Currently, I am working as an Assistant Professor at the Department of Mathematical Sciences, Rajiv Gandhi Institute of Petroleum Technology Jais Amethi. I have been with the RGIPT Jais since December 2016. Prior to joining the RGIPT Jais, I worked as a NBHM postdoctoral fellow at the Indian Institute of Technology Kanpur, from February 2001 6-December 2016. I received Ph D degree in Mathematics from the Indian Institute of Technology, Kanpur in 2015 and obtained an M Sc in Mathematics from the University of Allahabad in 2007.
Zhang, Shengliang, Zhengjie Sun, and Alpesh Kumar. "Meshless symplectic and multi-symplectic scheme for the coupled nonlinear Schrödinger system based on local RBF approximation." Computers & Mathematics with Applications 134 (2023): 16-32.
Akanksha Bhardwaj, Alpesh Kumar, and A.K., Tiwari, An RBF Based Finite Difference Method for the Numerical Approximation of Multi-term Nonlinear Time Fractional Two Dimensional Diffusion-Wave Equation. Int. J. Appl. Comput. Math 8(2), 84 (2022).
Akanksha Bhardwaj, Alpesh Kumar, A meshless method for time fractional nonlinear mixed diffusion and diffusion-wave equations. Applied Numerical Mathematics 160 (2021): 146-165.
Alpesh Kumar, Akanksha Bhardwaj, Shruti Dubey, A local meshless method to approximate the time-fractional telegraph equation. Engineering with Computers 37, (2021): 3473–3488
Akanksha Bhardwaj, Alpesh Kumar, A numerical solution of time-fractional mixed diffusion and diffusion-wave equation by an RBF-based meshless method. Engineering with Computers
Akanksha Bhardwaj, Alpesh Kumar, Numerical solution of time fractional tricomi-type equation by an rbf based meshless method. Engineering Analysis with Boundary Elements 118 (2020): 96-107.
Alpesh Kumar, and Akanksha Bhardwaj, A local meshless method for time fractional nonlinear diffusion wave equation. Numerical Algorithms 85, (2020): 1311–
Akanksha Bhardwaj, K.P Tripathi, and Alpesh Kumar. A Local Meshless Method for a Multi-term Time Fractional Non-linear Diffusion Equation. In: Awasthi, A., John, S.J., Panda, S. (eds) Computational Sciences - Modelling, Computing and Soft Computing. CSMCS (2020). Communications in Computer and Information Science, vol 1345. Springer, Singapore. https://doi.org/10.1007/978-981-16-4772-7_5
Alpesh Kumar, Akanksha Bhardwaj, and B.V.Rathish Kumar, A local meshless method for time fractional diffusion wave equation. Computer & Mathematics with Applications, 78(6) (2019), 1851-1861.
Alpesh Kumar, and B.V. Rathish Kumar, A RBF based finite difference method for option pricing under regime-switching jump-diffusion model. International Journal for Computational Methods in Engineering Science & Mechanics, 20(5) (2019), 451-459.
Mohan K Kadalbajoo, Alpesh Kumar, and Lok Pati Tripathi, Radial-basis-function-based finite difference operator splitting method for pricing American options. International Journal of Computer Mathematics, 95 (11) (2018), 2343-2359
M K Kadalbajoo, Lok Pati Tripathi, and Alpesh Kumar, An Error Analysis of a Finite Element Method with IMEX-Time Semidiscretizations for Some Partial Integro-differential Inequalities Arising in the Pricing of American Options. SIAM Journal on Numerical Analysis, 55 (2) (2017), 869-891.
Mohan K Kadalbajoo, Alpesh Kumar, and Lok Pati Tripathi, A radial basis function based implicit–explicit method for option pricing under jump-diffusion models. Applied Numerical Mathematics, 110 (2016), 159-173.
Alpesh Kumar, Lok Pati Tripathi, and Mohan K Kadalbajoo, A numerical study of Asian option with radial basis functions based finite differences method. Engineering Analysis with Boundary Elements, 50 (2015), 1-7.
Mohan K Kadalbajoo, Lok Pati Tripathi , and Alpesh Kumar, Second Order Accurate IMEX Methods for Option Pricing Under Merton and Kou Jump-Diffusion Models. Journal of Scientific Computing, 65(3) (2015): 979-1024.
Mohan K Kadalbajoo, Alpesh Kumar, and Lok Pati Tripathi, Application of the local radial basis function-based finite difference method for pricing American options. International Journal of Computer Mathematics, 92 (8) (2015), 1608 -1624.
Mohan K Kadalbajoo, Alpesh Kumar, and Lok Pati Tripathi, A radial basis function based finite difference method for wave equation with an integral condition. Applied Mathematics and Computation, 253(2015), 8–16.
Mohan K Kadalbajoo, Alpesh Kumar, and Lok Pati Tripathi, An efficient numerical method for pricing option under jump diffusion model. International Journal of Advances in Engineering Sciences and Applied Mathematics,7(3) (2015) 114-123
Mohan K Kadalbajoo, Alpesh Kumar, and Lok Pati Tripathi, Application of radial basis function with L-stable Padé time marching scheme for pricing exotic option. Computers & Mathematics with Applications, 66(4) (2013), 500-511.
Alpesh Kumar, Lok Pati Tripathi, and Mohan K Kadalbajoo, A numerical study of european options under merton's jump-diffusion model with radial basis function based finite differences method. Neural, Parallel & Scientific Computations, 21(3-4) (2013), 293-304.
Mohan K Kadalbajoo, Lok Pati Tripathi , and Alpesh Kumar, A cubic B-spline collocation method for a numerical solution of the generalized Black–Scholes equation. Mathematical and Computer Modelling 55, no. 3-4 (2012): 1483-1505.
Ph D Student
Deepak Kumar Yadav
Ph D Student
Ph D Student