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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In numerical mathematics, a non-compact stencil is a type of discretization method, where any node surrounding the node of interest may be used in the calculation. A non-compact stencil''s computational time increases with an increase of layers of nodes used. Non-compact stencils may be compared to Compact stencils. A simple way to avoid the difficulty is to add diffusion that smooths out the shock or current sheet. Higher order numerical methods (including spectral methods) tend to have less numerical diffusion than low order methods.