Research

Published research papers

1. Mukul Dwivedi and Tanmay Sarkar, Fully discrete finite difference schemes for the Fractional Korteweg-de Vries equation, J. Sci. Comput., 101 (2) (2024), 32 pp. (arxiv)

2. Mukul Dwivedi and Tanmay Sarkar, Stability and Convergence analysis of a Crank-Nicolson Galerkin scheme for the fractional Korteweg–de Vries equation, SMAI J. Comput. Math., 10 (2024), 107– 139. (arxiv)

3. Tanmay Sarkar, Optimal error estimates of an IPDG scheme for the resistive magnetic induction equation, Partial Differ. Equ. Appl., 4 (4) (2023), 33pp. (link)

4. Rajib Dutta, and Tanmay Sarkar, Operator splitting for the fractional Korteweg de-Vries equation, Numer. Methods Partial Differential Equations, 37(6) (2021), 3000–3022. (link)

5. Ujjwal Koley, Deep Ray, and Tanmay Sarkar, Multilevel Monte Carlo Finite Difference Methods for Degenerate Fractional Convection-Diffusion Equations with Random Input Data, SIAM/ASA J. Uncertain. Quantif., 9(1), (2021), 65–105. (arxiv)

6. Tanmay Sarkar, A priori error analysis of a discontinuous Galerkin scheme for the magnetic induction equation, Computational Methods in Applied Mathematics, 20 (1), (2020), 121–140. (link)

7. Tanmay Sarkar and Praveen Chandrashekar, Stabilized discontinuous Galerkin scheme for the magnetic induction equation, Applied Numerical Mathematics, Vol. 137 (2019), 116–135. (link)

8. Alexander Keimer, Günter Leugering, and Tanmay Sarkar, Analysis of a system of non-local balance laws with weighted Work in progress, Journal of Hyperbolic Differential Equations, 15(3) (2018), 375–406. (link).

9. Tanmay Sarkar, Interior penalty discontinuous Galerkin method for magnetic induction equation with resistivity, Applied Mathematics and Computation, Vol. 314 (2017), 212–227. (link)

10. Tanmay Sarkar, A numerical study on a nonlinear conservation law model pertaining to manufacturing system, Indian J. Pure and Appl. Math., 47(4) (2016), 655–671. (link)

11. Tanmay Sarkar, Sensitivity analysis for an optimal control problem of production system based on hyperbolic conservation law, J. Nonlinear Anal. Optim. Theory and Applications, 6(1) (2015), 27–39.

12. Tanmay Sarkar, Comment on: ”Traveling wave solutions for fifth-orderKdV type equations with time-dependent coefficients”[Commun Nonlinear Sci Numer Simulat 19 (2014) 404-408], Commun. Nonlinear Sci. Numer. Simulat., 23(1) (2015), 17–20.

13. Tanmay Sarkar and S. Sundar, Nonlinear conservation law model for production network considering yield loss, J. Nonlinear Sci. Appl., 7(3) (2014): 205 – 217.

14. Tanmay Sarkar and S. Sundar, On existence and stability analysis of a nonlinear conservation law model appearing in production system, Nonlinear Stud., 21(2) (2014): 339 – 347.

15. Tanmay Sarkar and S. Sundar, Conservation law model of serial supply chain network incorporating various velocity forms, Int. J. Appl. Math., 26(3) (2013): 363 – 377.

Preprints

1. Nitesh Kumar, Tanmay Sarkar and Manmohan Vashisth, Stable determination of a time-dependent matrix potential for a wave equation in an infinite waveguide, Submitted.

2. Nitesh Kumar, Tanmay Sarkar and Manmohan Vashisth, Boundary determination of coefficients appearing in a perturbed weighted p-Laplace equation, Submitted. (arxiv)

3. Mukul Dwivedi and Tanmay Sarkar, Convergence of a conservative Crank-Nicolson finite difference scheme for the KdV equation with smooth and non-smooth initial data, Submitted. (arxiv)

4. Mukul Dwivedi and Tanmay Sarkar, Local Discontinuous Galerkin method for fractional Korteweg-de Vries equation, Submitted. (arxiv)

5. Mukul Dwivedi and Tanmay Sarkar, A Local discontinuous Galerkin method for the Benajamin-Ono equation, Submitted. (arxiv)

Research Projects

• SERB (MATRICS) projects on Optimal control for nonlinear conservation laws involving fractional Laplacian.

(Duration: 2022 - 25).

Research Visits and Talks

• Delivered a series of lectures in the workshop 'Fundamentals of Differential Equations with Applications to Real-World Problems' during 8 - 13 July, 2024 at Jaypee University of Information Technology (JUIT), Waknaghat, HP.

(Talk title: Advection equation, Riemann Problems with applications).

• Delivered a series of lectures in 'AIS on Hyperbolic conservation laws' during 27th May to 15th June, 2024 at NISER Bhubaneswar.

(Talk title: Numerical methods of Hyperbolic conservation laws).

• Mathematics Colloquium at Indian Institute of Technology Jammu on April 10, 2024

(Talk title: Transport Equation: weak solution perspective).

• Delivered a lecture in National Conference on "Recent Advances in Mathematics" on March 27-28, 2024 at Central University of Jammu.

(Talk title: Error estimates for a DG scheme of magnetic induction equation).

• Delivered two talks in a workshop at University of Jammu, 19-20 January, 2023.

(Talk title: Well-posedness of the Evolution equation).

• Delivered several refresher course talks in University of Jammu (2022-23).

• Delivered a talk in International Conference on 'Advances in Scientific Computing' during November 28 - 30, 2016 at IIT Madras.

(Talk title: Stabilized discontinuous Galerkin method for the magnetic induction equation).

• Delivered a talk in the In-House Symposium at TIFR Centre for Applicable Mathematics, Bangalore  on August 4, 2015.

(Talk title: Flux Identification Problem for Scalar Conservation Laws).

• Delivered a talk on 28th Annual Conference of Ramanujan Mathematical Society (RMS), 2013.

(Talk title: Modelling of Supply Chain Network through PDEs).

• Delivered a talk on 130th Science Club Meet, Institute of Mathematical Sciences (IMSc), Chennai, 2012.

(Talk title: Introduction to Network Models of Supply Chain).