Specialization

Partial Differential Equations, Numerical Analysis, Numerical Linear Algebra

Email

paramjeet.singh@thapar.edu

Academic Positions

• Associate Professor, Department of Mathematics, Thapar Institute of Engineering & Technology (since July 2022)
• Assistant Professor, School of Mathematics, Thapar Institute of Engineering & Technology (July 2013 - June 2022)

Education and Research Experience

• Postdoctoral Researcher at the University of Cape Town in South Africa (August 2012 - July 2013)
• PhD (Mathematics) June 2012, Panjab University, Chandigarh. Thesis: Numerical Analysis of Transport Equations Motivated by Neuroscience

Teaching Interests

• Partial Differential Equations
• Numerical Analysis
• Functional Analysis
• Ordinary Differential Equations
• Probability and Statistics
• Mathematical Methods

Teaching resources: Numerical Mathematics

Research Interests

• Partial Differential Equations
• Numerical Modeling and Simulation
• High-Order Numerical Methods for Time Dependent Partial Differential Equations
• Mathematical Biology
• Computational Neuroscience

Sponsored Research Projects

• NBHM Major Research Project: Numerical Analysis of Tumor Growth Models using Discontinuous Galerkin Techniques (2018-21)
• SEED Project (TIET): Finite Volume Analysis of PDE Models Arising in Neuronal Variability (2014-16)

Fellowships and Awards

• French Government Sandwich Ph.D. Fellowship Award: During PhD at Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie Paris, France through French Government fellowship program (April-October, 2010). Supervisor: Professor Benoit Perthame and Professor Edwige Godlewski

Research Publications

1. M. Yadav, P. Singh. Stability analysis and numerical simulations of an age-structured tumor model, under review.
2. P. Singh, M. Yadav. Travelling-Wave reductions of a saturated activator-inhibitor reaction-diffusion-advection model, under review.
3. M. Yadav, P. Singh. Modeling tumor-immune interactions under immuno-chemotherapy: stability analysis and numerical simulation, Mathematics, 14 (2), 347, 2026.
4. M. Yadav, P. Singh. Stability analysis and numerical simulations for interactions of tumor-immune system with drug delivery, Chaos, Solitons & Fractals 192, 115971, 2025.
5. S. Sinha, P. Singh. A numerical investigation of nonlinear age-structured tumor with bidirectional proliferative and quiescent phase transitions, International Journal of Modern Physics C, 36 (09), 1-26, 2025.
6. S. Sinha, P. Singh. Optimal control for biphasic chemotaxis model of tumour growthunder chemotherapy, Acta Applicandae Mathematicae, 191 (1), 13, 2024.
7. S. Sinha, P. Singh, M. E. Koksal. Mathematical and numerical modeling of interference of immune cells in the tumour environment, Discrete Dynamics in Nature and Society, 2023(1), 9006678, 2023.
8. S. Sinha, P. Singh. Mathematical modeling and simulation of mechano-chemical effect on two-phase avascular tumor, International Journal of Modern Physics C, 33 (05), 2250063, 2022.
9. R. Jiwari, S. Singh, P. Singh. Local RBF-FD-Based mesh-free scheme for singularly perturbed convection-diffusion-reaction models with variable coefficients, Journal of Mathematics, 3119482, 2022.
10. D. Sharma, P. Singh. Discontinuous Galerkin method for a nonlinear age-structured tumor cell population model with proliferating and quiescent phases, International Journal of Modern Physics C 32 (03), 2150039, 2021.
11. D. Sharma, P. Singh. Discontinuous Galerkin approximation for excitatory-inhibitory networks with delay and refractory periods, International Journal of Modern Physics C, 31 (03), 2050041, 2020.
12. S. Kumar, P. Singh. High order WENO finite volume approximation for population density neuron model. Applied Mathematics and Computation, 356, 173–189, 2019.
13. D. Sharma, P. Singh, R.P. Agarwal, M.E. Koksal. Numerical approximation for nonlinear noisy leaky integrate-and-fire neuronal model, Mathematics 7 (4), 363, 2019.
14. P. Singh, S. Kumar, M.E. Koksal. High-order finite volume approximation for population density model based on quadratic integrate-and-fire neuron, Engineering Computations 36 (1), 84-102, 2019.
15. S. Kumar, P. Singh. High-order IMEX-WENO finite volume approximation for nonlinear age-structured population model, International Journal of Computer Mathematics 95 (1), 82-97, 2018.
16. S. Kumar, P. Singh. Finite volume approximations for size structured neuron model, Differ. Equ. Dyn. Syst. 25 (2), 251–265, 2017.
17. P. Singh, M. K. Kadalbajoo, K. Sharma. Probability density function of leaky integrate-and- fire model with Lévy noise and its numerical approximation, Numer. Anal. Appl. 9 (1), 66–73, 2016.
18. S. Kumar, P. Singh. Higher-order MUSCL scheme for transport equation originating in a neuronal model, Comput. Math. Appl. 70 (12), 2838-2853, 2015.
19. D. Garg, P. Singh. Dynamic task allocation in distributed computing systems by heuristic algorithms, Int. J. of Operational Research. 21 (4), 391-408, 2014.
20. P. Singh, K. Sharma. Numerical approximations to the transport equation arising in neuronal variability, Int. J. Pure Appl. Math. 69 (3), 341-356, 2011.
21. P. Singh, K. Sharma. Finite difference approximations for the first-order hyperbolic partial differential equation with point-wise delay, Int. J. Pure Appl. Math. 67 (1), 49-67, 2011.
22. P. Singh, K. Sharma. Numerical solution of first- order hyperbolic partial differential-difference equation with shift, Numer. Methods Partial Differential Equations 26 (1), 107-116, 2010.
23. K. Sharma, P. Singh. Hyperbolic partial differential-difference equation in the mathematical modeling of neuronal firing and its numerical solution, Appl. Math. Comput. 201 (1-2), 229-238, 2008.

