Explicit and implicit TVD schemes for conservation laws with Caputo derivatives

11 Oct 2016 Liu Jian-Guo Ma Zheng Zhou Zhennan

In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit upwind schemes for such equations, which are shown to be conditionally $\ell^1$ contracting and TVD... (read more)

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