A general framework for deriving integral preserving numerical methods for PDEs
Numerical Analysis
2011-05-05 v2
Abstract
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.
Cite
@article{arxiv.1009.3151,
title = {A general framework for deriving integral preserving numerical methods for PDEs},
author = {Morten Dahlby and Brynjulf Owren},
journal= {arXiv preprint arXiv:1009.3151},
year = {2011}
}
Comments
25 pages, 6 figures