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/mult2postode.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(0.1) 
x_end=c(1.0) 
$array_y_init[0 + 1] = exact_soln_y(x_start)
$glob_look_poles=true 
$glob_min_h=c(0.00000000001) 
#  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=3 
#  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)    - expt(cos(c(x)),c(2))/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-31 
y[1] (closed_form)               0.1504983355539689592218950870812956e1+/-0.171e-30 
y[1] (numeric)                   0.1504983355539689592218950870812956e1+/-0.321e-30 
absolute error                   0.0e0+/-0.492e-30 
relative error                   0.0e0+/-0.3269139144888203516369306088476179e-28%
Desired digits                   8 
Estimated correct digits         14 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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+/-0.5e-31 
y[1] (closed_form)               0.1519734751499278729300368316987046e1+/-0.245e-30 
y[1] (numeric)                   0.1519734751499278729302427413301717e1+/-0.928e-30 
absolute error                   0.2059096314671e-20+/-0.117e-29 
relative error                   0.1354905066584560005256489627395564e-18+/-0.769e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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+/-0.5e-31 
y[1] (closed_form)               0.1543666096272580425689761875261153e1+/-0.332e-30 
y[1] (numeric)                   0.1543666096272580425695441129647226e1+/-0.121e-29 
absolute error                   0.5679254386073e-20+/-0.154e-29 
relative error                   0.3679069197533349046226813739906095e-18+/-0.997e-28%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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+/-0.5e-31 
y[1] (closed_form)               0.1575823322663208644769812504589414e1+/-0.422e-30 
y[1] (numeric)                   0.1575823322663208644780528654525387e1+/-0.149e-29 
absolute error                   0.10716149935973e-19+/-0.191e-29 
relative error                   0.6800349875430355621526504201668541e-18+/-0.121e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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+/-0.5e-31 
y[1] (closed_form)               0.1614924423532965070649765848139237e1+/-0.521e-30 
y[1] (numeric)                   0.1614924423532965070666734825972888e1+/-0.186e-29 
absolute error                   0.16968977833651e-19+/-0.238e-29 
relative error                   0.1050759873736259476743460846087123e-17+/-0.147e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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+/-0.5e-31 
y[1] (closed_form)               0.1659410561380831605590406661094214e1+/-0.615e-30 
y[1] (numeric)                   0.1659410561380831605614595118656952e1+/-0.25e-29 
absolute error                   0.24188457562738e-19+/-0.311e-29 
relative error                   0.1457653586500634211799709494897303e-17+/-0.187e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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+/-0.5e-31 
y[1] (closed_form)               0.170750821427493976534581299119907e1+/-0.720e-30 
y[1] (numeric)                   0.1707508214274939765377899762447908e1+/-0.29e-29 
absolute error                   0.32086771248838e-19+/-0.362e-29 
relative error                   0.187915765093188877415555281259933e-17+/-0.212e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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+/-0.5e-31 
y[1] (closed_form)               0.175729988057532218155144261573661e1+/-0.805e-30 
y[1] (numeric)                   0.1757299880575322181591791653786462e1+/-0.339e-29 
absolute error                   0.40349038049852e-19+/-0.419e-29 
relative error                   0.2296081533713081095188038110599131e-17+/-0.238e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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]                             0.9e0+/-0.5e-31 
y[1] (closed_form)               0.1806800523673271763829168576632631e1+/-0.870e-30 
y[1] (numeric)                   0.180680052367327176387781444409415e1+/-0.39e-29 
absolute error                   0.48645867461519e-19+/-0.477e-29 
relative error                   0.2692376209999137309416302867323039e-17+/-0.264e-27%
Desired digits                   8 
Estimated correct digits         13 
Correct digits                   32 
h                                0.5e-1+/-0.1e-100 
NO POLE (given) for Equation 1
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!
diff  (  y  ,  x  ,  1  )   =  sin  (  x  )   *  cos  (  x  )   ; 
Iterations                      18 
Total Elapsed Time              36 Seconds
Elapsed Time(since restart)     35 Seconds
Time to Timeout                 19 Minutes 24 Seconds
Percent Done                    0.1055555555555555555555555555555555e3+/-0.28e-28%