Rakesh Kumar

About

Hi, I'm [Rakesh], an Assistant Professor at [Department of Mathematics], [Mahindra University]. Prior to that I worked as Post-Doctoral Fellow at [School of Mathematics, IISER-TVM] and [Tata Institute of Fundamental Research, Center of Applicable Mathematics (TIFR-CAM), Bangalore]. I have received my Ph.D in Mathematics from Department of mathematics, Indian Institute of Technology, Bombay. My Research work includes the development of numerical schemes for hyperbolic conservation Laws. In particular, I am interested in Weighted Essentially Non-Oscillatory (WENO), Discontinuous Galerkin (DG) and hybrid methods. In recent paper, we have developed constraint preserving Discontinuous Galerkin methods for Ideal Magnetohydrodynamics equation.

Employment

• Mahindra University Assistant Professor
  2025 - Present
• IISER Thiruvananthapuram Library Research Scientific staff
  2021 - 2024
• TIFR Centre for Applicable Mathematics
  2016 - 2021

Education

• Indian Institute of Technology Bombay Ph. D
  2010 - 2016

Projects & Funding

Projects & funding information is unavailable.

Publications (20)

• Hybrid LUP-WENO scheme for hyperbolic systems of conservation laws with troubled cell detection
  Physica Scripta 2026 DOI: 10.1088/1402-4896/ae9efa
  +Save
• Spectral analysis of higher-order cell-node and central compact finite difference schemes with SSPRK3 time integration for one- and two-dimensional convection-dispersion equations
  Computers & Mathematics with Applications 2026 DOI: 10.1016/j.camwa.2026.07.010
  +Save
• S-PINN: physics-informed neural networks for solving weakly hyperbolic systems
  Physica Scripta 2025 DOI: 10.1088/1402-4896/ae2391
  +Save
• Compact Finite Difference Scheme for Some Sobolev Type Equations with Dirichlet Boundary Condition
  Journal of Computational Mathematics 2025 DOI: 10.4208/jcm.2509-m2024-0296
  +Save
• Hybrid finite difference WENO schemes for the ten-moment Gaussian closure equations with source term
  Wave Motion 2025 DOI: 10.1016/j.wavemoti.2025.103614
  +Save
• Hybrid CBSQI‐WENO Schemes for Convection‐Diffusion Problems
  International Journal for Numerical Methods in Fluids 2025 DOI: 10.1002/fld.5380
  +Save
• WENO smoothness indicator based troubled‐cell indicator for hyperbolic conservation laws
  International Journal for Numerical Methods in Fluids 2024 DOI: 10.1002/fld.5237
  +Save
• Multi-level WENO schemes with an adaptive characteristic-wise reconstruction for system of Euler equations
  Computers & Fluids 2022 DOI: 10.1016/j.compfluid.2022.105386
  +Save
• A new fifth order finite difference WENO scheme to improve convergence rate at critical points
  Wave Motion 2022 DOI: 10.1016/j.wavemoti.2021.102859
  +Save
• Globally divergence-free DG scheme for ideal compressible MHD
  Communications in Applied Mathematics and Computational Science 2021 DOI: 10.2140/camcos.2021.16.59
  +Save