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/divpostode.ode#################
diff  (  y  ,  x  ,  1  )   =   sin  (  x  )   /  cos  (  x  )    ; 
!
#BEGIN FIRST INPUT BLOCK
# Digits:=32; ELIMINATED in preodein.rb
max_terms=30 
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start=c(0.0) 
x_end=c(1.5) 
$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=1 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][1]=c(1.570796327) 
#  ELIMINATED in preodein.rb
$array_given_rad_poles[1][2]=c(0.0) 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][1]=c(0.0) 
#  ELIMINATED in preodein.rb
$array_given_ord_poles[1][2]=c(0.0) 
#  ELIMINATED in preodein.rb
#  ELIMINATED in preodein.rb
#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(2.0)    - ln(float_abs(cos(c(x))))) 
end

#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
 
 
TOP MAIN SOLVE Loop
x[1]                             0.0e0+/-0.50e-31 
y[1] (closed_form)               0.1999999999999999999999999999996783e1+/-0.911e-30 
y[1] (numeric)                   0.1999999999999999999999999999996783e1+/-0.101e-29 
absolute error                   0.0e0+/-0.1921e-29 
relative error                   0.0e0+/-0.9605000000000000000000000000024199e-28%
Desired digits                   8 
Estimated correct digits         14 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.1570796327000000000000000000000877e1+/-0.538e-29 
Order of pole (given)                             0.0e0+/-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)               0.2005008355623235309079132997721267e1+/-0.108e-30 
y[1] (numeric)                   0.2005008355623235309078923940280379e1+/-0.161e-29 
absolute error                   0.209057440888e-21+/-0.171e-29 
relative error                   0.104267615794058244831426560521966e-19+/-0.852e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.1470796327000000000000000000000949e1+/-0.536e-29 
Order of pole (given)                             0.0e0+/-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)               0.2020134773052408348925755928105683e1+/-0.135e-30 
y[1] (numeric)                   0.2020134773052408348924480454243355e1+/-0.241e-29 
absolute error                   0.1275473862328e-20+/-0.254e-29 
relative error                   0.631380578831762125367681725132212e-19+/-0.125e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.1370796327000000000000000000001071e1+/-0.534e-29 
Order of pole (given)                             0.0e0+/-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)               0.2045691655926058019453301984654094e1+/-0.181e-30 
y[1] (numeric)                   0.2045691655926058019450013843998635e1+/-0.321e-29 
absolute error                   0.3288140655459e-20+/-0.339e-29 
relative error                   0.1607349106564401305046598575233423e-18+/-0.165e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.1270796327000000000000000000001191e1+/-0.531e-29 
Order of pole (given)                             0.0e0+/-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)               0.2082229019075055429399409173994339e1+/-0.253e-30 
y[1] (numeric)                   0.2082229019075055429392985123166029e1+/-0.401e-29 
absolute error                   0.642405082831e-20+/-0.426e-29 
relative error                   0.3085179761428750171611933722070335e-18+/-0.204e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.117079632700000000000000000000128e1+/-0.529e-29 
Order of pole (given)                             0.0e0+/-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+/-0.10e-99 
y[1] (closed_form)               0.2130584240443722716787612591825988e1+/-0.356e-30 
y[1] (numeric)                   0.2130584240443722716776629517705461e1+/-0.481e-29 
absolute error                   0.10983074120527e-19+/-0.516e-29 
relative error                   0.515495886623080796230224377079989e-18+/-0.242e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.1070796327000000000000000000001493e1+/-0.526e-29 
Order of pole (given)                             0.0e0+/-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+/-0.12e-99 
y[1] (closed_form)               0.2191965169419437719670525662506479e1+/-0.441e-30 
y[1] (numeric)                   0.2191965169419437719653071938341726e1+/-0.561e-29 
absolute error                   0.17453724164753e-19+/-0.605e-29 
relative error                   0.7962591928126203085209613203453851e-18+/-0.276e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.9707963270000000000000000000000057e0+/-0.504e-30 
Order of pole (given)                             0.0e0+/-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+/-0.14e-99 
y[1] (closed_form)               0.2268085757567931100529413292614205e1+/-0.699e-30 
y[1] (numeric)                   0.2268085757567931100502776433316307e1+/-0.648e-29 
absolute error                   0.26636859297898e-19+/-0.717e-29 
relative error                   0.117442028851945662699079059318515e-17+/-0.316e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.87079632700000000000000000000002e0+/-0.509e-30 
Order of pole (given)                             0.0e0+/-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+/-0.16e-99 
y[1] (closed_form)               0.2361390746811343700739551877017128e1+/-0.982e-30 
y[1] (numeric)                   0.236139074681134370069966459730582e1+/-0.738e-29 
absolute error                   0.39887279711308e-19+/-0.836e-29 
relative error                   0.1689143559369366654349071927006186e-17+/-0.354e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.7707963270000000000000000000000219e0+/-0.514e-30 
Order of pole (given)                             0.0e0+/-0.50e-31 
Radius of convergence (ratio test) for eq  1      0.8029128404134209220626644792495769e0+/-0.432e-28 
Order of pole (ratio test)                        0.9999999999999999999999999999998599e0+/-0.5e-31 
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+/-0.18e-99 
y[1] (closed_form)               0.2475442443585814285009717936105181e1+/-0.138e-29 
y[1] (numeric)                   0.2475442443585814284950101819605031e1+/-0.834e-29 
absolute error                   0.5961611650015e-19+/-0.972e-29 
relative error                   0.240830145958848399787387507956907e-17+/-0.392e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.6707963270000000000000000000000239e0+/-0.511e-30 
Order of pole (given)                             0.0e0+/-0.50e-31 
Radius of convergence (ratio test) for eq  1      0.6987461737447068760668518722641379e0+/-0.335e-28 
Order of pole (ratio test)                        0.9999999999999999999999999999926209e0+/-0.5e-31 
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.1e1+/-0.20e-99 
y[1] (closed_form)               0.2615626470386014262147037516408842e1+/-0.195e-29 
y[1] (numeric)                   0.261562647038601426205660913893051e1+/-0.936e-29 
absolute error                   0.90428377478332e-19+/-0.113e-28 
relative error                   0.345723590513237833726773669739803e-17+/-0.432e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.570796327000000000000000000000255e0+/-0.514e-30 
Order of pole (given)                             0.0e0+/-0.50e-31 
Radius of convergence (ratio test) for eq  1      0.5945795070780175089790254644982986e0+/-0.25e-28 
Order of pole (ratio test)                        0.9999999999999999999999999993943652e0+/-0.5e-31 
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.11e1+/-0.22e-99 
y[1] (closed_form)               0.2790548077254231578323607612842124e1+/-0.289e-29 
y[1] (numeric)                   0.2790548077254231578181601677609255e1+/-0.101e-28 
absolute error                   0.142005935232869e-18+/-0.129e-28 
relative error                   0.5088818801953635563246551886313398e-17+/-0.462e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.4707963270000000000000000000003343e0+/-0.501e-30 
Order of pole (given)                             0.0e0+/-0.50e-31 
Radius of convergence (ratio test) for eq  1      0.4904128404113506847332970609207738e0+/-0.196e-28 
Order of pole (ratio test)                        0.9999999999999999999999998976041338e0+/-0.5e-31 
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.12e1+/-0.24e-99 
y[1] (closed_form)               0.301512328314065961666425318875818e1+/-0.372e-29 
y[1] (numeric)                   0.3015123283140659616426629662787734e1+/-0.106e-28 
absolute error                   0.237623525970446e-18+/-0.143e-28 
relative error                   0.7881055056658541884511239503847683e-17+/-0.474e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.3707963270000000000000000000004337e0+/-0.502e-30 
Order of pole (given)                             0.0e0+/-0.50e-31 
Radius of convergence (ratio test) for eq  1      0.3862461737446840092661318578972211e0+/-0.141e-28 
Order of pole (ratio test)                        0.9999999999999999999999465137134264e0+/-0.5e-31 
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.13e1+/-0.26e-99 
y[1] (closed_form)               0.331864009162916856660279594824668e1+/-0.719e-29 
y[1] (numeric)                   0.3318640091629168566157271766062727e1+/-0.109e-28 
absolute error                   0.445524182183953e-18+/-0.18e-28 
relative error                   0.1342490206478638409576045679485629e-16+/-0.542e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
Radius of convergence (given) for eq  1           0.2707963270000000000000000000000202e0+/-0.273e-30 
Order of pole (given)                             0.0e0+/-0.50e-31 
Radius of convergence (ratio test) for eq  1      0.2820795070780173342656540720562679e0+/-0.137e-28 
Order of pole (ratio test)                        0.9999999999999999998161197114371583e0+/-0.5e-31 
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
 
