Contributed talk at ICIAM 2023, Waseda University.
Presenting our work at Waseda University, Tokyo 
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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
Convergence of a second-order scheme for non-local conservation laws
Published:
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.
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.
Analysis of a central MUSCL-type 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.
talks
teaching
Tutorials at NCM workshop
Workshop, Indian Institute of Petroleum and Energy (IIPE), Visakhapatnam, 2024
Managed tutorial sessions on numerical approximations to solutions of differential equations.
Teaching assistantship at IISER TVM
Undergraduate/ postgraduate courses, IISER Thiruvananthapuram, School of Mathematics, 2025
Courses
MAT211- Multivariable calculus
MAT111- Single variable calculus
IDC121- Mathematical Tools II
MAT314- Numerical Analysis
MAT315- Mathematical Statistics
MAT323- General Topology