A general framework for deriving integral preserving numerical methods for PDEs

Details A general framework for deriving integral preserving numerical methods for PDEs A general framework for deriving integral preserving numerical methods for PDEs

2010-09-16

arxiv.org/abs/1009.3151v2

Mathematics

Numerical Analysis

25 pages, 6 figures

Scientific paper

A general procedure for constructing conservative numerical integrators for time dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretised version of the invariant is developed for systems of partial differential equations with polynomial nonlinearities. The framework is rather general and allows for an arbitrary number of dependent and independent variables with derivatives of any order. It is proved formally that second order convergence is obtained. The procedure is applied to a test case and numerical experiments are provided.

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