Title Dr. First Name PRATIMA Last Name RAI
Designation Associate Professor
Department Department of Mathematics
Email prai@maths.du.ac.in
Webpage
Phone.no 01127666658
Employement Info
Employee Type Nature Of Employment
Teaching Permanent
Educational Qualifications
Degree/Certification Name Institution Year of Completion
Ph.D. - Ph. d. Mathematics Panjab University 2013
PG Panjab University 2008
UG Panjab University 2006
Qualifications
Examination Name Conducting Body Date of Passing
NET UGC 22-06-2008
Fellowship Details
Name Of Fellowship Awarding Body Fellowship Level
CSIR-JRF CSIR National
CSIR-SRF CSIR National
Research Supervision Overview
PhD Scholars Supervised PhD Degrees Awarded Theses Submitted
4 1 0
M.Phil Scholars Supervised M.Phil Degrees Awarded M.Phil Theses Submitted
0 2 0
Research Publications
Title of Article Type of Publication Name of Journal ISSN Journal Volume Year Link to Article DOI (Digital Object Identifier)
A hybrid numerical treatment of time-dependent convection dominated diffusion problems with integral boundary conditions and large spatial delay Research Papers in Scopus Listed Journals Journal of Difference Equations and Applications 31 2025 10.1080/10236198.2025.2497806

A streamline-diffusion FEM for singularly perturbed degenerate parabolic problem with large delay argument Research Papers in Scopus Listed Journals Mathematics and Computers in Simulation 247 2026 (Accepted Only) https://doi.org/10.1016/j.matcom.2026.04.001
Finite element approximation of singularly perturbed parabolic problems with discontinuous reaction coefficient and source function Research Papers in Scopus Listed Journals International journal of Computational Methods 2025 (Accepted Only) DOI: 10.1142/S0219876226500118
Close-to-convex functions associated with a cubic polynomial 1+z Research Papers in Scopus Listed Journals Filomat 39 2025 10.2298/FIL2524289P
Balanced norm convergence of DGFEM for singularly perturbed parabolic problems with discontinuous diffusion Research Papers in Scopus Listed Journals Mathematical Methods in Applied Sciences 48 2025 https://doi.org/10.1002/mma.11017
Analysis of finite element method for unsteady convection reaction-diffusion problem with discontinuous data Research Papers in Scopus Listed Journals International Journal of Computer Mathematics 102 2025 10.1080/00207160.2025.2462745
Error analysis of SDFEM for time-dependent singularly perturbed problem with interior turning point Research Papers in Web of Science Listed Journals Journal of Applied Mathematics and Computing 2025 doi.org/10.1007/s12190-025-02416-0
Numerical approximation of parabolic singularly perturbed problems with large spatial delay and turning point Research Papers in Scopus Listed Journals Engineering Computation 0264-4401 41 2024 10.1108/EC-09-2023-0534
Analysis of SDFEM for Singularly Perturbed Delay Differential Equation with Boundary Turning Point Research Papers in Scopus Listed Journals International Journal of Applied and Computational Mathematics 2199-5796
Uniformly convergent numerical approximation for parabolic singularly perturbed delay problems with turning points Research Papers in Scopus Listed Journals International Journal of Computational Methods 0219-8762 DOI:10.1142/S0219876223500317
Finite element analysis of singularly perturbed problems with discontinuous diffusion Research Papers in Scopus Listed Journals Computational and Applied Mathematics https://doi.org/10.1007/s40314-023-02391-x
Radius Estimates of Certain Analytic Functions Research Papers in Peer Reviewed Journals Honam Math. J. 1225-293X 43 http://hmj.honammath.or.kr/ http://hmj.honammath.or.kr/
A hybrid numerical scheme for singular perturbation delay problems with integral boundary condition Research Papers in Scopus Listed Journals Journal of Applied Mathematics and Computing 1598-5865 https://www.springer.com/journal/12190 https://doi.org/10.1007/s12190-021-01667-x
An almost second order hybrid scheme for the numerical solution of singularly perturbed parabolic turning point problems Research Papers in Scopus Listed Journals Mathematics and Computers in simulation 0378-4754 185 https://www.sciencedirect.com/journal/mathematics-and-computers-in-simulation https://doi.org/10.1016/j.matcom.2021.01.017
A parameter uniform scheme for delay parabolic singularly perturbed turning point problem Research Papers in Scopus Listed Journals Differential Equations and Dynamical Systems 0971-3514 https://www.springer.com/journal/12591 https://doi.org/10. 1007 /s 12591-021-00577-5, 2021
A higher order scheme for singularly perturbed delay parabolic turning point problem Research Papers in Scopus Listed Journals Engineering Computation 0264-4401 38 https://www.emerald.com/insight/publication/issn/0264-4401 https://doi.org/10.1108/EC-03-2020-0172
A higher order numerical scheme for singularly perturbed parabolic turning point problems exhibiting twin boundary layers Research Papers in Scopus Listed Journals Applied Mathematics and Computation 0096-3003 https://www.sciencedirect.com/journal/applied-mathematics-and-computation https://doi.org/10.1016/j.amc.2020.125095
Robust numerical schemes for singularly perturbed delay parabolic convection diffusion problems with degenerate coefficient Research Papers in Scopus Listed Journals International Journal of Computer Mathematics 0020-7160 98 https://www.tandfonline.com/action/journalInformation?journalCode=gcom20 https://doi.org/10.1080/00207160.2020.1737030
