My research lies in Numerical Functional Analysis and Integral Equations. I focus on the analysis of approximate solutions to integral equations and eigenvalue problems, particularly developing higher-order numerical schemes based on projection methods for solving kernel-based integral equations of the second kind. I am also exploring Partial Differential Equations using FDM and FEM.
[1] G. Rakshit, S. K. Shukla, A. S. Rane, A note on improvement by iteration for the approximate solutions of second kind Fredholm integral equations with Green’s kernels, Journal of Analysis, 33: 1599–1621, (2025). DOI: 10.1007/s41478-025-00882-0
[2] S. K. Shukla, G. Rakshit, Acceleration of convergence in approximate solutions of Urysohn integral equations with Green’s kernels, Mathematics and Computers in Simulation, 240: 681-697 (2026). DOI: 10.1016/j.matcom.2025.07.044
[3] S. K. Shukla, G. Rakshit, A. S. Rane, Projection-based approximations for eigenvalue problems of Fredholm integral operators with Green's kernels, Accepted for publication in Numerical Algorithms, (2026). DOI: 10.48550/arXiv.2602.16191
[4] S. K. Shukla, A note on superconvergence in projection-based approximations of eigenvalue problems for compact integral operators, 2026. [Under preparation]
[5] S. K. Shukla, G. Rakshit, Projection-based discrete approximation methods for approximate solutions of Fredholm integral equations and eigenvalue problems, 2026. [Under preparation]
[1] Fractals and the Cantor Set (2021)
I have given a talk/presentation on the topic Fractals and the Cantor Set on December 22, 2021 at Rajiv Gandhi Institute of Petroleum Technology, Jais.
Link of Document: Fractals_and_the_Cantor_set
[2] Extension theorems for Sobolev spaces (2022)
I have given a talk/presentation on the topic Extension theorems for Sobolev spaces on March 28, 2022 at Rajiv Gandhi Institute of Petroleum Technology, Jais.
Link of Document: Extension_theorem_for_Sobolev_spaces
[3] Improvement by iteration for the approximate solutions of second kind Fredholm integral equations with Green’s kernels (2025)
I have given a talk on my published article "A note on improvement by iteration for the approximate solutions of second kind Fredholm integral equations with Green’s kernels" in a conference NCCGAML 2025 on April 18, 2025 at Institute of Chemical Technology, Mumbai, Maharashtra, India.
Link of Document: NCCGAML_2025_Talk