ADITYA KAUSHIK

Applied Mathematics

Phone:+91-8427580104
Email: akaushik@dtu.ac.in

Qualifications

Ph.D.

Areas of Interest

Numerical Analysis and Differential Equations

Professional Experience

  • 2021 - Till date: Professor, Delhi Technological University, Delhi.
  • 2018 - 2021: Associate Professor, Delhi Technological University, Delhi.
  • 2011 - 2018: Assistant Professor, Panjab University, Chandigarh.
  • 2009 - 2011: Assistant Professor, Kurukshetra University, Kurukshetra.

Teaching

International/Academic Visits

  • Division of Applied Mathematics, Brown University, USA.
  • Hausdorff Center of Mathematics (HCM), Germany.
  • Massachusetts Institute of Technology (MIT), USA.
  • Austrian Academy of Sciences, Austria.
  • RAND Corporation, California (Santa Monica), USA.
  • Carnegie Mellon University, USA.
  • Institut National de Recherche En Informatique Et En Automatique, France.

Membership Academic/Administrative Committees

  • In-charge, Research Lab/Project Lab (RL2) -  (2024 - Till Date)
  • Member, Grade Moderation Committee - (2023 - Till Date)
  • Member, Disciplinary Committee - (2023 - Till Date)
  • In-charge, Research Lab/Project Lab (RL3) -  (2023 - 2024)
  • Spot Purchase Committee - (2023 - 2024)
  • Question Paper Audit Committee - (2023 - Till Date)
  • Coordinator, Society for Industrial & Applied Mathematics, DTU Chapter - (2022-2023)
  • PhD Committee - (2022 - 2023)
  • Department Coordinator, NBA Committee - (2022 - Till date)
  • Department Co-coordinator, NAAC Committee - (2022 - 2023)
  • PhD Coordinator, Applied Mathematics - (2021 - 2022)
  • Member of BoS, Applied Mathematics - (2021 - Till date)
  • Member, Fee Concession Scrutiny Committee - (2021 - Till date)
  • Faculty Advisor, Inception Wave DTU Chapter - (2020 - Till date)
  • Performance Monitoring Committee for PhD students - (2020 - 2021)
  • Coordinator, Mathematics & Computing Society (MACS) - (2019 - 2022)
  • Member, Department Purchase Committee - (2019 - Till date)
  • Member, Department Research Committee (DRC) - (2019 - 2021)
  • Department Coordinator, ISO Certification - (2018 - 2023)
  • Department Co-coordinator, NBA Accreditation Committee - (2018 - 2019)
  • Department Co-coordinator, NAAC Accreditation Committee - (2018 - 2019)
  • Member, Technical Committee - (2018 - 2019)
  • Member, Institute Reforms Committee - (2012 - 2018)
  • Member, Technical Committee of the Institute - (2017 - 2018)
  • Member, Purchase Committee of the Institute - (2017 - 2018)
  • Member, Academic Committee of the Institute - (2017 - 2018)
  • Convener, Information Cell - (2016 - 2017)
  • Member, Academic Affairs Committee of the Institute - (2014 - 2018)
  • Coordinator, EDUSAT Terminal of Kurukshetra University - (2009 - 2011)
  • Associate Coordinator, M.Sc. Mathematics, Kurukshetra University - (2009 - 2011)

Membership Professional/Learned Societies

  • American Mathematical Society
  • Indian Mathematical Society
  • Indian Society of Industrial & Applied Mathematics
  • International Association of Engineers
  • Soft Computing Research Society

Awards/Scholarship/Honours

  • Research Excellence Award, Delhi Technological University, Delhi - 2020, 2021, 2022
  • Research Award, Panjab University, Chandigarh - 2015
  • Graduate Aptitude Test in Engineering (GATE), Indian Institute of Technology, Kharagpur - 2006
  • Junior Research Fellowship, Council of Scientific & Industrial Research, Delhi - 2005, 2006
  • University Research Scholarship, Kurukshetra University, Kurukshetra - 2005

Research/Academic Grants

  • MATRICES, SERB, DST (2022 - 2025) - Higher-order Adaptive Difference Schemes for Singularly Perturbed Ordinary and Partial Differential Equations.
  • SERB, DST (2016-2017) - Theoretical and Computational Partial Differential Equations.
  • NBHM (2015-2016) - Numerical Methods for Partial Differential Equations.
  • TEQIP-II (2013-2014) - Mathematical Modelling and Computational Techniques.
  • UGC (2013-2015) - Analytic approximation to nonlinear convection-dominated systems.

