[R-sig-dyn-mod] bvp chemical reactor?

[Radovan Omorjan]

Hello,

This one is also one of my standard examples (chemical reactor) of two 
point boundary problem.
I tried the three functions (bvptwp(), bvpcol(), bvpshoot()) with the 
default parameters and only bvpshoot() gave the results.
Many other examples gave me no problem in solving them with all the 
three solvers, but this particular one.

QUESTION: I would be very grateful if someone could take a look at this 
example and give me a hint if there is a way to get the result with the 
other two solvers.
Just to mention that I do not have to much experience with these solvers 
and I do not know how to explain my students why these two do not work 
for this particular example.

Best Regards,
Radovan

---------------------------
require(bvpSolve)

fun <- function(x, y, p) {
   dy1 <- y[2]
   dy2 <- Pe*Da*y[1]^n + Pe*y[2]
   return(list(c(dy1,dy2)))
}

Pe <- 1
Da <- 2
n <- 0.5

# initial and ending conditions
init <- c(y <- 1, dy <- NA)
end <- c(y <- NA, dy <- 0)

# Solve bvp
#
# This will not work
#
# sol  <- bvptwp(yini = init, x = seq(0,1,len=50),
#               func = fun, yend = end)
# Error in bvpsolver(1, yini, x, func, yend, parms, order, ynames, 
xguess,  :
#                     The Expected No. Of mesh points Exceeds Storage 
Specifications.
# sol  <- bvpcol(yini = init, x = seq(0,1,len=50),
#               func = fun, yend = end)
# Error in bvpsolver(2, yini, x, func, yend, parms, order, ynames, 
xguess,  :
#                     The collocation matrix is singular for the final 
continuation problem
# This one will work
#
sol  <- bvpshoot(yini = init, x = seq(0,1,len=50),
                func = fun, yend = end, guess=-1)

x <- sol[,1]
y <- sol[,2]
par(mar=c(4,4,1.5,1.5),mex=.8,mgp=c(2,.5,0),tcl=0.3)
plot(x,y)