Jyoti Vinay Kumar

An astute and result-oriented researcher with expertise in numerical analysis, scientific computing, and simulation of complex systems. My Ph.D. thesis is entitled as “Numerical Analysis and Simulation of Stiff Reaction-Diffusion Systems and Nonlinear Wave Equations with Damping Effects,” where I developed efficient structure-preserving numerical methods for stiff reaction-diffusion systems, convection-diffusion, and wave equations with or without damping. The work emphasizes stability, efficiency, and conservation of physical properties, reflecting both technical depth and passion for advancing research.

Motivated individual with strong work ethic and working independently. Research interests include:

• Finite-difference and multiderivative time-integration methods,
• Higher-order compact schemes,
• Finite element methods (FEM) and PINNs algorithms,
• Pattern formation, wave propagation, applications in fluid dynamics, elasticity, kinetics, and mathematical biology.

1. International Travel Support to attend the workshop “Women in PDEs” at Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.

2. International Travel Support by the National Science Foundation (NSF) to present research work (poster presentation) at AWM Research Symposium-2025 hosted by the University of Wisconsin-Madison, USA.

3. DST INSPIRE Fellowship for PhD (JRF/SRF) from December 2020 to 2025 by the Department of Science and Technology (DST), India.

4. DST INSPIRE Scholarship for Higher Education (SHE) from July 2014 to 2019.

5. Qualified Joint Admission Test for Masters (JAM) in Mathematics, 2017.

6. State Award in Scout and Guide, 2013.

1. Jyoti Jaglan, V. Maurya, V. S. Yadav, M. K. Rajpoot, “Acoustic and soliton propagation using a fully discrete energy-preserving partially implicit scheme in homogeneous and heterogeneous mediums,” Computers and Mathematics with Applications, 174, 379-396 (2024), https://doi.org/10.1016/j.camwa.2024.09.033.

2. Jyoti Jaglan, A. Singh, V. Maurya, V. S. Yadav, M. K. Rajpoot, “Strong stability preserving multiderivative time marching methods for stiff reaction-diffusion systems,” Mathematics and Computers in Simulation, 225, 267-282 (2024), https://doi.org/10.1016/j.matcom.2024.05.020.

3. V. S. Yadav, V. Maurya, M. K. Rajpoot, Jyoti Jaglan, “Spatiotemporal pattern formation in stiff reaction-diffusion systems by new time marching methods,” Applied Mathematics and Computation, 431, 127299 (2022), https://doi.org/10.1016/j.amc.2022.127299.

4. M. K. Rajpoot, V. S. Yadav, Jyoti Jaglan, A. Singh, “Sound and soliton wave propagation in homogeneous mediums with the new two derivative implicit-explicit Runge-Kutta-Nyström method,” AIP Advances, 12, 075110 (2022), https://doi.org/10.1063/5.0099853.

1. Jyoti Jaglan, M. K. Rajpoot, “Computationally explicit strong stability preserving multiderivative IMEX methods for linear convection-diffusion problems,” Communicated to the Journal (2025).

2. Jyoti Jaglan, A. Singh, M. K. Rajpoot, “Space-time discretizing dispersion relation preserving schemes for inhomogeneous damped wave equations,” Communicated to the Journal (2025).

1. Jyoti Jaglan , M. K. Rajpoot, “Time-Marching Methods for Numerical Simulations of Convection-Dominated Diffusion Equations,” AWM Research Symposium 2025, 16-18 May 2025, University of Wisconsin-Madison, USA.

2. Jyoti Jaglan , M. K. Rajpoot, “Sound and soliton wave propagation in homogeneous and heterogeneous mediums with the new two-derivative IMEX Runge-Kutta-Nyström method,” International Conference on Advances in Pure & Applied Mathematics (ICAPAM) vision INDIA@2047, 08-10 February 2024, University of Delhi, Delhi, India.

3. Jyoti Jaglan, M. K. Rajpoot, “A new strong stability preserving multiderivative time marching method for stiff reaction diffusion systems,” International Conference on Computational Partial Differential Equations and Applications (ICCPDEA-2022), 06-08 September 2022, BML Munjal University, Gurugram, India.

4. Jyoti Jaglan, M. K. Rajpoot, “Wave propagation in heterogeneous media: Formulation and analysis of novel high-order energy and dispersion relation preserving schemes,” International Conference on Computational Methods in Sciences and Engineering (CMSE-2022), 22-24 April 2022, BITS Pilani, Hyderabad, India.

1. International Workshop “Women in PDEs @ Karlsruhe 2025” at Karlsruhe Institute of Technology (KIT), 23-24 October, Karlsruhe, Germany.

2. 3rd International Workshop on Advanced Topics in Mathematics (IWATM-2024), Centre for Applied Mathematics, 16-20 December 2024, IIIT Naya Raipur, India.

3. 5-Day International FDP on Advances in Non-linear Dynamics: Methods and Applications (ANDMA), VIT-AP University, 11-15 June 2024, A.P., India.

4. International Seminar on Mathematical Modeling and Turing's Pattern Formation, Department of Mathematics, School of Advanced Sciences, 11-15 September 2023, VIT Vellore, India.

5. Workshop on Scientific Computing, Department of Mathematics, DIT University, 11-15 July 2022, Uttarakhand, India.

6. International Workshop on Mathematical Modeling and Numerical Analysis, Centre for Applied Mathematics, 08-12 October 2021, IIIT Naya Raipur, India.

Real Analysis and Calculus, Linear Algebra and Complex Analysis, Differential Equations

• Reading, playing badminton, and traveling to new places.