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/lin_sinhpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=40 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=c(0.1) 
x_end=c(2.0) 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_min_h=0.000000001 
#  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(cosh(c(2.0)*c(x)+c(3.0))/c(2.0)) 
end

#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
 
TOP MAIN SOLVE Loop
x[1]                             0.1e0+/-0.50e-33 
y[1] (closed_form)               0.61433231002719287146815857475271536e1+/-0.402e-31 
y[1] (numeric)                   0.61433231002719287146815857475271536e1+/-0.462e-31 
$glob_prec                        0.1e-15+/-0.50e-49%
absolute error                   0.0e0+/-0.864e-31 
relative error                   0.0e0+/-0.140640494712341568204460970107258224e-29%
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  0.24999861961752490325152612076145251e0+/-0.773e-29 
Order of pole (three term test)                   0.324983384473139951635176802676133947e2+/-0.125e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.11e0+/-0.550e-32 
y[1] (closed_form)               0.62670188098996158101009032098535233e1+/-0.164e-30 
y[1] (numeric)                   0.62670188098996158100977558569374715e1+/-0.172e-30 
absolute error                   0.31473529160518e-20+/-0.336e-30 
relative error                   0.502208946793030901766815825141947716e-19+/-0.536e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   20 
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  0.24999872574610250233346428206912778e0+/-0.783e-29 
Order of pole (three term test)                   0.324984035973878426370087480526239505e2+/-0.126e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.12e0+/-0.105e-31 
y[1] (closed_form)               0.63932214106126276951412751486052325e1+/-0.293e-30 
y[1] (numeric)                   0.6393221410612627695134916656331192e1+/-0.265e-30 
absolute error                   0.63584922740405e-20+/-0.558e-30 
relative error                   0.994567818891040128931041809992414979e-19+/-0.872e-29%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   20 
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  0.24999882371516729341288637701877434e0+/-0.771e-29 
Order of pole (three term test)                   0.324984661929290720284302655393449582e2+/-0.125e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.13e0+/-0.155e-31 
y[1] (closed_form)               0.65219813851339733535750386982123472e1+/-0.429e-30 
y[1] (numeric)                   0.652198138513397335356540399563982218e1+/-0.37e-30 
absolute error                   0.963470257252502e-20+/-0.799e-30 
relative error                   0.147726618700355362863460912382976132e-18+/-0.122e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999891415204652003490136807304789e0+/-0.777e-29 
Order of pole (three term test)                   0.324985263340980071779189835020847735e2+/-0.126e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.14e0+/-0.205e-31 
y[1] (closed_form)               0.66533502391702838747758187275694166e1+/-0.565e-30 
y[1] (numeric)                   0.665335023917028387476284143323010842e1+/-0.47e-30 
absolute error                   0.1297729433930818e-19+/-0.103e-29 
relative error                   0.195049018506600265171682288605532172e-18+/-0.154e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999899763583708949538181791827321e0+/-0.778e-29 
Order of pole (three term test)                   0.324985841171281194023529183609547611e2+/-0.125e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.15e0+/-0.255e-31 
y[1] (closed_form)               0.678738052201478185806599395374318265e1+/-0.715e-30 
y[1] (numeric)                   0.678738052201478185804960634908751734e1+/-0.583e-30 
absolute error                   0.1638760465566531e-19+/-0.129e-29 
relative error                   0.241442256000121461120089065709943504e-18+/-0.19e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999907470111356804506164633717436e0+/-0.778e-29 
Order of pole (three term test)                   0.324986396344799461826437859704035047e2+/-0.126e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.16e0+/-0.305e-31 
y[1] (closed_form)               0.69241258475676993683415571868888124e1+/-0.865e-30 
y[1] (numeric)                   0.692412584756769936832169018919761841e1+/-0.705e-30 
absolute error                   0.1986699769119399e-19+/-0.157e-29 
relative error                   0.286924272154482155808806667192404943e-18+/-0.226e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999914584135111098671880514329328e0+/-0.78e-29 
Order of pole (three term test)                   0.324986929749889808777350216679234e2+/-0.126e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.17e0+/-0.355e-31 
y[1] (closed_form)               0.706364091578255289043259604868891575e1+/-0.102e-29 
y[1] (numeric)                   0.706364091578255289040917918343941448e1+/-0.85e-30 
absolute error                   0.2341686524950127e-19+/-0.187e-29 
relative error                   0.331512679207405717150783374939683228e-18+/-0.264e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.249999211512085241686600279653306e0+/-0.78e-29 
Order of pole (three term test)                   0.324987442240077691563373636468809673e2+/-0.126e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.18e0+/-0.405e-31 
y[1] (closed_form)               0.720598153454685407813528377974561385e1+/-0.119e-29 
y[1] (numeric)                   0.720598153454685407810824515242067089e1+/-0.97e-30 
absolute error                   0.2703862732494296e-19+/-0.216e-29 
relative error                   0.375224765638304896424029175125754632e-18+/-0.299e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999927213382870910903511533579934e0+/-0.777e-29 
Order of pole (three term test)                   0.324987934635424386759567584299214393e2+/-0.126e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.19e0+/-0.455e-31 
y[1] (closed_form)               0.735120464200600887396169285126014135e1+/-0.136e-29 
y[1] (numeric)                   0.735120464200600887393095911858950217e1+/-0.101e-29 
absolute error                   0.3073373267063918e-19+/-0.237e-29 
relative error                   0.418077501135276628990552134162996749e-18+/-0.322e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999932809476409851296202064587143e0+/-0.783e-29 
