Nothing
## =============================================================================
# Example 6 from Shampine et al.
#
# This is Example 2 from M. Kubicek et alia, Test examples for comparison
# of codes for nonlinear boundary value problems in ordinary differential
# equations, B. Childs et al., eds., Codes for Boundary-Value Problems in
# Ordinary Differential Equations, Lecture Notes in Computer Science #76,
# Springer, New York, 1979. This example shows how to deal with a singular
# coefficient arising from reduction of a partial differential equation to
# an ODE by symmetry. Also, for the physical parameters considered here,
# the problem has three solutions.
## =============================================================================
catalyst <- function (x, y, parms) {
with (as.list(parms),{
dydx <- c(y[2],0)
tmp <- f^2 * y[1] * exp(g*b*(1-y[1])/(1+b*(1-y[1])))
if (x == 0) dydx[2] <- 1/3*tmp
else dydx[2] <- -(2/x)*y[2] + tmp
return(list(dydx))
})
}
# Define the physical parameters for this problem.
parms <- c(
f = 0.6 ,
g = 40 ,
b = 0.2 )
yini <- c(y = NA, dy = 0)
yend <- c(y = 1, dy = NA)
x <- seq(0, 1, by = 0.05)
## =============================================================================
## three solutions, found with different initial guesses
## =============================================================================
xguess <- c(0,1)
yguess <- matrix(data = 1, nr = 2, nc = 2)
Sol <- bvptwp(func = catalyst, x = x,
yini = yini, yend = yend,
parms = parms, xguess = xguess, yguess = yguess)
plot(Sol, which = "y", type = "l", ylim = c(0, 1))
yguess <- matrix(data = 0.5, nr = 2, nc = 2)
Sol2 <- bvptwp(func = catalyst, x = x,
yini = yini, yend = yend,
parms = parms, xguess = xguess, yguess = yguess)
lines(Sol2[,c("x", "y")])
yguess <- matrix(data = 0.0, nr=2,nc=2)
Sol3 <- bvptwp(func = catalyst, x = x,
yini = yini, yend = yend,
parms = parms, xguess = xguess, yguess = yguess)
lines(Sol3[,c("x", "y")])
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.