Conference/Workshop/FDP/Seminars - Organized

  • In collaboration with the Institution’s Innovation Council, “My Story – Motivational Session by Successful Innovators” on 26/11/2021. 
  • A Hackathon in collaboration with bitgrit, an AI competition and recruiting platform for data scientists from 01/03/2021 to 10/03/2021. 
  • An orientation program on 22/12/2020 for first-year students of B.Tech. and proposed a Roadmap session on academic(s) and other stuff like coding, internships, and placements.
  • A short-term training program on "Recent Trends in Security and Cryptography" from 18/11/2019 to 22/11/2019.
  • International Conference on "Advances in Computational Mathematics" from 23/12/2018 – 24/12/2018.
  • International Conference on "Recent Advances in Theoretical and Computational Partial Differential Equations with Applications" from 05/12/2016 to 09/12/2016.
  • International Conference on "Numerical Methods for Partial Differential Equations" from 21/12/2015 to 25/12/2015.
  • Faculty Development Program (FDP) on "Role of Basic Sciences in Engineering" during 11/11/2013 – 16/11/2013.
  • A National Conference on "Mathematical Modelling and Computational Techniques" from 27/09/2013 - 28/09/2013.

Professional Training

  1. Faculty development program on “NBA Accreditation Procedures” - 09/05/2022 – 11/05/2022, National Institute of Technical Teachers Training and Research Institute, Chennai.
  2. Short-term course on “Academic Writing using LaTeX” - 04/01/2021 – 08/01/2021, Sardar Vallabhbhai National Institute of Technology, Surat
  3. Faculty development program on "Mathematical Approaches in Mechanics" - 24/12/2020 – 31/12/2020, Indian Institute of Technology, Indore.
  4. Faculty development program on "Mathematics with MATLAB and MATHEMATICA" - 23/11/2020 – 28/11/2020, Indian Institute of Technology, Indore.
  5. Faculty development program on "Nascent Methodologies-Challenges and Realms of Research" - 03/10/2020 – 07/10/2020, Delhi Technological University, Delhi.
  6. Faculty development program on "Outcome Based Engineering Education and Accreditation" - 21/09/2020 – 23/09/2020, National Institute of Technology, Meghalaya.
  7. Faculty development program on "Exploring Science and Technology Interconnections" - 03/08/2020 – 08/08/2020, Panjab University, Chandigarh.
  8. Faculty development program on "Emerging Trends in Data Science & IoT" - 20/07/2020 – 25/07/2020, Arka Jain University, Jamshedpur.
  9. Faculty development program on "Python Programming" - 15/07/2020 – 18/07/2020, K.L. University, Hyderabad.
  10. Faculty development program on "Power Quality and Reactive Power Management" - 06/07/2020 – 10/07/2020, Delhi Technological University, Delhi.
  11. Short-term training program on "Graph Theory and its Applications" - 25/11/2019 – 29/11/2019, Delhi Technological University, Delhi.
  12. UGC sponsored refresher course in "Mathematical Sciences" - 22/06/2017 – 12/07/2017, Human Resource Development Centre, Panjabi University, Patiala.
  13. Advanced workshop on "Finite Difference Methods" - 13/03/2017 – 17/03/2017, South Asian University, New Delhi.
  14. Faculty development program on "Achieving Excellence in Technical Education" - 16/07/2013 – 19/07/2013, Panjab University, Chandigarh.
  15. UGC sponsored refresher course in "Information Technology (Interdisciplinary)" - 15/06/2012 – 05/07/2012, Academic Staff College, Panjab University, Chandigarh.
  16. UGC sponsored "Orientation programme (Interdisciplinary)" - 10/05/2011 – 06/06/2011, Academic Staff College, Kurukshetra University. Kurukshetra.

