Convergence of a second-order scheme for non-local conservation laws
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In this article, we present the convergence analysis of a second-order numerical scheme for traffic flow models that incorporate non-local conservation laws. We combine a MUSCL-type spatial reconstruction with strong stability preserving Runge-Kutta time-stepping to devise a fully discrete second-order scheme. The resulting scheme is shown to converge to a weak solution by establishing the maximum principle, bounded variation estimates and L1 Lipschitz continuity in time. Further, using a space-step dependent slope limiter, we prove its convergence to the entropy solution. We also propose a MUSCL-Hancock type second-order scheme which requires only one intermediate stage unlike the Runge-Kutta schemes and is easier to implement. The performance of the proposed second-order schemes in comparison to a first-order scheme is demonstrated through several numerical experiments.
Recommended citation: Gowda G.D.V., Kenettinkara S.K., Manoj N. (2023). "Convergence of a second-order scheme for non-local conservation laws Number 1." ESAIM: M2AN 1. 1(2).
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