Abstract
Abstract A fourth-order compact finite difference scheme is presented for second-order partial differential equations. The scheme is derived for a one-dimensional non-equidistant mesh, which makes it particularly useful in problems with sharp boundary layers. The inclusion of general boundary conditions does not reduce the order of the scheme for the boundary points. The scheme is tested on a representative model equation; we shortly discuss its stability in the simplest time-dependent heat flow problem and its use in more dimensions.
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