Books/Edited Volumes

  • Aditya Kaushik & Kapil Sharma, Theoretical and Computational Differential Equations with Applications, Differential Equations and Dynamical Systems, Springer 2019.

List of Publications

  1. An adaptive moving mesh and hybrid difference approximation for a time-dependent reaction-diffusion equation with shift and integral boundary conditions.
  2. A uniformly accurate hybrid difference approximation of a system of singularly perturbed reaction-diffusion equations with delay using grid equidistribution.
  3. Shivani Jain, Aditya Kaushik, A semi-analytical approximation for a coupled system of singularly perturbed convection-diffusion equations with shifts, International Journal of Computational Methods (2024). 
  4. Aditya Kaushik, Nitika Sharma, Manju Sharma, Monika Arora, Shivani Jain, A uniformly convergent method for two-parameter singularly perturbed parabolic partial differential equations with a large shift, Journal of Difference Equations and Applications (2024).
  5. Aditya Kaushik, Shivani Jain, A posteriori error analysis of defect correction method for singular perturbation problems with discontinuous coefficient and point source, Journal of Computational and Nonlinear Dynamics, Vol. 19 (9) (2024) 091005-1-8.
  6. Aditya Kaushik, Aastha Gupta, Shivani Jain, Suayip Toprakseven, Manju Sharma, An adaptive mesh generation and higher-order difference approximation for the system of singularly perturbed reaction-diffusion problems, Partial Differential Equations in the Applied Mathematics, Vol. 11 (2024) 100750.
  7. Komal Bansal, Kapil K. Sharma, Aditya Kaushik, Gajendra Babu, Numerical analysis of singularly perturbed parabolic reaction-diffusion differential-difference equations, International Journal of Computer Mathematics, Vol. 101 (2) (2024) 217-235.
  8. Suayip Toprakseven, Aditya Kaushik, Manju Sharma, A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes, Numerical Algorithms, (2023).
  9. Monika Choudhary, Aditya Kaushik, Manju Sharma, A parameter-robust numerical method based on a defect-correction technique for parabolic singular perturbation problems with discontinuous convection coefficient and source, International Journal of Computational Methods, Vol. 20 (2023) 2350017.
  10. Aditya Kaushik, Monika Choudhary, A higher-order defect correction method over an adaptive Bakhvalov-Shishkin mesh for advection-diffusion equations, Iranian Journal of Science and Technology Transactions A: Science, Vol. 47 (2023) 1221-1232.
  11. Himanshu Chaudhary, Aditya Kaushik, Ankita Kohli, Cosmological test of anisotropy as a function of scale factor in f(R,T) framework, New Astronomy, Vol. 103 (2023) 102044.
  12. Monika Choudhary, Aditya Kaushik, A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay, Journal of Applied Mathematics and Computing, Vol. 69 (2023) 1377-1401.
  13. Aastha Gupta, Aditya Kaushik, Manju Sharma, A higher-order hybrid spline difference method on adaptive mesh for solving singularly perturbed parabolic reaction-diffusion problems with robin-boundary conditions, Numerical Methods for Partial Differential Equations, Vol. 39 (2023) 1220-1250.
  14. Nitika Sharma, Aditya Kaushik, A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary conditions, Journal of Applied Mathematics and Computing, Vol. 69 (2023) 1071-1093.
  15. Nitika Sharma, Aditya Kaushik, A hybrid finite difference method for singularly perturbed delay partial differential equations with discontinuous convection coefficient and source term, Journal of Marine Science and Technology, Vol. 30 (3) (2022) 216-235.
  16. Aditya Kaushik, Monika Choudhary, A higher-order uniformly convergent defect correction method for singularly perturbed convection-diffusion problems on an adaptive mesh, Alexandria Engineering Journal, Vol. 61 (2022) 9911-9920.
