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Contributed talk at ICIAM 2023, Waseda University.
Presenting our work at Waseda University, Tokyo 
EQUADIFF-2024, Karlstad University, Sweden
Attending EQUADIFF-2024 
NCM workshop on Numerical Methods for Partial Differential Equations (2024), Indian Institute of Petroleum and Energy (IIPE), Visakhapatnam
At National Centre for Mathematics workshop held at IIPE Visakhapatnam. Honored to share a moment with Prof. G.D. Veerappa Gowda. 
publications
A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws
Published:
A fully discrete, provably positive second-order scheme is proposed for a general system of non-local conservation laws in multiple spatial dimensions.
Convergence analysis of a MUSCL-type central scheme for conservation laws with discontinuous flux
Published:
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.
A MUSCL-Hancock scheme for non-local conservation laws
Published:
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.