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)
- 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
- S. Sinha, P. Singh. Mathematical Modelling and Simulation of Mechano-Chemical Effect on Two-Phase Avascular Tumor, under review.
- 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.
- 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.
- S. Kumar, P. Singh, High order WENO finite volume approximation for population density neuron model, Applied Mathematics and Computation 356, 173-189. 2019.
- 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.
- 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.
- 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
- S. Kumar, P. Singh. Finite volume approximations for size structured neuron model, Differ. Equ. Dyn. Syst. 25 (2), 251–265, 2017.
- 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.
- S. Kumar, P. Singh. Higher-order MUSCL scheme for transport equation originating in a neuronal model, Comput. Math. Appl. 70 (12), 2838–2853, 2015.
- D. Garg, P. Singh. Dynamic task allocation in distributed computing systems by heuristic algorithms, Int. J. of Operational Research. 21 (4), 391–408, 2014.
- P. Singh, K. Sharma. Numerical approximations to the transport equation arising in neuronal variability, Int. J. Pure Appl. Math. 69 (3), 341–356, 2011.
- 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.
- 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.
- 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:
- 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)
- Finite volume approximation of leaky integrate-and-fire model with Levy noise in ICIAM 2015 (August 10-14, 2015 in Beijing, China)
- 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)
- Numerical analysis of leaky integrate-and-fire model originating in neuronal firing at ICIAM 2011 (July 18-22, 2011 at Vancouver, BC, Canada)
- 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)
- 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)
- Sweta Sinha (Ongoing)
- Dipty Sharma : Numerical Analysis of the Time-Dependent Partial Differfential Equations Motivated by the Biological Processes (Thesis defended in April 2021)
- Santosh Kumar : Finite Volume Approximations of Hyperbolic Conservation Laws Arising in Biological Sciences (Thesis defended in July 2018)
MSc Thesis Supervised:
- Pallavi, Iterative Methods for the System of Non-linear Equations (2021)
- Parul Bhalla, Waves Equation in Higher Dimensions (2021)
- Ripanjot Kaur, Numerical methods for solving the system of differential equations (2018)
- Satinder Pal Singh Sandhu, Some Properties and Numerical Approximations of One-Dimensional Hyperbolic Conservation laws (2017).
- Rajvinder Kaur, Function Spaces and Weak Formulation of Partial Differential Equations (2016)
- Priyanka Sharma, Finite Volume Approximations of Hyperbolic Conservation Law Arising in Neuronal Variability (2014)
Please see the URL below for current teaching.
- American Mathematical Society (AMS)
- Society for Industrial and Applied Mathematics (SIAM)
- SIAM activity group on Analysis of Partial Differential Equations (SIAG/APDE)