https://github.com/cran/pracma
Tip revision: 03698027c2d84118bd0c53c4a9a5b5d23676f388 authored by HwB on 01 October 2012, 00:00:00 UTC
version 1.2.0
version 1.2.0
Tip revision: 0369802
laplacian.Rd
\name{laplacian}
\alias{laplacian}
\title{
Laplacian Operator
}
\description{
Numerically compute the Laplacian of a function.
}
\usage{
laplacian(f, x0, h = 1e-4, ...)
}
\arguments{
\item{f}{univariate function of two variables.}
\item{x0}{point in \eqn{R^n}.}
\item{h}{step size.}
\item{...}{variables to be passed to \code{f}.}
}
\details{
Computes the Laplacian operator \eqn{f_{xx} + f_{yy}}
based on the three-point central difference formula, expanded to this
special case.
Assumes that the function has continuous partial derivatives.
}
\value{
Real number.
}
\author{
HwB <hwborchers@googlemail.com>
}
\references{
Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab.
Second edition, Prentice Hall.
}
\seealso{
\code{\link{fderiv}}, \code{\link{hessian}}
}
\examples{
f <- function(x) x[1]^2 + 2*x[1]*x[2] + x[2]^2
laplacian(f, c(1,1))
}
\keyword{ math }