https://github.com/cran/pracma
Tip revision: a9b4d5f19cb88cd9d0d31fdde0d654737327d085 authored by HwB on 15 April 2012, 00:00:00 UTC
version 1.0.5
version 1.0.5
Tip revision: a9b4d5f
cranknic.R
##
## c r a n k n i c . R Crank-Nicolson
##
cranknic <- function(f, t0, t1, y0, ..., N = 100) {
stopifnot(is.numeric(y0), is.numeric(t0), length(t0) == 1,
is.numeric(t1), length(t1) == 1)
if (is.vector(y0)) {
y0 <- as.matrix(y0)
} else if (is.matrix(y0)) {
if (ncol(y0) != 1)
stop("Argument 'y0' must be a row or column vector.")
}
fun <- match.fun(f)
f <- function(t, y) fun(t, y, ...)
n <- length(y0)
y <- y0
yout <- matrix(NA, N, n)
yout[1, ] <- c(y0)
h <- (t1 - t0)/(N-1)
t <- 0
ts <- linspace(t0, t1, N)
# internal function used for root finding
cnfun <- function(w) w - y - 0.5* h * (f(t, w) + f(t, y))
m <- length(f(t0, y0))
if (m != n)
stop("Function f must return a vector the same length as 'y0'.")
# solver used for root finding
if (n == 1) solver <- fzero
else solver <- fsolve
for (i in 2:N) {
t <- ts[i]
w <- solver(cnfun, y)$x
yout[i, ] <- w
y <- w
}
if (n == 1) yout <- drop(yout)
return(list(t = ts, y = yout))
}