ADITYA KAUSHIK

Dr. Aditya Kaushik is a Professor in the discipline of Mathematics & Computing at Delhi Technological University. His research interests are in Numerical Analysis and Differential Equations. His work includes the development of finite-difference and finite-element techniques, adaptive mesh-generation procedures, and computational approaches for ordinary and partial differential equations.

• 2018 - Till date: Delhi Technological University, Delhi.
• 2011 - 2018: Panjab University, Chandigarh.
• 2008 - 2011: Kurukshetra University, Kurukshetra.

• Ordinary Differential Equations (MSMAT-105) - Course File
  • Assignments: Assignment 1, Assignment 2, Assignment 3, Assignment 4, Assignment 5
  • Lecture Notes: Introduction to ODEs, First-order ODEs, Review of Linear Algebra, Linear Differential Equations, Series Solution of Linear Differential Equations, Generalized Functions, Method of Variation of Parameter and Reduction of Order for n^th-order Linear Differential Equations
  • Online Resource Material
    • NPTEL - Ordinary Differential Equations and Applications, IISc Bangalore
    • NPTEL - Ordinary Differential Equations, IIT Kanpur
• Partial Differential Equations (MC-406) - Course File
  • Assignments: Assignment 1, Assignment 2, Assignment 3, Assignment 4, Assignment 5
  • Lecture Notes: Laplace Equation, Heat Equation, Inhomogeneous Heat Equation, Heat Equation in Rⁿ, Wave Equation, Inhomogeneous Wave Equation, Wave Equation in Rⁿ, First-order Nonlinear PDEs
  • Online Resource Material
    • NPTEL - First Course on Partial Differential Equations - I, IISc Bangalore
    • NPTEL - First Course on Partial Differential Equations - II, IISc Bangalore
    • MIT Open Course Ware - Differential Analysis II: Partial Differential Equations And Fourier Analysis
    • MIT Open Course Ware - Advanced Partial Differential Equations With Applications

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

List of Publications (Last Five Years)

1. Aditya Kaushik, Manju Sharma, Suayip Toprakseven, Palle E. T. Jørgensen, A weak Galerkin finite element method on Bakhvalov-type meshes for nonlinear singularly perturbed parabolic reaction-diffusion problems.
2. Aditya Kaushik, Asish Saini, Manju Sharma, A fourth-order parameter-uniform compact hybrid scheme for coupled singularly perturbed reaction–diffusion systems.
3. Aditya Kaushik, Nitesh Kumar, Hygrothermoelastic response of finite cylinders under ramp heating with memory-dependent derivatives, Mechanics of Solids, (2026).
4. Aditya Kaushik, Mamta Godara, Manju Sharma, Adaptive mesh generation and a hybrid method for time-dependent singular perturbation problems with a shift and integral boundary conditions, Journal of Computational and Nonlinear Dynamics, Vol 21 (4) (2026) 41008.
5. Aditya Kaushik, Shivani Jain, Manju Sharma, A uniformly accurate hybrid difference approximation of a system of singularly perturbed reaction-diffusion equations with delay using grid equidistribution, Mathematical Modelling and Analysis, Vol. 31 (1) (2026) 26-46.
6. Nitesh Kumar, Aditya Kaushik, Ahmed Abouelregal, Thermal and stress analysis of a semi-infinite hollow cylinder under ramp-type heating with memory-dependent derivatives, Mechanics of Solids, Vol. 60 (2025) 4863-4878.
7. 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, Vol. 22 (5) (2025) 2450076.
8. 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, Vol. 30 (12) (2024) 1923-1960.
9. 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.
10. 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.
11. 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.
12. 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).
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. 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. 
22. 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.
23. 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. 
24. 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. 
25. 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.
26. 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.
27. 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.

Books/Edited Volumes

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

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.

• AICTE Research Promotion Scheme (RPS): Lab to Market (RPS-1-837103261-2025-4944) 2026 - 2029 - Explainable Hybrid Quantum Machine Learning based framework for Robust Android Mobile Malware Detection
• MATRICES, DST (MTR/2021/000117)  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.