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.

Research Papers

[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, Numerical Algorithms, (2026). DOI:  10.1007/s11075-026-02369-w 

[4]  S. K. Shukla, A note on superconvergence in projection-based approximations of eigenvalue problems for compact integral operators, 2026, Preprint, (2026). DOI:  10.48550/arXiv.2603.24707 

[5]  S. K. Shukla, G. Rakshit, Projection-based discrete approximation methods for approximate solutions of Fredholm integral equations and eigenvalue problems, In preparation.

Expositions & Talks

[1] Fractals and the Cantor Set (2021) 

Presented on December 22, 2021 at Rajiv Gandhi Institute of Petroleum Technology, Jais, India.

Document: FCS_2021_Talk 

[2] Extension theorems for Sobolev spaces (2022) 

Presented on March 28, 2022 at Rajiv Gandhi Institute of Petroleum Technology, Jais, India.

Document: ETSS_2025_Talk 

[3] Approximate solutions of second kind Fredholm integral equations with Green’s kernels (2025) 

Presented at a conference NCCGAML 2025, April 18, 2025, Institute of Chemical Technology, Mumbai, India.

Document: NCCGAML_2025_Talk 

[4] Approximate solutions of Urysohn integral equations with Green’s kernels (2025) 

Presented at a conference ICNAAO 2025, December 05, 2025, Indian Institute of Technology, Jodhpur, India.

Document: ICNAAO_2025_Talk