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/addpostode.ode#################
diff  (  y  ,  x  ,  1  )   =  sin  (  x  )   +  sin  (  x  )   ; 
!
#BEGIN FIRST INPUT BLOCK
max_terms=40 
# Digits:=32; ELIMINATED in preodein.rb
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=c(-5.0) 
x_end=c(5.0) 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
#  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_y (x)
x = c(x)
return(c(2.0) - c(cos(x)) - c(cos(x))) 
end
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
 
TOP MAIN SOLVE Loop
x[1]                             -0.5e1+/-0.50e-32 
y[1] (closed_form)               0.143267562907354747106672165697288484e1+/-0.134e-29 
y[1] (numeric)                   0.143267562907354747106672165697288484e1+/-0.134e-29 
$glob_prec                        0.1e-15+/-0.50e-49%
absolute error                   0.0e0+/-0.268e-29 
relative error                   0.0e0+/-0.187062580364617914696842357729325275e-27%
Desired digits                   8 
Estimated correct digits         14 
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  0.27201055544468489935503758234188935e0+/-0.891e-29 
Order of pole (three term test)                   0.329195357645382262307167959948582448e2+/-0.126e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.499e1+/-0.100e-31 
y[1] (closed_form)               0.145188216090914551207381680460610458e1+/-0.202e-29 
y[1] (numeric)                   0.145188216090914551207381712466846445e1+/-0.134e-29 
absolute error                   0.32006235987e-24+/-0.336e-29 
relative error                   0.220446513145104036488613513417895826e-22+/-0.231e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   23 
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  0.2635659992260428328750375695353638e0+/-0.902e-29 
Order of pole (three term test)                   0.329248917086175930412621170319945993e2+/-0.127e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.498e1+/-0.150e-31 
y[1] (closed_form)               0.147114350407188929516749335863844212e1+/-0.274e-29 
y[1] (numeric)                   0.147114350407188929516749399967828653e1+/-0.134e-29 
absolute error                   0.64103984441e-24+/-0.408e-29 
relative error                   0.43574256531446763204758540188308425e-22+/-0.277e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   23 
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  0.2550160201218768164411677351084013e0+/-0.908e-29 
Order of pole (three term test)                   0.329300777016786600604018596898521716e2+/-0.127e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.497e1+/-0.200e-31 
y[1] (closed_form)               0.149045773244351361176809297197491158e1+/-0.34e-29 
y[1] (numeric)                   0.149045773244351361176809393487526902e1+/-0.134e-29 
absolute error                   0.96290035744e-24+/-0.474e-29 
relative error                   0.646043384176607408364232098606126637e-22+/-0.318e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   23 
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  0.24636403800983031505637766691161101e0+/-0.913e-29 
Order of pole (three term test)                   0.329350916693933485135285215424511494e2+/-0.129e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.496e1+/-0.250e-31 
y[1] (closed_form)               0.150982291461727643610310395412935406e1+/-0.408e-29 
y[1] (numeric)                   0.15098229146172764361031052397410652e1+/-0.134e-29 
absolute error                   0.128561171114e-23+/-0.542e-29 
relative error                   0.851498343741781453071374828917735514e-22+/-0.358e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   23 
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  0.2376135135673899239462496768000106e0+/-0.919e-29 
Order of pole (three term test)                   0.329399316062414245367580160697031576e2+/-0.13e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.495e1+/-0.300e-31 
y[1] (closed_form)               0.152923711409109798990948517673052298e1+/-0.472e-29 
y[1] (numeric)                   0.152923711409109798990948678587215868e1+/-0.134e-29 
absolute error                   0.16091416357e-23+/-0.606e-29 
relative error                   0.105225123093902495226889539674878253e-21+/-0.396e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.22876794688766051567216964118495812e0+/-0.908e-29 
Order of pole (three term test)                   0.329445955763126805305619753077826725e2+/-0.13e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.494e1+/-0.350e-31 
y[1] (closed_form)               0.154869838946120933666513839192056582e1+/-0.54e-29 
y[1] (numeric)                   0.154869838946120933666514032537834344e1+/-0.134e-29 
absolute error                   0.193345777762e-23+/-0.674e-29 
relative error                   0.124844049091614803075685490011860205e-21+/-0.435e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.21983087607937466546813340073575129e0+/-0.919e-29 
Order of pole (three term test)                   0.329490817140812734310156187216742502e2+/-0.13e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.493e1+/-0.400e-31 
y[1] (closed_form)               0.156820479461629114065147910702846806e1+/-0.6e-29 
y[1] (numeric)                   0.156820479461629114065148136555617533e1+/-0.134e-29 
absolute error                   0.225852770727e-23+/-0.734e-29 
relative error                   0.144019946567158487371363579107491646e-21+/-0.468e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.21080587585169633236476188609139558e0+/-0.908e-29 