  17. Aastha Gupta, Aditya Kaushik, A high-order hybrid finite difference method based on grid equidistribution for fourth-order singularly-perturbed differential equations, Journal of Applied Mathematics and Computing, Vol. 68 (2022) 1163-1191. 
  18. Aditya Kaushik, Manju Sharma, Aastha Gupta, Monika Choudhary, Iterative analytic approximation to one-dimensional nonlinear reaction-diffusion equations, Mathematical Methods in the Applied Sciences, Vol. 44 (16) (2021) 12152-12168.
  19. Aastha Gupta, Aditya Kaushik, A robust spline difference method for Robin-type reaction-diffusion problem using grid equidistribution, Applied Mathematics and Computation, Vol. 390 (2021) 125597. 
  20. Aditya Kaushik, Vijayant Kumar, Manju Sharma, Nitika Sharma, A modified graded mesh and higher-order finite element method for singularly perturbed reaction-diffusion problems, Mathematics and Computers in Simulation, Vol. 185 (2021) 486-496. 
  21. Aastha Gupta, Aditya Kaushik, A higher-order parameter-uniform numerical discretization of singularly perturbed reaction-diffusion problem via grid equidistribution, Ain-Shams Engineering Journal, Vol. 12 (4) (2021) 4211-4221.
  22. Abhinav Sanghi, Aayush, Ashutosh Katakwar, Anshul Arora, Aditya Kaushik, Detecting Fake Drugs using Blockchain, International Journal of Recent Technology and Engineering, Vol. 10 (1) (2021) 100-109.
  23. Aditya Kaushik, Nitika Sharma, An adaptive difference scheme for parabolic delay differential equation with discontinuous coefficients and interior layers, Journal of Difference Equations and Applications, Vol. 26 (2020) 1450-1470.
  24. Aditya Kaushik, Vijayant Kumar, Manju Sharma, Anil K. Vashishth, A higher-order finite element method with modified graded mesh for singularly perturbed two-parameter problems, Mathematical Methods in the Applied Sciences, Vol. 43 (15) (2020) 8644-8656.
  25. Vishal Gupta, Aditya Kaushik, Manu Verma, Some new fixed-point results on V-ψ-fuzzy contraction endowed with graph, Journal of Intelligent & Fuzzy Systems, Vol. 36 (6) (2019) 6549-6554.
  26. Aditya Kaushik, Anil K. Vashishth, Vijayant Kumar, Manju Sharma, A modified graded mesh and higher-order finite element approximation for singular perturbation problems, Journal of Computational Physics, Vol. 395 (2019) 275-285.
  27. Aditya Kaushik, Geetika Gupta, Manju Sharma, Vishal Gupta, A wavelet-based rationalized approach for the numerical solution of differential and integral equations, Differential Equations and Dynamical Systems, Vol. 27 (1-3) (2019) 181-202.
  28. Aditya Kaushik, Anil K. Vashishth, Vijayant Kumar, Manju Sharma, An asymptotic-numerical method for a class of weakly coupled convection dominated systems, Numerical Functional Analysis and Optimization, Vol. 40 (13) (2019) 1550-1571.
  29. Vishal Gupta, Naveen Mani, Aditya Kaushik, Fixed point theorems satisfying Cψβ- condition and application to boundary value problem, Functional Analysis - Theory, Methods & Applications, Vol. 3 (2017) 26-34.
  30. Minto Rattan, Aditya Kaushik, Neeraj Chamoli, Tania Bose, Steady-state creep behavior of thermally graded isotropic rotating disc of composite taking into account the thermal residual stress, European Journal of Mechanics A/Solids, Vol. 60 (2016) 315- 326.
  31. Aditya Kaushik, Manju Sharma, An optical asymptotic-numerical method for convection dominated systems having exponential boundary layers, Journal of Difference Equations and Applications, Vol. 22 (2016) 1307-1324.
  32. Aditya Kaushik, Vijayant Kumar, Anil K. Vashishth, A higher-order accurate numerical method for singularly perturbed two-point boundary value problems, Differential Equation and Dynamical Systems, Vol. 25 (2017) 267-285.
