Roland Pulch, Abhishek Kumar Singh, Stochastic Galerkin method for linear fractional differential equations. Accepted in International Journal for Uncertainty Quantification.
Aneesh Panchal, Abhishek Kumar Singh, Vivek Kumar and Mani Mehra, SWARMESH: Swarm driven adaptive mesh for singular perturbation problems. Accepted in Swarm and Evolutionary Computation.
Abhishek Kumar Singh, Mani Mehra, and Roland Pulch, Non-local physics informed neural networks for forward and inverse problems containing non-local operators, Accepted in Neural Computing and Applications (October, 2024).
Yash Vats, Mani Mehra, Dietmar Oelz, Abhishek Kumar Singh, A new perspective for scientific modelling: Sparse reconstruction based approach for learning time-space fractional differential equations, Journal of Computational and Nonlinear Dynamics. Article Link
Shweta Kumari, Abhishek Kumar Singh, Vaibhav Mehandiratta and Mani Mehra, High order approximation to Caputo derivative on graded mesh and time-fractional diffusion equations for nonsmooth solutions, Journal of Computational and Nonlinear Dynamics. Article Link.
Abhishek Kumar Singh and Mani Mehra, An algorithm to estimate parameter in M\''untz-Legendre polynomial approximation for the numerical solution of stochastic fractional integro-differential equation, Journal of Applied Mathematics and Computing, 69(3), 2675-2694. Article Link.
Abhishek Kumar Singh and Mani Mehra, Difference methods for stochastic space fractional diffusion equation driven by additive space–time white noise via Wong–Zakai approximation, Journal of Mathematical Chemistry, 61(1), 47-74. Article Link.
Abhishek Kumar Singh, Mani Mehra and Vaibhav Mehandiratta, Numerical solution of variable order stochastic fractional integro-differential equation with a collocation method based on M\''untz Legendre polynomial, Mathematical Methods in the Applied Sciences, 45(13), 8125-8141. Article Link.
Abhishek Kumar Singh and Mani Mehra, Wavelet collocation method based on Legendre polynomials and its application in solving the stochastic fractional integro-differential equations, Journal of Computational Science, 51, pp. 101342. Article Link.
Abhishek Kumar Singh, Mani Mehra and Samarth Gulyani, Learning parameters of a system of variable order fractional differential equations, Numerical Methods for Partial Differential Equations, 39(3), pp. 1962-1976. Article Link.
Abhishek Kumar Singh, Mani Mehra and Samarth Gulyani, A modified variable-order fractional SIR model to predict the spread of COVID-19 in India, Mathematical Methods in the Applied Sciences, 46(7), pp. 8208-8222. Article Link . This paper was the most downloaded during its first 12 months of publication.
Abhishek Kumar Singh, A. K. Singh and S. Roy, Analysis of mixed convection in water boundary layer flows over a moving vertical plate with variable viscosity and Prandtl number, International Journal of Numerical Methods for Heat & Fluid Flow, 29. Article Link
Abhishek Kumar Singh, Mani Mehra and A. A. Alikhanov, Data-Driven Discovery of Time Fractional Differential Equations. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13351. Springer, Cham. Article Link
Abhishek Kumar Singh and Mani Mehra, Analytic and Numerical Solutions of Space-Time Fractional Diffusion Wave Equations with Different Fractional Order. In: Paszynski M., Kranzlm¨uller D., Krzhizhanovskaya V.V., Dongarra J.J., Sloot P.M.A. (eds) Computational Science – ICCS 2021. ICCS2021. Lecture Notes in Computer Science, vol 12742. Springer, Cham. Article Link
Abhishek Kumar Singh and Mani Mehra, Uncertainty Quantification in Fractional Stochastic Integro-Differential Equations Using Legendre Wavelet Collocation Method. In: Krzhizhanovskaya V. et al. (eds) Computational Science – ICCS 2020. ICCS 2020. Lecture Notes in Computer Science, vol 12138. Springer, Cham. Article Link
Ritu Kumari, Mani Mehra, Abhishek Kumar Singh, Fractional quadrature rule and using its exactness for the M\"untz-Legendre scaling functions for solving fractional differential equations.
Abhishek Kumar Singh, Mani Mehra and Anatoly A. Alikhanov, Modified least squares method and a review of its applications in machine learning and fractional differential equations.
Abhishek Kumar Singh and Mani Mehra, Legendre wavelet collocation method for stochastic fractional integro-differential equation.