Total variation diminishing nonstandard finite difference schemes for conservation laws

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Anguelov, Roumen
Lubuma, Jean M.-S.
Minani, Froduald

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Elsevier

Abstract

Nonstandard finite difference schemes for conservation laws preserving the property of diminishing total variation of the solution are proposed. Computationally simple implicit schemes are derived by using nonlocal approximation of nonlinear terms. Renormalization of the denominator of the discrete derivative is used for deriving explicit schemes of first or higher order. Unlike the standard explicit methods, the solutions of these schemes have diminishing total variation for any time step-size.

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Keywords

Nonstandard finite difference method, Total variation diminishing

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Citation

R. Anguelov, et al., Total variation diminishing nonstandard finite difference schemes for conservation laws, Mathematical and Computer Modelling (2009), doi:10.1016/j.mcm.2009.08.038