Research

Publications/ Preprints

A convergent MUSCL-Hancock scheme for non-local conservation laws
Nikhil Manoj, G.D. Veerappa Gowda and Sudarshan Kumar K.
(preprint, 2025).
arXiv:2506.04176
A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws
Nikhil Manoj, G.D. Veerappa Gowda, Sudarshan Kumar K.
Zeitschrift für angewandte Mathematik und Physik (2026).
https://link.springer.com/article/10.1007/s00033-026-02742-8
Convergence analysis of a MUSCL-type central scheme for conservation laws with discontinuous flux
Nikhil Manoj and Sudarshan Kumar K.
IMA Journal of Numerical Analysis (2025).
https://doi.org/10.1093/imanum/draf136
Convergence of a second-order scheme for non-local conservation laws
Nikhil Manoj, G.D. Veerappa Gowda and Sudarshan Kumar K.
ESAIM: M2AN, 57(6), 3439–3481 (2023).
https://www.esaim-m2an.org/articles/m2an/abs/2023/06/m2an230129/m2an230129.html

Numerical approximation of conservation laws with non-local and discontinuous fluxes
Ph.D. thesis, (2025).

A provably convergent MUSCL-type central scheme for conservation laws with discontinuous flux
Hyperbolic Problems: Theory, Numerics and Applications (HYP2026),
University of Stuttgart, Germany, May 25–29, 2026.
A convergent MUSCL–Hancock scheme for nonlocal conservation laws
Contributed talk at Hyperbolic Problems: A Comprehensive Approach,
University of Würzburg, Germany, March 23–27, 2026.
On the numerical approximation of non-local conservation laws (via Zoom)
Oberseminar Mathematische Strömungsmechanik,
Institut für Mathematik, Julius-Maximilians-Universität Würzburg, Germany, Sept. 18, 2025.
Convergence of a second-order scheme for non-local conservation laws
Contributed talk at EQUADIFF-2024,
Karlstad University, Sweden.
Convergence of a second-order scheme for non-local traffic flow problems
Contributed talk at International Congress on Industrial and Applied Mathematics (ICIAM-2023),
Waseda University, Tokyo, Japan.