Stencil (numerical analysis)

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, especially the areas of <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a> concentrating on the <a href="/facts/Numerical_partial_differential_equations/69kwj7mL">numerical solution of partial differential equations</a>, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine. Stencils are the basis for many algorithms to numerically solve <a href="/facts/Partial_differential_equation/DyPsBlv7">partial differential equations</a> (PDE). Two examples of stencils are the <a href="/facts/Five-point_stencil/9PHAJh2B">five-point stencil</a> and the <a href="/facts/Crank%25E2%2580%2593Nicolson_method/6RnaoWIP">Crank–Nicolson method</a> stencil.
Stencils are classified into two categories: <a href="/facts/Compact_stencil/ydNDY3hK">compact</a> and <a href="/facts/Non-compact_stencil/YPUsaKwd">non-compact</a>, 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.

Stencil (numerical analysis) open-in-new

Stencil (numerical analysis)