Spatial discretization of partial differential equations with integrals

Details Spatial discretization of partial differential equations with integrals Spatial discretization of partial differential equations with integrals

1998-08-26

arxiv.org/abs/math/9808109v1

Mathematics

Numerical Analysis

24 pages, LaTeX source

Scientific paper

We consider the problem of constructing spatial finite difference approximations on a fixed, arbitrary grid, which have analogues of any number of integrals of the partial differential equation and of some of its symmetries. A basis for the space of of such difference operators is constructed; most cases of interest involve a single such basis element. (The ``Arakawa'' Jacobian is such an element.) We show how the topology of the grid affects the complexity of the operators.

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