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Reference.org
Nine-point stencil
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<p>In <a href="/facts/Numerical_analysis/QT9cYa9z">numerical analysis</a>, given a <a href="/facts/Square_grid/3ym86mvv">square grid</a> in two dimensions, the nine-point stencil of a point in the grid is a <a href="/facts/Stencil_(numerical_analysis)/rNIq2e37">stencil</a> made up of the point itself together with its eight "neighbors". It is used to write <a href="/facts/Finite_difference/aY1txFhj">finite difference</a> approximations to <a href="/facts/Derivative/7Ito70Dh">derivatives</a> at grid points. It is an example for <a href="/facts/Numerical_differentiation/vlbI7vhL">numerical differentiation</a>. This stencil is often used to approximate the <a href="/facts/Laplacian/kov9u3PT">Laplacian</a> of a function of two variables. </p>