pracma (version 1.7.9)

fornberg: Fornberg's Finite Difference Approximation

Description

Finite difference approximation using Fornberg's method for the derivatives of order 1 to k based on irregulat grid values.

Usage

fornberg(x, y, xs, k = 1)

Arguments

x

grid points on the x-axis, must be distinct.

y

discrete values of the function at the grid points.

xs

point at which to approximate (not vectorized).

k

order of derivative, k<=length(x)-1< code=""> required.

Value

• Returns a matrix of size (length(xs)), where the (k+1)-th column gives the value of the k-th derivative. Especially the first column returns the polynomial interpolation of the function.

Details

Compute coefficients for finite difference approximation for the derivative of order k at xs based on grid values at points in x. For k=0 this will evaluate the interpolating polynomial itself, but call it with k=1.

References

LeVeque, R. J. (2007). Finite Difference Methods for Ordinary and Partial Differential Equations. Society for Industrial and Applied Mathematics (SIAM), Philadelphia.

See Also

neville, newtonInterp

Examples

x <- 2 * pi * c(0.0, 0.07, 0.13, 0.2, 0.28, 0.34, 0.47, 0.5, 0.71, 0.95, 1.0)
y <- sin(0.9*x)
xs <- linspace(0, 2*pi, 51)
fornb <- fornberg(x, y, xs, 10)
matplot(xs, fornb, type="l")
grid()