Total variation diminishing nonstandard finite difference schemes for conservation laws
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Date
Authors
Anguelov, Roumen
Lubuma, Jean M.-S.
Minani, Froduald
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
Keywords
Nonstandard finite difference method, Total variation diminishing
Sustainable Development Goals
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