Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 33, Issue 5, Pages 2318-2340Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100810174
Keywords
finite difference methods; integral preservation; discrete variational derivatives; linearly implicit methods
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A general procedure for constructing conservative numerical integrators for time-dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time discretized version of the invariant are 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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