Workshops Organised at Thapar Institute

1. SERB (DST) and CSIR sponsored Autumn Workshop Advances in Differential Equations : Theory and Computation (October 02-07, 2023)
2. TMS sponsored workshop Partial Differential Equations and their Applications during March 29-30, 2019.

Invited Talks and Conference Presentations

1. Delivered a talk on Numerical investigation of nonlinear age-structured tumor cell population model at 20th International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2026), during May 25 - 29, 2026 at University of Stuttgart, Germany.
2. (Invited Speaker) Mathematical and Numerical Study of Tumor-Immune Dynamics under Drug Treatment in International Conference on Mathematical Sciences and Engineering (ICMSE 2025) organized by Mizoram University, Aizawl, Mizoram during June 09-11, 2025.
3. (Invited Speaker) A Numerical Investigation of Nonlinear Age-Structured Tumor with Bidirectional Proliferative and Quiescent Phase Transitions in International Conference on Pure and Applied Mathematical Science (ICPAMS 2024) organized by Govt. College Kullu during December 03-04, 2024.
4. (Resource Person) Four Lectures on PDEs: Heat, Wave, and Laplace Equation during the National Mathematics Workshop on Emerging Areas in Differential Equations: Theory, Modelling, Discretization & Numerical Solvers (September 16-20, 2024 at Department of Mathematics, Govt. College Kullu, Himachal Pradesh)
5. (Resource Person) Two Lectures on MATLAB in DBT Sponsored Workshop on MATLAB (March 12–13, 2024 at S. D. College, Barnala, Punjab)
6. (Resource Person) Two Lectures on Computational Mathematics with MATLAB during the Online-Value Added Course/Skill Development Program (August 17-22, 2022 at Department of Mathematics, Panjab University, Chandigarh)
7. High-order finite volume approximation based on IMEX-WENO for nonlinear age-structured population model in XVII International Conference on Hyperbolic Problems Theory, Numerics, Applications (June 25-29, 2018 at Pennsylvania State University, Pennsylvania, USA)
8. Finite volume approximation of leaky integrate-and-fire model with Levy noise in ICIAM 2015 (August 10-14, 2015 in Beijing, China)
9. Finite-volume approximation of conservation laws with fading memory in the XV International Conference on Hyperbolic Problems (July 27, 2014 - August 1, 2014 in Rio de Janeiro, Brazil)
10. Numerical analysis of leaky integrate-and-fire model originating in neuronal firing at ICIAM 2011 (July 18-22, 2011 at Vancouver, BC, Canada)
11. Numerical Solution of Hyperbolic Partial Functional Differential Equation in Neuronal Variability at Indo-German Conference on PDE, Scientific Computing and Optimization in Applications (October 7-9, 2009 at Department of Mathematics, Indian Institute of Technology, Kanpur, India)
12. Numerical Approximations of Hyperbolic Partial Differential Difference Equation in Neuronal Variability at Spring School on Analytical and Numerical Aspects of Evolution Equations (March 30, 2009 - April 4, 2009 at Institut für Mathematik, Technische Universität Berlin, Germany)

PhD Theses Supervised

1. Manisha Yadav : Mathematical Modeling of Some Real Life Applications and their Numerical Solution (ongoing)
2. Sweta Sinha : Numerical Analysis of Mathematical Models Originating in Biological and Physical Applications (Thesis defended in December 2024)
3. Dipty Sharma : Numerical Analysis of the Time-Dependent Partial Differential Equations Motivated by the Biological Processes (Thesis defended in April 2021)
4. Santosh Kumar : Finite Volume Approximations of Hyperbolic Conservation Laws Arising in Biological Sciences (Thesis defended in July 2018)

MSc Theses Supervised

1. Menpal Dhundhara, Improving cross-layer IoT intrusion detection through multiclass classification and synthetic data augmentation (2025) (Jointly with Dr. Manisha Malik)
2. Hrithik Gupta, EEG based multi-class classification of epileptic seizure types using machine learning approach, 2025 (Jointly with Dr.Ashima Khosla)
3. Sukhleen Kaur, Stability and phase plane analysis of some nonlinear ordinary differential equations and their numerical solutions (2023)
4. Slony, Stochastic differential equations and their numerical solution (2022)
5. Pallavi, Iterative methods for the system of non-linear equations (2021)
6. Parul Bhalla, Wave equation in higher dimensions (2021)
7. Ripanjot Kaur, Numerical methods for solving the system of differential equations (2018)
8. Satinder Pal Singh Sandhu, Some properties and numerical approximations of one-dimensional hyperbolic conservation laws (2017)
9. Rajvinder Kaur, Function spaces and weak formulation of partial differential equations (2016)
10. Priyanka Sharma, Finite volume approximations of hyperbolic conservation law arising in neuronal variability (2014)

Professional Memberships

• American Mathematical Society (AMS)
• Society for Industrial and Applied Mathematics (SIAM), including SIAG on Analysis of Partial Differential Equations

Last updated: August 14, 2026