View source for Stencil (numerical analysis)

In [[mathematics]], especially the areas of [[numerical analysis]] concentrating on the numerical solution of partial differential equations, a '''stencil''' is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine.

== Description ==

Stencils are the basis for many algorithms to numerically solve partial differential equations (PDE). Two examples of stencils are the five-point stencil and the Crank–Nicolson method stencil.

Stencils are classified into two categories: compact and non-compact, the difference being the layers from the point of interest that are also used for calculation.

In the notation used for one-dimensional stencils n-1, n, n+1 indicate the time steps where timestep n and n-1 have known solutions and time step n+1 is to be calculated.

The spatial location of finite volumes used in the calculation are indicated by j-1, j and j+1.

== See also ==

* [[Compact stencil]]
* [[Non-compact stencil]]
* [[Numerical analysis]]
* [[Five-point stencil]]

== External links ==

* [https://en.wikipedia.org/wiki/Stencil_(numerical_analysis) Stencil (numerical analysis)] @ Wikipedia

[[Category:Mathematics]]