Dr. Paramjeet Singh

Associate Professor


Numerical Partial Differential Equations




Numerical Partial Differential Equations



Experience and Degrees

  • Assistant Professor, School of Mathematics, Thapar Institute of Engineering & Technology (July 2013 – present)
  • PhD (Mathematics), Panjab University, Chandigarh. Thesis: Numerical Analysis of Transport Equations Motivated by Neuroscience (June 2012)
  • Postdoctoral Researcher at the University of Cape Town in South Africa (August 2012 - July 2013)

Research Awards

  • 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).
  • 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.

Scholarly and Professional Work


  1. S. Sinha, P. Singh. Mathematical Modelling and Simulation of Mechano-Chemical Effect on Two-Phase Avascular Tumor, under review.
  2. 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), 1-18, 2021.
  3. 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.
  4. S. Kumar, P. Singh, High order WENO finite volume approximation for population density neuron model, Applied Mathematics and Computation 356, 173-189. 2019.
  5. 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.
  6.  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.
  7. 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
  8. S. Kumar, P. Singh. Finite volume approximations for size structured neuron model, Differ. Equ. Dyn. Syst. 25 (2), 251–265, 2017.
  9. 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.
  10. S. Kumar, P. Singh. Higher-order MUSCL scheme for transport equation originating in a neuronal model, Comput. Math. Appl. 70 (12), 2838–2853, 2015.
  11.  D. Garg, P. Singh. Dynamic task allocation in distributed computing systems by heuristic algorithms, Int. J. of Operational Research. 21 (4), 391–408, 2014.
  12.  P. Singh, K. Sharma. Numerical approximations to the transport equation arising in neuronal variability, Int. J. Pure Appl. Math. 69 (3), 341–356, 2011.
  13.  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.
  14.  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.
  15.  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.

Presentations (Talks) in International Conferences:

  1. 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)
  2. Finite volume approximation of leaky integrate-and-fire model with Levy noise in ICIAM 2015  (August 10-14, 2015 in Beijing, China)
  3. Finite-volume approximation of conservation laws with fading memory in the XV International Conference on Hyperbolic Problems (July 27, 2014 - August 1, 2014 in the city of Rio de Janeiro, Brazil)
  4. Numerical analysis of leaky integrate-and-fire model originating in neuronal firing at ICIAM 2011 (July 18-22, 2011 at Vancouver, BC, Canada)
  5. 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)
  6. 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 Students:

  1. Sweta Sinha (Ongoing)
  2. Dipty Sharma : Numerical Analysis of the Time-Dependent Partial Differfential Equations Motivated by the Biological Processes (Thesis defended in April 2021)
  3. Santosh Kumar : Finite Volume Approximations of Hyperbolic Conservation Laws Arising in Biological Sciences (Thesis defended in July 2018)

MSc Thesis Supervised:

  1. Pallavi, Iterative Methods for the System of Non-linear Equations (2021)
  2. Parul Bhalla, Waves Equation in Higher Dimensions (2021)
  3. Ripanjot Kaur, Numerical methods for solving the system of differential equations (2018)
  4. Satinder Pal Singh Sandhu, Some Properties and Numerical Approximations of One-Dimensional Hyperbolic Conservation laws (2017).
  5. Rajvinder Kaur, Function Spaces and Weak Formulation of Partial Differential Equations (2016)
  6. Priyanka Sharma, Finite Volume Approximations of Hyperbolic Conservation Law Arising in Neuronal Variability (2014)

Teaching Interests

Please see the URL below for current teaching. 

URL: https://sites.google.com/site/nummaths/


  1. American Mathematical Society (AMS)
  2. Society for Industrial and Applied Mathematics (SIAM)
  3. SIAM activity group on Analysis of Partial Differential Equations (SIAG/APDE)
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