  33. Manju Sharma, Aditya Kaushik, Chenglin Li , Analytic approximation to delayed convection dominated systems through transforms, Journal of Mathematical Chemistry, Vol. 52 (2014) 2459-2474.
  34. Chenglin Li, Aditya Kaushik, Guocheng Yin, Global existence of classical solutions to an acid-mediated invasion model for tumour-stromal interactions, Applied Mathematics and Computation, Vol. 234 (2014) 599-605.
  35. Aditya Kaushik, Error estimates for a class of partial functional differential equation with small dissipation, Applied Mathematics and Computation, Vol. 226 (2014) 250-256.
  36. Aditya Kaushik, Iterative analytic approximation to nonlinear convection dominated systems, Computer Physics Communications, Vol. 184 (9) (2013) 2061-2069.
  37. Aditya Kaushik, Ved Prakash Kaushik, Analytic solution of nonlinear singularly perturbed initial value problems through iteration, Journal of Mathematical Chemistry, Vol. 50 (9) (2012) 2427-2438.
  38. Aditya Kaushik, Vijayant Kumar, Anil K. Vashishth, An efficient mixed asymptotic-numerical scheme for singularly perturbed convection-diffusion problems, Applied Mathematics and Computation, Vol. 118 (17) (2012) 8645-8658.
  39. Aditya Kaushik, Manju Sharma, A robust numerical approach for singularly perturbed time delayed parabolic partial differential equations, Computational Mathematics and Modeling, Vol. 23 (1) (2012) 96-106.
  40. Aditya Kaushik, Manju Sharma, Convergence analysis of weighted difference approximations on piecewise uniform grids to a singularly perturbed functional differential equation, Journal of Optimization Theory and Application, Vol. 155 (1) (2012) 252-272.
  41. Aditya Kaushik, Vijayant Kumar, Manju Sharma, Analysis of factorization method for elliptic differential equation, Computational Mathematics and Modeling, Vol. 22 (1) (2011) 98-110.
  42. Aditya Kaushik, K.K. Sharma, Manju Sharma, A parameter uniform difference scheme for parabolic partial differential equation with a retarded argument, Applied Mathematical Modeling, Vol. 34 (12) (2010) 4232-4242.
  43. Aditya Kaushik, Mohan D. Sharma, Numerical analysis of a mathematical model for propagation of an electrical pulse in a neuron, Numerical Methods for Partial Differential Equations, Vol. 24 (4) (2008) 1055-1079.
  44. Aditya Kaushik, Nonstandard perturbation approximation and traveling wave solutions of non-linear reaction-diffusion equations, Numerical Methods for Partial Differential Equations, Vol. 24 (1) (2008) 217-238.  
  45. Aditya Kaushik, S. Serra Capizzano, A uniformly convergent difference scheme for parabolic partial differential equation with a retarded argument, Proc. Of National Conf. Advances in Math. & Appl., Vol. 01 (2008) 309-319.
  46. Aditya Kaushik, Mohan D. Sharma, A uniformly convergent numerical method on non-uniform meshes for singularly perturbed unsteady Burger-Huxley equation, Applied Mathematics and Computation, Vol. 195 (2) (2008) 688-706.  
  47. Aditya Kaushik, Singular perturbation analysis of bistable differential equation arising in the nerve pulse propagation, Nonlinear Analysis RWA, Vol. 09 (5) (2008) 2106-2127.  
  48. Aditya Kaushik, Pointwise uniformly convergent numerical treatment for non-stationary Burger-Huxley equation using grid equidistribution, International Journal of Computer Mathematics, Vol. 84 (10) (2007) 1527-1546.
  49. K.K. Sharma, Aditya Kaushik, A solution of the discrepancy occurs due to using the fitted mesh approach rather than to the fitted operator for solving singularly perturbed differential equations, Applied Mathematics and Computation, Vol. 181 (1) (2006) 756-766.

