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Dr. Kapil Kant

Dr. Kapil Kant

Designation: Assistant Professor

Department: Engineering Sciences

Honour: Postdoc (IIT Kanpur), Ph.D. (IIT Kharagpur, Mathematics)

Experience: 3+ years

Area of Interest: Numerical Functional Analysis, Approximation Theory

Office Phone : 07512449717

Address: 108, E-Block, Department of Engineering Sciences, ABV-IIITM Gwalior

Email: kapil@iiitm.ac.in

Biography

Dr. Kapil Kant is currently working as Assistant Professor at Atal Bihari Vajpayee - Indian Institute of Information Technology & Management Gwalior. Prior to this, he was associated with the Indian Institute of Technology Kanpur as Institute Post-doc fellow for one year and three months.

He completed his Bachelor of Science in Mathematics from University of Allahabad, UP, India (2013) and his Master of Science in Mathematics at Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India (2015). He also completed his Doctor of Philosophy (Ph.D) from the Department of Mathematics at Indian Institute of Technology Kharagpur (2020). His area of research is numerical functional analysis and approximation theory.

 

Academic Positions:

1. Research Associate at IIT Kharagpur From December 1, 2020-August 18, 2021 (With Prof. Gnaneshwar Nelakanti).

2.  Institute post-doctoral fellow at IIT Kanpur From-November 1, 2021-January 20, 2023 (With Prof. BV Rathish Kumar).

3. Assistant Professor at ABV IIITM Gwalior from January 27, 2023 to till date.

 

Administrative Positions:

1. Faculty-in-charge security at ABV-IIITM Gwalior from April 2023 to till date.

 

Journal papers:

 