TOP MAIN SOLVE Loop
x[1]                             0.14e1+/-0.28e-99 
y[1] (closed_form)               0.377215013766969902721411068686746e1+/-0.134e-28 
y[1] (numeric)                   0.3772150137669699026168446313143126e1+/-0.115e-28 
absolute error                   0.1045664373724334e-17+/-0.249e-28 
relative error                   0.2772064566789243642516909281255444e-16+/-0.66e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
SETTING H FOR POLE
Radius of convergence (given) for eq  1           0.1707963270000000000000000000000932e0+/-0.349e-30 
Order of pole (given)                             0.0e0+/-0.50e-31 
Radius of convergence (ratio test) for eq  1      0.1779128404113506592656539950331477e0+/-0.121e-28 
Order of pole (ratio test)                        0.9999999999999746771116281728397433e0+/-0.5e-31 
Radius of convergence (three term test) for eq 1  0.1707963267948959387787557384490387e0+/-0.557e-27 
Order of pole (three term test)                   0.8905600000031211150280151211274139e-13+/-0.885e-25 
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff  (  y  ,  x  ,  1  )   =   sin  (  x  )   /  cos  (  x  )    ; 
Iterations                      34 
Total Elapsed Time              1 Minutes 27 Seconds
Elapsed Time(since restart)     1 Minutes 26 Seconds
Time to Timeout                 18 Minutes 33 Seconds
Percent Done                    0.1013038285837618104763419344609547e3+/-0.257e-25%