Introduction

Welcome to my homepage !!

I am currently working as Assistant Professor in the Department of Humanities and Basic Sciences at Indian Institute of Information Technology, Senapati, Manipur, since December 2024. Before this, I was working as Assistant Professor at Vellore Institute of Technology, Andhra Pradesh, India during May 2022- December 2024. Prior to this, I was an Adhoc Assistant Professor at VNIT Nagpur, INDIA.

I completed my doctoral degree in MATHEMATICS in December 2020 from Visvesvaraya National Institute of Technology Nagpur, INDIA, under the supervision of Prof. P. Pramod Chakrvarthy, Department of Mathematics, VNIT Nagpur. I mainly explore numerical solutions of differential equations.

“A little progress each day adds up to big results.”

Qualification

  • Ph.D. (Numerical Analysis) from Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 2020
    • Advisor : Prof. P. Pramod Chakravarthy
  • M.Sc. Mathematics, Central University of Rajasthan, Ajmer, 2014
  • B.Sc. Mathematics, University of Rajasthan, Jaipur, 2012

Experience

  • Assistant Professor, Indian Institute of Information Technology, Manipur, India. (December 26, 2024 - Present)
  • Assistant Professor, School of Advanced Sciences, Department of Mathematics, Vellore Institute of Technology, Andhra Pradesh, India. (May 18, 2022 - December 24, 2024)
  • Assistant Professor(Adhoc), Department of Mathematics, Visvesvaraya National Institute of Technology , Nagpur, India. (Jan 6, 2021 – May 17, 2022)

Publications

  1. K. Kumar and P.P. Chakravarthy, A new stable finite difference scheme and its error analysis for two-dimensional singularly perturbed convection-diffusion equations. Numerical Methods for Partial Differential Equations, (38)1215-1232 (2022) doi:10.1002/num.22732 (Wiley, SCIE, IF-3.9) (Citations- 7)
  2. K. Kumar, P.P. Chakravarthy, P. Das and H. Ramos, A graded mesh refinement approach for boundary layer originated in singularly perturbed time-delayed parabolic convection-diffusion problems. Mathematical Methods in the Applied Sciences, 44(16)12332-12350 (2021) (Wiley, SCIE, IF-2.9) doi:10.1002/mma.7358 (Citations- 52)
  3. K. Kumar, P.P. Chakravarthy, H. Ramos and J. Vigo-Aguiar, A stable finite difference scheme and error estimates for parabolic singularly perturbed PDEs with shift parameters. Journal of Computational and Applied Mathematics, (405)113050 (2022) (Elsevier, SCI, IF-2.4) doi:10.1016/j.cam.2020.113050 (Citations- 15)
  4. K. Kumar, P.P. Chakravarthy and J. Vigo-Aguiar, Numerical solution of time-fractional singularly perturbed convection-diffusion problem with a delay in time. Mathematical Methods in the Applied Sciences, 44(4)3080-3097(2021) (Wiley, SCIE, IF-2.9) doi:10.1002/mma.6477 (Citations- 17)
  5. P.P. Chakravarthy and K. Kumar, A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs. Computational and Applied Mathematics, 39(3)140-156 (2020) (Springer, SCIE, IF-2.6) doi:10.1007/s40314-020-01170-2 (Citations- 25)
  6. P.P. Chakravarthy and K. Kumar, A class of finite difference schemes for singularly perturbed delay differential equations of second order. Turkish Journal of Mathematics, 43(3)1061-1079 (2019) (Tubitak, SCIE, IF-1) doi:10.3906/mat-1807-184 (Citations- 5)
  7. P.P. Chakravarthy and K. Kumar, A novel method for singularly perturbed delay differential equations of reaction-diffusion type. Differential Equations and Dynamical Systems, 29,723-734(2017) (Springer, SCOUPS, IF-1) doi:10.1007/s12591-017-0399-x (Citations- 17)
  8. P.P. Chakravarthy and K. Kumar, An adaptive mesh method for time dependent singularly perturbed differential-difference equations. Nonlinear Engineering, 8(1)328-339 (2019) (De Gruyter, SCOUPS) doi:10.1515/nleng-2018-0075 (Citations- 20)
  9. K. Kumar, T. Gupta, P.P. Chakravarthy and R.N. Rao, An adaptive mesh selection strategy for solving singularly perturbed parabolic partial differential equations with a small delay. Trends in Mathematics, 67-76 (2019)(Springer, SCOUPS) doi:10.1007/978-3-030-01123-9_8 (Citations- 12)
    10.

Referee

    Reviewer in International Journals
  • Applied Numerical Mathematics, Elsevier
  • Applied Mathematics & Computation, Elsevier
  • Mathematics and Computers in Simulation, Elsevier
  • Mathematical Modeling and Analysis, VGTU
  • Examples and Counterexamples, Elsevier
  • International Journal of Differential Equations, Hindawi