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SIAM J. Sci. Comput. 33, pp. 2318-2340 (23 pages)
A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
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Add to FacebookA 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.
© 2011 Society for Industrial and Applied Mathematics
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KEYWORDS
Keywords
finite difference methods, integral preservation, discrete variational derivatives, linearly implicit methodsAMS Subject Headings
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Received September 30, 2010
Accepted June 23, 2011
Published online September 22, 2011
Accepted June 23, 2011
Published online September 22, 2011
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