1. Kapil Kant, Jacobi Spectral Methods for Volterra-Urysohn Integral Equations of Second
Kind with Weakly Singular Kernels, Numerical Functional Analysis, and Optimization 40
(15) (2019), 1787–1821 (With Gnaneshwar Nelakanti).
2. Kapil Kant, Convergence analysis for derivative dependent Fredholm-Hammerstein integral
equations with Green’s kernel, Journal of Computational and Applied Mathematics,
368 (2019): 112599 (With Moumita Mandal and Gnaneshwar Nelakanti).
3. Kapil Kant Approximation methods for second kind weakly singular Volterra integral
equations, Journal of Computational and Applied Mathematics, 368 (2019): 112531 (With
Gnaneshwar Nelakanti).
4. Kapil Kant, Error Analysis of Jacobi Spectral Galerkin and Multi-Galerkin Methods for
Weakly Singular Volterra Integral Equations, Mediterranean Journal of Mathematics, 17
(2019), 20 (With Moumita Mandal and Gnaneshwar Nelakanti).
5. Kapil Kant, Galerkin and Multi Galerkin Methods for Weakly Singular Volterra-Hammerstein
Integral Equations and their Convergence Analysis, Computational and Applied Mathematics
39 (2) (2020) 57 (With Gnaneshwar Nelakanti).
6. Kapil Kant, Error Analysis of Jacobi-Galerkin Method for SolvingWeakly Singular Volterra-
Hammerstein Integral Equations, International Journal of Computer Mathematics 97(12)
(2020): 2395-2420 (With Gnaneshwar Nelakanti).
7. Kapil Kant, Projection and multi-projection methods for second kind Volterra-Hammerstein
integral equation, International Journal of Nonlinear Analysis and Applications, 12 (2) (2021)
275-291 (With Moumita Mandal and Gnaneshwar Nelakanti).
8. Kapil Kant, Legendre Spectral Projection Methods for Linear Second Kind Volterra Integral
Equations with Weakly Singular Kernels, International Journal of Nonlinear Analysis
and Applications, (With Samiran Chakraborty and Gnaneshwar Nelakanti).
9. Kapil Kant, Jacobi Spectral Galerkin Methods for a Class of Nonlinear Weakly Singular
Volterra Integral Equations, Advances in Applied Mathematics and Mechanics, 13 (5) (2021)
0163-1260 (With Moumita Mandal and Gnaneshwar Nelakanti).
10. Kapil Kant, Discrete Legendre Spectral Methods for Hammerstein typeWeakly Singular
Nonlinear Fredholm Integral Equations, International Journal of Computer Mathematics, 98
(11) (2021) 2251–2267 (With Moumita Mandal and Gnaneshwar Nelakanti).
11. Kapil Kant, Eigenvalue Problem of a Weakly Singular Compact Integral Operator by
discrete Legendre Projection Methods, Journal of Applied Analysis and Computation, 11 (4)
(2021) 2090-2101 (With Moumita Mandal and Gnaneshwar Nelakanti).
12. Kapil Kant, Approximation Methods for System of Linear Fredholm Integral Equations
of Second Kind, Applied Mathematics and Computation, 403 (2021) 126173 (With Samiran
Chakraborty and Gnaneshwar Nelakanti).
13. Kapil Kant, Error Analysis of Reiterated Projection Methods for Hammerstein Integral
Equations, International Journal of Computer Mathematics, 99 (10) (2022), 2001-2017 (With
Samiran Chakraborty and Gnaneshwar Nelakanti).
14. Kapil Kant, Modified Galerkin method for Volterra-Fredholm-Hammerstein integral
equations, Computational and Applied Mathematics, DOI 10.1007/s40314-022-01945-9 (With
Payel Das and B V Rathish Kumar).
15. Kapil Kant, Approximation of Weakly Singular Non-linear Volterra-Urysohn Integral
Equations by Piecewise Polynomial Projection Methods based on Graded Mesh, Journal
of Applied Analysis and computation (Doi-10.11948/20220147 ) (With R Nigam, BVRK
and Gnaneshwar Nelakanti).
16. Kapil Kant, Convergence Analysis for Linear Fredholm and Nonlinear Fredholm Hammerstein
Integral Equations, Journal of Basic & Applied Sciences, 18, 2022, 158-165 (With
R Kumar and BVRK).
17. Kapil Kant, Superconvergence of Volterra-Urysohn integral with weakly singular kernel
by iterated Jacobi spectral multi Galerkin method, International Journal of Nonlinear
Analysis and Applications (Accepted).
18. Kapil Kant, Modified Galerkin Method for Derivative Dependent Fredholm-Hammerstein
Integral Equations of Second Kind, Advances in Applied Mathematics and Mechanics, Accepted
(With Payel Das, B V Rathish Kumar and G. Nelakanti).
19. Kapil Kant, Discrete Galerkin and iterated discrete Galerkin methods for derivative dependent
Fredholm-Hammerstein integral equations with Green’s kernel, Mediterranean
Journal of Mathematics, Accepted (With Rakesh Kumar, Samiran Chakraborty and G.
Nelakanti).

20. Kapil Kant, Spectral Projection Methods for Derivative Dependent Hammerstein Equations with Green's Kernels, Mediterranean Journal of Mathematics, Accepted (With Chafik Allouch, and Ritu Nigan).

21. Kapil Kant, Numerical solution of eigenvalue problems for a compact integral operator with Green’s kernels, Advances in Operator Theory, Accepted (With H. Bouda, Chafik Allouch, and Zakaria El Allali).

 

Grants and Funding:

1. Projection methods for integral equations, sponsored by ABV-IIITM Gwalior, India, Grant
No: 011/2023 dated 21/3/2023, Amount: Rs. 550,000/-, Duration 2 years. (P.I. Dr. Kapil
Kant, Co-PI: Prof. Joydip Dhar).

 

Selected Conferences and Talks:

1. CONTRIBUTED TALK entitled “Super convergence of Jacobi spectral methods for weakly singular Volterra Integral Equations", in Joint Mathematics Meeting (JMM) 2019 at Baltimore, MY, USA.

 

हमसे जुडे

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