Five-point stencil

Summary

A five-point stencil is a set of five grid points used to approximate derivatives by finite differences. On a line, it is a point with two neighbours on each side, and it gives fourth-order formulas for the first and second derivative. In the plane, it is a point with its four nearest neighbours, and it gives the standard second-order approximation of the Laplacian. The planar version is the basic discretisation of the Poisson equation in the finite difference method.