Order of pole (three term test)                   0.329533882251519101736770617773039017e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.492e1+/-0.450e-31 
y[1] (closed_form)               0.158775437893208317713298151837645116e1+/-0.662e-29 
y[1] (numeric)                   0.158775437893208317713298410269536857e1+/-0.134e-29 
absolute error                   0.258431891741e-23+/-0.796e-29 
relative error                   0.162765661471404782438950838105825742e-21+/-0.501e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.20169655608438485575904269997434603e0+/-0.902e-29 
Order of pole (three term test)                   0.329575133869775818858615193547559115e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.491e1+/-0.500e-31 
y[1] (closed_form)               0.16073451874664451328648536009612099e1+/-0.72e-29 
y[1] (numeric)                   0.160734518746644513286485651176003704e1+/-0.134e-29 
absolute error                   0.291079882714e-23+/-0.854e-29 
relative error                   0.181093572795530313412645833497053084e-21+/-0.531e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.19250656038389118276694440401951727e0+/-0.902e-29 
Order of pole (three term test)                   0.32961455549548559723203155956017451e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.49e1+/-0.550e-31 
y[1] (closed_form)               0.162697526115484919101134171175616056e1+/-0.778e-29 
y[1] (numeric)                   0.162697526115484919101134494969095166e1+/-0.134e-29 
absolute error                   0.32379347911e-23+/-0.912e-29 
relative error                   0.199015613107827454121090502090255797e-21+/-0.56e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.18323956462596386861616885421042142e0+/-0.896e-29 
Order of pole (three term test)                   0.329652131360523767613564466347920042e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.489e1+/-0.600e-31 
y[1] (closed_form)               0.164664263700628485137908282057231998e1+/-0.834e-29 
y[1] (numeric)                   0.164664263700628485137908638626641621e1+/-0.134e-29 
absolute error                   0.356569409623e-23+/-0.968e-29 
relative error                   0.216543287298371503070821858255747899e-21+/-0.587e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.17389927548534778824722357901301091e0+/-0.902e-29 
Order of pole (three term test)                   0.329687846435045319588800093314671954e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.488e1+/-0.650e-31 
y[1] (closed_form)               0.166634534829955639564673450593675404e1+/-0.896e-29 
y[1] (numeric)                   0.166634534829955639564673839998071739e1+/-0.134e-29 
absolute error                   0.389404396335e-23+/-0.103e-28 
relative error                   0.233687690689311635819504114078100165e-21+/-0.618e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   22 
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  0.16448942895316366003441797697629671e0+/-0.908e-29 
Order of pole (three term test)                   0.329721686433496639181270291284290927e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.487e1+/-0.700e-31 
y[1] (closed_form)               0.168608142477995336800794042874392844e1+/-0.954e-29 
y[1] (numeric)                   0.168608142477995336800794465169549044e1+/-0.134e-29 
absolute error                   0.4222951562e-23+/-0.108e-28 
relative error                   0.2504595270392192212041624060403524e-21+/-0.64e-27%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
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  0.15501378884256141004928549267515607e0+/-0.891e-29 
Order of pole (three term test)                   0.329753637820329539826534615273175551e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.486e1+/-0.750e-31 
y[1] (closed_form)               0.170584889285627440434345850802919046e1+/-0.101e-28 
y[1] (numeric)                   0.170584889285627440434346306041319066e1+/-0.134e-29 
absolute error                   0.45523840002e-23+/-0.114e-28 
relative error                   0.266869124180013712290231565579332817e-21+/-0.668e-27%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
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  0.14547614528324509559637025132144413e0+/-0.896e-29 
Order of pole (three term test)                   0.329783687815415301175236578509422247e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             -0.485e1+/-0.800e-31 
y[1] (closed_form)               0.172564577579818470770372056306943138e1+/-0.106e-28 
y[1] (numeric)                   0.172564577579818470770372544537776392e1+/-0.134e-29 
absolute error                   0.488230833254e-23+/-0.119e-28 
relative error                   0.282926449970981115303493336747012182e-21+/-0.689e-27%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   22 
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  0.13588031320547155797923045523479034e0+/-0.879e-29 
Order of pole (three term test)                   0.329811824399156550181799126754883775e2+/-0.131e-26 
NO COMPLEX POLE (six term test) for Equation 1
Finished!
Maximum Time Reached before Solution Completed!
diff  (  y  ,  x  ,  1  )   =  sin  (  x  )   +  sin  (  x  )   ; 
Iterations                      157 
Total Elapsed Time              3 Minutes 1 Seconds
Elapsed Time(since restart)     3 Minutes 1 Seconds
Expected Time Remaining         3 Hours 7 Minutes 54 Seconds
Optimized Time Remaining        3 Hours 7 Minutes 54 Seconds
Expected Total Time             3 Hours 10 Minutes 55 Seconds
Time to Timeout                  0.0 Seconds
Percent Done                    0.158e1+/-0.89e-30%