## A genuinely high order total variation diminishing scheme for one-dimensional scalar conservation laws.(English)Zbl 1226.65083

The authors develop a high order accuracy total variation diminishing (TVD) scheme in the $$L^1$$-norm for one-dimensional scalar conservation laws. Numerical results for five test problems including a traffic flow model are discussed using a fifth order scheme. The advantage of the proposed high order scheme is that it satisfies strictly a maximum principle; therefore, it has better resolution than the usual TVD scheme, when the solution contains many waves, and it does not generate any unphysical solution.

### MSC:

 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 35B50 Maximum principles in context of PDEs
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