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

[Radovan Omorjan]

I found out that if I define the function this way (use absolute value 
of y[1]) then the result will be correct and both solvers will work.
Could someone try to explain this to me please.

Best Regards,
Radovan

THIS WILL WORK!
-----------------------
fun <- function(x, y, p) {
   dy1 <- y[2]
   dy2 <- Pe*Da*abs(y[1])^n + Pe*y[2]
   return(list(c(dy1,dy2)))
}
--------------------------
On 5/5/2016 2:51 PM, Radovan Omorjan wrote:
> 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)
>
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