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In this article, we propose a MUSCL-Hancock-type second-order scheme for the discretization of a general class of non-local conservation laws and present its convergence analysis. The main difficulty in designing a MUSCL-Hancock-type scheme for non-local equations lies in the discretization of the convolution term, which we carefully formulate to ensure second-order accuracy and facilitate rigorous convergence analysis.
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Entropy convergence analysis of second-order MUSCL-type scheme for conservation laws with discontinuous flux has remained an open problem. We propose a single-stage Nessyahu-Tadmor central scheme and provide a rigorous convergence analysis of this scheme to the entropy solution, using the theory of compensated compactness.
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A fully discrete, provably positive second-order scheme is proposed for a general system of non-local conservation laws in multiple spatial dimensions.
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Convergence analysis of a second-order MUSCL-RK type numerical scheme for traffic flow models that incorporate non-local conservation laws. A novel MUSCL-Hancock type single-stage scheme, which is computationally more efficient, is also introduced.