Spatial discretization of partial differential equations with integrals
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Dynamical Systems
Abstract
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.
Cite
@article{arxiv.math/9808109,
title = {Spatial discretization of partial differential equations with integrals},
author = {Robert I McLachlan},
journal= {arXiv preprint arXiv:math/9808109},
year = {2025}
}
Comments
24 pages, LaTeX source