Chapters in Book/Monograph

  • Integration and Differentiation, Real Analysis, Lecture Notes of DDE, Kurukshetra University, Kurukshetra.
  • Lebesgue Measurable Sets, Real Analysis, Lecture Notes of DDE, Kurukshetra University, Kurukshetra.
  • Regularity of Measure and Measurable Functions, Real Analysis, Lecture Notes of DDE, Kurukshetra University, Kurukshetra.
  • Integration of Non-negative Functions, Real Analysis, Lecture Notes of DDE, Kurukshetra University, Kurukshetra.

Conference - Presentation

  1. An adaptive difference scheme for a class of singularly perturbed linear parabolic functional differential equation with discontinuous coefficients, International Conference on Scientific Developments in the Current Era, I.B. (PG) College, Panipat, 9-10 April 2021.
  2. A non-local finite element method for nonlinear turning point problem, 31st Annual Conference of Rajasthan Ganita Parisad on Recent Trends of Mathematics in Science and Engineering, The LNM Institute of Information Technology, Rajasthan, 13-14 March 2021.
  3. A residual-based artificial viscosity finite difference method for scalar conservation laws, International Conference on Mathematical Modelling and Computations, South Asian University, New Delhi, 1-3 December 2018.
  4. Domain decomposition FEM for the conductivity reconstruction in a hyperbolic equation, National workshop on Current Developments in Mathematics and Computer Science, SD College Ambala, 18 March 2016.
  5. An optical asymptotic numerical method for convection dominated systems, National Conference on Role of Mathematics & Computer Science in Advancement of Physics, Govt. Degree College Kathua, 26-27 February 2016.
  6. Numerical approach for solving singularly perturbed partial differential equations using domain decomposition method, National Conference on Innovative Trends in Mathematical Sciences, MM University Mullana, 30 March 2015.
  7. Posteriori error analysis and adaptive finite element methods for singularly perturbed partial differential equations, International Conference on Modeling, Simulation and Optimization Techniques, DAV College Jalandhar, 12-14 February 2015.
  8. Convergence Analysis of weighted difference approximations to a class of partial functional differential equations, 7th Chandigarh Science Congress, Panjab University Chandigarh, 1-3 March 2013.
  9. Method of factorization for an elliptic differential equation using discrete invariant embedding. National Conference on Mathematical Modeling and Simulation, Guru Jambheshwar University of Science and Technology, 20-21 March 2010.
  10. Numerical Analysis and Scientific Computing. National seminar on “Social Development Under the Aegis of Operational Research”, Department of Mathematics, M.M. (P.G.) College Fatehabad, 21-22 Mar. 2009.
  11. The method of factorization in the simulation of linear elliptic type differential equation. National Conference on Advances in Mathematics and its Application, Department of Applied Sciences and Humanities, NIT Hamirpur, 19-21 December 2008.
  12. Numerical Analysis of a Singularly Perturbed Propagating Nerve Impulse. 94th Indian Science Congress, Annamalai University Chidambaram, 03-07 Jan. 2007.
  13. A Parameter Uniform Fitted Mesh Method for Singularly Perturbed Time Delayed Partial Differential of Convection Diffusion Type. VIIIth Conference of International Academy of Physical Sciences, Department of Mathematics C.C.S. University Meerut, 29-31 Dec. 2005.

Seminars

  • International Conference on “History and Development of Mathematics”, Maharshi Dayanand University, Rohtak, 22 December 2020.
  • 14th Chandigarh Science Congress, Panjab University, Chandigarh, 17 – 19 December 2020.
  • International Conference on “Number Theory and Discrete Mathematics”,  Rajagiri School of Engineering & Technology, Kochi, 11 – 14 December 2020.
  • International Conference on “Recent Trends in Mathematics and its Applications to Graphs, Networks and Petri Nets”, Jawaharlal Nehru University, New Delhi, 20 – 24 July 2020.
  • National Webinar on "Mathematics and its Applications", Chotu Ram Arya College, Sonepat, 08 July 2020.
  • National Webinar on "Metric Space and Fixed-Point Theorem", I.B. (P.G.) College, Panipat, 06 June 2020.
  • National Conference on "Exploring Basic and Applied Sciences for Next Generation Frontiers", Lovely Professional University, 14-15 November 2014.
  • Faculty Development Program on "Achieving Excellence in Technical Education", Panjab University Chandigarh, 16-19 July 2013.
  • Colloquium in Mathematics in the thrust areas of Algebra, Number Theory and Applied Mathematics, Panjab University Chandigarh, 22-23 February 2013.
  • 12th International Conference of International Academy of Physical Sciences, University of Rajasthan Jaipur, 22-24 December 2010.
  • State-level seminar on “Relevance of Basic Sciences in Higher education”. Gandhi Memorial National College, 06 March 2009.
  • State-level seminar on “Emerging Trends in Computer and Information Technology”. Gandhi Memorial National College, 07 March 2009.

