Dr. Nikhil Manoj

Nikhil Manoj, G.D. Veerappa Gowda, Sudarshan Kumar K.
A convergent MUSCL-Hancock scheme for non-local conservation laws
submitted (2025)

Nikhil Manoj, G.D. Veerappa Gowda, Sudarshan Kumar K.
A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws
Zeitschrift für angewandte Mathematik und Physik (to appear, 2026).

Nikhil Manoj, Sudarshan Kumar K.
Convergence analysis of a MUSCL-type central scheme for conservation laws with discontinuous flux
IMA Journal of Numerical Analysis (2025).

Nikhil Manoj, G.D. Veerappa Gowda, Sudarshan Kumar K.
Convergence of a second-order scheme for non-local conservation laws
ESAIM: M2AN, 57(6), 3439–3481 (2023).

I am interested in the theory and numerics of hyperbolic conservation laws, a fundamental class of partial differential equations that are used to model various physical and engineering phenomena ranging from aerodynamics to traffic flow. Since exact analytical solutions to such problems are often elusive, developing efficient approximation techniques is crucial. My research focuses on the design and analysis of high-order numerical methods for these equations. Currently, I am working on developing generalized high-order finite-volume schemes with physically relevant structure-preserving properties.