Journal Publications:
Submitted
M. K. Singh, J Hope-Collins, C.J. Cotter, D. Crisan: Data assimilation using a global Girsanov nudged particle filter, Statistics and Computing (submitted), arXiv preprint arXiv:2507.17685
D.D. Holm, M.K. Singh, O. D. Street: A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations, Proceedings of the Royal Society A(submitted), arXiv preprint arXiv:2507.14264
D.D. Holm, M.K. Singh: Multiscale geodesic flows, Physics Review Letters(submitted), arXiv preprint arXiv:2507.05018
Accepted
M. K. Singh and S. Natesan; Richardson extrapolation technique for singularly perturbed system of parabolic partial differential equations with exponential boundary layers, Applied Mathematics and Computation (2018).
M. K. Singh and S. Natesan; Numerical analysis of singularly perturbed system of parabolic convection-diffusion problem with regular boundary layers. Differential Equation and Dynamical System (2019).
M. K. Singh and S. Natesan; A parameter-uniform hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems, International Journal of Computer Mathematics (2019).
M. K. Singh and S. Natesan; Numerical solution of 2D singularly perturbed reaction-diffusion system with multiple scales. Computers & Mathematics with Applications (2020).
M. K. Singh, G. Singh and S. Natesan; A unified study of superconvergence analysis of the Galerkin FEM for singularly perturbed systems of multiscale nature. Journal of Applied Mathematics and Computing (2021).
M. K. Singh; A discrete-ordinate weak Galerkin method for radiative transfer equation. Applied Numerical Mathematics (2024).
S. Frei and M. K. Singh; An Implicitly Extended Crank–Nicolson Scheme for the Heat Equation on a Time-Dependent Domain. Journal of Scientific Computing (2024)
S. Ganesan and M. K. Singh; Operator-splitting finite element method for solving the radiative transfer equation. Numerical Algorithms (2024)
Book Chapter:
C. Cotter, D. Crisan and M. K. Singh; Data assimilation for the stochastic Camassa-Holm equation using particle filtering: a numerical investigation, Stochastic Transport in Upper Ocean Dynamics III. STUOD 2023. Mathematics of Planet Earth arXiv preprint arXiv:2402.06927.
Conference Publications:
M. K. Singh and S. Natesan; A finite element super convergence approximations for singularly perturbed system of convection-diffusion problems, AIP Conference Proceedings, (2018).
C. Cotter, D. Crisan and M. K. Singh; The GONG Particle Filter: A Novel Framework for Data Assimilation in Stochastic PDEs, CASML 2024, IISc Bangalore, (2024)