Invited Talks/Session Chaired

  • Differential equations and mathematical modelling, 26th International Conference of IAPS on Advances in Differential Equations & Mathematical Modeling, Jawaharlal Nehru University, New Delhi, 18-20 December 2020.
  • Finite element approximation over adaptive grids for singular perturbation problems, International Conference on Theory, Computations and Applications of Differential Equations, South Asian University, New Delhi, 21-23 January 2019.
  • Problems with interior layers and weak boundary layers, International Conference on Mathematical Modeling and Computations, South Asian University, New Delhi, 01-03 December 2018.
  • Singular perturbation: Adaptive computational techniques, International Conference on Innovative Trends in Mathematics, Computer & Information Sciences, MMU Mullana, Ambala, 09-10 March 2017.
  • A higher-order Galerkin FEM for singular perturbation problems on modified smooth W-grids, International Conference on Current Trends in Theoretical and Computational Differential Equations with Applications, South Asian University, New Delhi, 01-05 December 2017. 
  • Weighted difference approximations, International Conference on Recent Advances in Theoretical and Computational Partial Differential Equations with Applications, Panjab University, Chandigarh, 05-09 Dec. 2016.
  • Factorization method using discrete invariant embedding, National Conference on Recent Advances in Mathematics and its Computational Aspects, SMP Govt. College, Meerut, 11-12 November, 2016.
  • Iterative analytic approximation for nonlinear perturbation problems, International Conference on Current Trends in PDEs: Theory & Computations, South Asian University, New Delhi, 28-30 December 2015.
  • Uniformly convergent difference schemes for singularly perturbed differential equations, Institute of Computational Mathematics, Johannes Kepler University, Austria, 26 January 2010.
  • Singular perturbation: Dominance of convection in flow problems, University Bremen Germany, May 2008.
  • Perturbation Approximation and travelling waves solutions of convection reaction-diffusion equations, University Bordeaux II France, February 2007.

Research Supervision/Guidance

  • PhD Thesis
    • Ashish Saini - Fractional order differential equations
    • Mamta Godara - Finite Element Methods
    • Nitesh Kumar - Study of thermoelastic problems within the context of fractional order derivative
    • Shivani Jain - Singular perturbation problems in chemical kinetics.
    • Monika Choudhary - Defect correction methods for singularly perturbed differential equations
    • Nitika Sharma - Numerical methods for the solution of singularly perturbed parabolic convection-diffusion problems with discontinuous coefficient and delay
    • Aastha Gupta - Adaptive numerical schemes for the solution of singularly perturbed reaction-diffusion equations
    • Madhu Bala Sheokand - Analysis of factorization method based on the discrete invariant embedding using finite elements
  • M.Phil. Dissertation
    • Meenu - Boundary layer theory
    • Anju Verma - The method of factorization for elliptic partial differential equation on a circular domain
    • Reema Aggarwal - Hodgkin-Huxley equations
    • Usha Rani - Adaptive finite difference method for convection-dominated diffusion problems
    • Isha Jham - Numerical schemes for non-linear diffusion problems
    • Ranju - Numerical analysis of singularly perturbed reaction-diffusion equations
    • Devinder Kaur - Method of factorization for elliptic partial differential equations
  • M.Sc. Dissertation 
    • Nikita Kaushik - Numerical method for solving singular perturbed problems
    • Himanshu Pandey - Finite difference methods for partial differential equations
    • Himanshu Chaudhary - Cosmological test of anisotropy as a function of scale factor in f(R,T) framework
    • Chaitanya Pathak - Variation iteration method for the solution of ordinary and partial differential equations
    • Aditya Prashar and Dipesh - A novel technique for the numerical approximation of the solution of a singularly perturbed reaction-diffusion equation with delay and advance.
    • Drishti Vashisth – An efficient numerical technique for the solution of singularly perturbed convection-diffusion equation with delay.
  • B.Tech. Projects/Dissertation
    • Smart traffic analyser and controller using real-time object detection with tensor flow
    • Medical chain using blockchain technology
    • Tackle COVID–19 with machine learning
    • Geofencing solutions
    • Google Bert
    • KYC verification using blockchain technology
    • Automatic video captioning using an encoder-decoder model
    • Test cricket analysis (2017-2022) using data analytics

Last Updated : 2024-10-29 14:44:50