Dr. Rakesh Kumar is an Assistant Professor in the Department of Mathematics at Mahindra University. Previously, he was a Post-Doctoral Fellow at IISER-TVM, and at the Tata Institute of Fundamental Research, Center of Applicable Mathematics (TIFR-CAM), Bangalore. He received his Ph.D. in Mathematics from Indian Institute of Technology, Bombay. His research focuses on developing numerical schemes for hyperbolic conservation laws, with particular interest in Weighted Essentially Non-Oscillatory (WENO), Discontinuous Galerkin (DG), and hybrid methods.

• Ph.D. from Department of Mathematics, Indian Institute Technology, Bombay. (2016)

• Master of Science (M. Sc), Guru Nanak Dev University, Amritsar (2003-2005)

• Bachelor of Science (B.Sc), D. A. V College Amritsar, Punjab (2000-2003)

Publications

• K. R. Arun, Asha K. Dond, Rakesh Kumar, “WENO Smoothness Indicator Based Troubled-cell Indicator for Hyperbolic Conservation Laws”. International Journal for Numerical Methods in Fluids, 96, 44-86 ,2024.

• Rakesh Kumar, Praveen Chandrashekar “Multi-level WENO Schemes with an Adaptive Characteristic-wise Reconstruction for System of Euler equations”. Computers & Fluids, 239, 2022.
• Anurag Kumar, Bhavneet Kaur, Rakesh Kumar, “A new fifth order finite difference WENO scheme to improve convergence rate at critical points.” Wave Motion, 109, 2022.

• Asha K. Dond, Rakesh Kumar, “Finite difference modified WENO schemes for hyperbolic conservation laws with non-convex flux.” International Journal for Numerical Methods in Fluids, 93, 3005-3019, 2021.
• Dinshaw S. Balsara, Rakesh Kumar, Praveen Chandrashekar, “Globally divergence-free DG scheme for ideal compressible MHD.” Communications in Applied Mathematics and Computational Science, 16(1), (2021).

• Praveen Chandrashekar, Rakesh Kumar, “Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids.” Journal of Scientific Computing, 84(39), 2020.
• Ameya D. Jagtap, Rakesh Kumar, “Kinetic theory based improved multi-level adaptive finite difference WENO schemes for compressible Euler equations.” Wave Motion, 98, 2020.
• Asha Kumari Meena, Rakesh Kumar, Praveen Chandrashekar, “Positive preserving WENO scheme of adaptive order for Ten-Moment Gaussian closure equations.” Journal of Scientific Computing, 82 (15), 2020.
• Samala Rathan, Rakesh Kumar, Ameya D. Jagtap, “L1-type smoothness indicators based WENO scheme for nonlinear degenerate parabolic equations.” Applied Mathematics and Computations, 375, 2020.
• Rakesh Kumar, Ashok chodhary, S. Baskar, “Modified cubic B-spline quasi-interpolation numerical scheme for hyperbolic conservation laws”. Applicable Analysis, 99, 158-179, 2020.

• Rakesh Kumar, Praveen Chandrashekar, “Efficient seventh order WENO schemes of adaptive order for hyperbolic conservation laws.” Computers & Fluids, 190, 49-76, 2019.

• Rakesh Kumar, Praveen Chandrashekar, “Simple smoothness indicator and multi-level adaptive order WENO scheme for hyperbolic conservation laws.” Journal of Computational Physics, 375, 1059-1090, 2018.
• Rakesh Kumar, “Adaptive semi-discrete formulation of BSQI-WENO scheme for the modified Burgers’ equation”. BIT Numerical Mathematics, 58, 103-132, 2018.

• Rakesh Kumar, S. Baskar, “B-spline quasi-interpolation based numerical methods for some Sobolev type equations”. Journal of Computational and Applied Mathematics, 292, 41-66, 2016.

• Assistant Professor, Department of Mathematics, Ecole Centrale School of Engineering, Mahindra University (January 2025 to present)

• Ad hoc faculty at the School of Data Science, Indian Institute of Science Education and Research, Thiruvananthapuram (IISER-TVM) (September 2024 to December 2024)

• Research Associate at the School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram (IISER-TVM) (February 2023 to September 2024)

• Research Scientific Staff at School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram (IISER-TVM) (March 2021 to January 2023)

• National Post-Doctoral Fellow, Tata Institute of Fundamental Research, Centre for Applicable Mathematics (March 2019 to March 2021)

• Institute Post-Doctoral Fellow, Tata Institute of Fundamental Research, Centre for Applicable Mathematics (August 2016 to March 2019)

• Numerical schemes for hyperbolic conservation laws
• Weighted Essentially Non-Oscillatory (WENO) scheme
• Discontinuous Galerkin method
• Hybrid methods
• Numerical schemes for degenerate parabolic equations
• B-spline based numerical schemes
• Positive preserving scheme