimated correct digits 13 Correct digits 24 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.11885131321356729042825213311293077e0+/-0.374e-29 Order of pole (three term test) 0.329856689874260148028868565838251888e2+/-0.13e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.11885131321356729389159594967405232e0+/-0.374e-29 Order of pole (three term test) 0.320143310125739851979606814953301793e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.13e0+/-0.155e-31 y2[1] (closed_form) 0.870365857380305140458794189291688518e0+/-0.158e-31 y2[1] (numeric) 0.87036585738030514045879369346227758e0+/-0.379e-31 absolute error 0.495829410938e-24+/-0.537e-31 relative error 0.569679298347462674452659379888709102e-22+/-0.616e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.199156189371478803959451217115181459e1+/-0.256e-32 y1[1] (numeric) 0.199156189371478803959451210670659825e1+/-0.603e-31 absolute error 0.6444521634e-25+/-0.628e-31 relative error 0.323591330720797632315563500937396704e-23+/-0.315e-29% Desired digits 8 Estimated correct digits 13 Correct digits 24 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.128540275946077544628209507380123997e0+/-0.406e-29 Order of pole (three term test) 0.329831949890672566132747867708936083e2+/-0.13e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.12854027594607754835481054120814923e0+/-0.408e-29 Order of pole (three term test) 0.320168050109327433877165693815240175e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.14e0+/-0.205e-31 y2[1] (closed_form) 0.860456885355763518282011648294628389e0+/-0.207e-31 y2[1] (numeric) 0.860456885355763518282010988081057386e0+/-0.489e-31 absolute error 0.660213571003e-24+/-0.696e-31 relative error 0.767282570735695668375763462407955174e-22+/-0.808e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.199021599621263717189894822701140027e1+/-0.341e-32 y1[1] (numeric) 0.199021599621263717189894813447779284e1+/-0.73e-31 absolute error 0.9253360743e-25+/-0.764e-31 relative error 0.464942536921070919708144663166255026e-23+/-0.383e-29% Desired digits 8 Estimated correct digits 13 Correct digits 24 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.138177824282056862318864164934078087e0+/-0.438e-29 Order of pole (three term test) 0.329805277191553854745350881762608844e2+/-0.13e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.13817782428205686630276064934070348e0+/-0.44e-29 Order of pole (three term test) 0.32019472280844614526610498491138495e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.15e0+/-0.255e-31 y2[1] (closed_form) 0.850561867526400778502274561312358192e0+/-0.257e-31 y2[1] (numeric) 0.850561867526400778502273737243308258e0+/-0.591e-31 absolute error 0.824069049934e-24+/-0.848e-31 relative error 0.968852568397585185583664246517691754e-22+/-0.996e-29% Desired digits 8 Estimated correct digits 13 Correct digits 23 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.198877107793604228673498099865433895e1+/-0.438e-32 y1[1] (numeric) 0.198877107793604228673498087474058085e1+/-0.83e-31 absolute error 0.1239137581e-24+/-0.873e-31 relative error 0.623066975755693254797164329535059711e-23+/-0.438e-29% Desired digits 8 Estimated correct digits 13 Correct digits 24 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.147760103330669782923330137103247021e0+/-0.468e-29 Order of pole (three term test) 0.329776682445628030104761463116059666e2+/-0.131e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.14776010333066978715814868756601206e0+/-0.47e-29 Order of pole (three term test) 0.320223317554371969908338365765714471e2+/-0.127e-26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.16e0+/-0.305e-31 y2[1] (closed_form) 0.840681793385754036688536840314010376e0+/-0.306e-31 y2[1] (numeric) 0.840681793385754036688535852967534501e0+/-0.685e-31 absolute error 0.987346475875e-24+/-0.991e-31 relative error 0.117445921113453639215286064060851666e-21+/-0.117e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.198722728337562694904095252401833768e1+/-0.544e-32 y1[1] (numeric) 0.198722728337562694904095236544059893e1+/-0.93e-31 absolute error 0.15857773875e-24+/-0.984e-31 relative error 0.797984911321416958615508849790301392e-23+/-0.495e-29% Desired digits 8 Estimated correct digits 12 Correct digits 24 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.157283280308058878417581050597736266e0+/-0.502e-29 Order of pole (three term test) 0.329746177090412204345297942302504822e2+/-0.13e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.1572832803080588828965468608156765e0+/-0.504e-29 Order of pole (three term test) 0.320253822909587795669544875856173223e2+/-0.127e-26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] 0.17e0+/-0.355e-31 y2[1] (closed_form) 0.830817650933003989842375623329148488e0+/-0.354e-31 y2[1] (numeric) 0.830817650933003989842374473332564148e0+/-0.795e-31 absolute error 0.114999658434e-23+/-0.114e-30 relative error 0.138417447324158278754385473618027969e-21+/-0.137e-28% Desired digits 8 Estimated correct digits 12 Correct digits 22 h 0.1e-2+/-0.5e-33 y1[1] (closed_form) 0.198558476690956070917192999021250311e1+/-0.657e-32 y1[1] (numeric) 0.198558476690956070917192979369554128e1+/-0.1e-30 absolute error 0.19651696183e-24+/-0.106e-30 relative error 0.989718319283172372824473565616119678e-23+/-0.533e-29% Desired digits 8 Estimated correct digits 12 Correct digits 24 h 0.1e-2+/-0.5e-33 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 0.166743546070407193198272720129328091e0+/-0.53e-29 Order of pole (three term test) 0.329713773327641731150854239456291515e2+/-0.13e-26 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 0.16674354607040719791422040026784178e0+/-0.532e-29 Order of pole (three term test) 0.320286226672358268865827806637388878e2+/-0.126e-26 NO COMPLEX POLE (six term test) for Equation 2 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations 71 Total Elapsed Time 3 Minutes 7 Seconds Elapsed Time(since restart) 3 Minutes 7 Seconds Expected Time Remaining 14 Minutes 11 Seconds Optimized Time Remaining 14 Minutes 11 Seconds Expected Total Time 17 Minutes 18 Seconds Time to Timeout 0.0 Seconds Percent Done 0.18e2+/-0.929e-29%