Heat Equation via Forward-Time Central-Space

solve heat equation via forward-time central-space method

heat(u, alpha, xdelta, tdelta, n)

Arguments

u	the initial values of u
alpha	the thermal diffusivity coefficient
xdelta	the change in x at each step in u
tdelta	the time step
n	the number of steps to take

Value

a matrix of u values at each time step

Details

The heat solves the heat equation using the forward-time central-space method in one-dimension.

Examples

alpha <- 1
x0 <- 0
xdelta <- .05
x <- seq(x0, 1, xdelta)
u <- sin(x^4 * pi)
tdelta <- .001
n <- 25
z <- heat(u, alpha, xdelta, tdelta, n)