Order of pole (three term test)                   0.324988407723838797274618671282451654e2+/-0.127e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.2e0+/-0.505e-31 
y[1] (closed_form)               0.749936832933933485691128829130028535e1+/-0.153e-29 
y[1] (numeric)                   0.749936832933933485687678463192228773e1+/-0.111e-29 
absolute error                   0.3450365937799762e-19+/-0.264e-29 
relative error                   0.460087541546812623546569895586348466e-18+/-0.352e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999937975322943447803123089379129e0+/-0.783e-29 
Order of pole (three term test)                   0.324988862262337860895943672094281948e2+/-0.127e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.21e0+/-0.555e-31 
y[1] (closed_form)               0.76505318639973075288874897252788411e1+/-0.171e-29 
y[1] (numeric)                   0.765053186399730752884913980981087347e1+/-0.121e-29 
absolute error                   0.3834991546796763e-19+/-0.292e-29 
relative error                   0.501271233813674716604850115137574518e-18+/-0.381e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999942744001269027627705042237529e0+/-0.789e-29 
Order of pole (three term test)                   0.324989298978257571891206687368226931e2+/-0.129e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.22e0+/-0.605e-31 
y[1] (closed_form)               0.78047557134093307481079503365276624e1+/-0.19e-29 
y[1] (numeric)                   0.780475571340933074806567629703339368e1+/-0.131e-29 
absolute error                   0.4227403949426872e-19+/-0.321e-29 
relative error                   0.541644620876958407644627259832324495e-18+/-0.411e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.2499994714604698942979710966702821e0+/-0.779e-29 
Order of pole (three term test)                   0.324989718570416548268152528330907859e2+/-0.127e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.23e0+/-0.655e-31 
y[1] (closed_form)               0.796210156917151473378973738220421225e1+/-0.21e-29 
y[1] (numeric)                   0.796210156917151473374345978104537798e1+/-0.141e-29 
absolute error                   0.4627760115883427e-19+/-0.351e-29 
relative error                   0.581223446558590191640790628962575607e-18+/-0.44e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999951209648039495264819050131842e0+/-0.783e-29 
Order of pole (three term test)                   0.324990121710234001955874801440003338e2+/-0.127e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.24e0+/-0.705e-31 
y[1] (closed_form)               0.81226323717241370758192951460105417e1+/-0.23e-29 
y[1] (numeric)                   0.812263237172413707576893294407082999e1+/-0.151e-29 
absolute error                   0.5036220193971171e-19+/-0.381e-29 
relative error                   0.620023160410763005056345952562825133e-18+/-0.469e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   19 
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  0.24999954960825180297467974463747622e0+/-0.789e-29 
Order of pole (three term test)                   0.324990509042803896736220295031938717e2+/-0.128e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.25e0+/-0.755e-31 
y[1] (closed_form)               0.82864123355286580628482589106880567e1+/-0.25e-29 
y[1] (numeric)                   0.82864123355286580627937294349563818e1+/-0.161e-29 
absolute error                   0.545294757316749e-19+/-0.411e-29 
relative error                   0.658058922531230983544174180775941884e-18+/-0.495e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   19 
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  0.24999958423598616769806365495891835e0+/-0.783e-29 
Order of pole (three term test)                   0.32499088118792700911571984255446356e2+/-0.127e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.26e0+/-0.805e-31 
y[1] (closed_form)               0.84535069747543614706443719296283184e1+/-0.272e-29 
y[1] (numeric)                   0.84535069747543614705855908401285129e1+/-0.171e-29 
absolute error                   0.587810894998055e-19+/-0.443e-29 
relative error                   0.69534560834160235286573780207909817e-18+/-0.524e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   19 
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  0.24999961620141805547035257610765369e0+/-0.792e-29 
Order of pole (three term test)                   0.324991238741102540381578090976526187e2+/-0.128e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.27e0+/-0.855e-31 
y[1] (closed_form)               0.862398312948489580950595615560343985e1+/-0.295e-29 
y[1] (numeric)                   0.86239831294848958094428374116571403e1+/-0.181e-29 
absolute error                   0.6311874394629955e-19+/-0.476e-29 
relative error                   0.731897813325958886779226441709042142e-18+/-0.551e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   19 
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  0.24999964570923437826675348901205203e0+/-0.788e-29 
Order of pole (three term test)                   0.324991582274480863728738591633977554e2+/-0.128e-26 
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.28e0+/-0.905e-31 
y[1] (closed_form)               0.879790899245519899666411145437835605e1+/-0.32e-29 
y[1] (numeric)                   0.879790899245519899659656728018758423e1+/-0.191e-29 
absolute error                   0.6754417419077182e-19+/-0.511e-29 
relative error                   0.767729857727506729255032273795400794e-18+/-0.58e-28%
Desired digits                   8 
Estimated correct digits         12 
Correct digits                   19 
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  0.24999967294838506349487387733906012e0+/-0.799e-29 
Order of pole (three term test)                   0.324991912337778928481219150406672751e2+/-0.13e-26 
NO COMPLEX POLE (six term test) for Equation 1
Finished!
Maximum Time Reached before Solution Completed!
diff  (  y  ,  x  ,  1  )   =   sinh  ( 2.0  *  x  +  3.0 )   ; 
Iterations                      188 
Total Elapsed Time              3 Minutes 0 Seconds
Elapsed Time(since restart)     3 Minutes 0 Seconds
Expected Time Remaining         27 Minutes 9 Seconds
Optimized Time Remaining        27 Minutes 9 Seconds
Expected Total Time             30 Minutes 9 Seconds
Time to Timeout                 0 Seconds
Percent Done                    0.994736842105263157894736842105263157e1+/-0.503e-29%