Numerical approximation for a class of singularly perturbed delay differential equations with boundary and interior layer (s) Research Papers in Scopus Listed Journals Numerical Algorithm 1017-1398 85 https://www.springer.com/journal/11075 https://doi.org/10.1007/s11075-019-00815-6
A Robust Numerical Scheme for Singularly Perturbed Delay Differential Equations with Turning Point Research Papers in Scopus Listed Journals International Journal for Computational methods in Engineering Science and Mechanics 1550-2295 https://www.tandfonline.com/journals/ucme20 https://doi.org/10.1080/15502287.2019.1687608
A higher order uniformly convergent method for singularly perturbed parabolic turning point problems Numerical Methods for Partial Differential Equations 36 https://onlinelibrary.wiley.com/journal/10982426 https://doi.org/10.1002/num.22431
Parameter uniform numerical method for singularly perturbed differential-difference equations with interior layer Research Papers in Scopus Listed Journals International Journal of Computer Mathematics 88 2011
Hermitian-Toeplitz determinant for certain Univalent functions Research Papers in Scopus Listed Journals Mathematical Foundation of Computing 2024 (Accepted Only)
Analysis of finite element method for unsteady convection reaction-diffusion problem with discontinuous data Research Papers in Web of Science Listed Journals International Journal of Computer Mathematics 2025 doi.org/10.1080/00207160.2025.2462745
SDFEM for Time-Dependent Singularly Perturbed Boundary Turning Point Problem Research Papers in Web of Science Listed Journals International Journal of Computational Methods 2024 https://doi.org/10.1142/S0219876224500622
Analysis of a higher order uniformly convergent method for singularly perturbed parabolic delay problems, Research Papers in Scopus Listed Journals Applied Mathematics and Computation 00963006 448 https://doi.org/10.1016/j.amc.2023.127906
Numerical analysis of singularly perturbed delay differential turning point problem Research Papers in Scopus Listed Journals Applied Mathematics and Computation 218 2011 https://doi.org/10.1016/j.amc.2011.08.095
A parameter uniform higher order scheme for 2D singularly perturbed parabolic convection–diffusion problem with turning point Research Papers in Scopus Listed Journals Mathematics and Computers in Simulation 03784754 205 https://doi.org/10.1016/j.matcom.2022.10.011
NIPG finite element method for convection dominated diffusion problems with discontinuous data Research Papers in Scopus Listed Journals International Journal of Computational Methods 02198762 20 https://doi.org/10.1142/S0219876223500019
Research Projects
Project Title Project Type Year Of Sanction Outcome/Output Duration
Numerical Methods for singularly Perturbed time dependent differential difference equations Minor 2014 obtained a parameter uniform numerical scheme for the singularly perturbed parabolic turning point problem with small time delay. Obtained parameter uniform error estimated and established the efficiency of the proposed scheme through numerical experiments. 15-10-2014 To 30-06-2015 (8 months, 15 days)
Numerical Methods for singularly Perturbed time dependent differential difference equations Minor 2014 obtained a parameter uniform numerical scheme for the singularly perturbed parabolic turning point problem with small time delay. Obtained parameter uniform error estimated and established the efficiency of the proposed scheme through numerical experiments. 15-10-2014 To 30-06-2015 (8 months, 15 days)
Geometric estimates of some normalised analytic functions Minor 2021 In this project, the bounds on fourth order Hankel determinants for the lemniscate starlike functions are computed. Hermitian-Toeplitz determinants are discussed for the starlike functions with respect to symmetric points allied with the hyperbolic cosine function. The estimates on the initial successive inverse coefficients as well as logarithmic coefficients, on third Hankel determinants and symmetric Toeplitz determinants are determined. Further, the necessary and sufficient convolution conditions for the starlike functions defined on the open unit disk and related to some geometric aspects of the hyperbolic tangent function are established. A subordination inclusion involving Bernardi integral operator for starlike functions associated with tanh z is established. 29-10-2021 To 30-06-2022 (8 months, 1 days)
The Development and Analysis of the Finite Element Methods for a Class of Singular Perturbation Problems with Discontinuous Data Major 2022 Ongoing since 10-06-2022 (3 years, 11 months, 26 days)
Estimates of close to convex, starlike and convex functions Minor 2022 31-08-2022 To 31-03-2023 (7 months)
Sharp bounds on coefficient functionals of Sakaguchi starlike functions Minor 2023 Research publication 01-09-2023 To 31-03-2024 (6 months, 30 days)
Bounds on Hermitian-Toeplitz determinants and other coefficient functionals of certain Analytic functions Minor 2024 01-09-2024 To 31-03-2025 (6 months, 30 days)
Discontinuous Galerkin finite element method for singularly perturbed problems with interior layers Minor 2025 Ongoing since 01-11-2025 (7 months, 4 days)
Professional Development Programmes
Programme Title Sponsoring Institution Organizing Institution Role Type of Programme
National Workshop cum FDP on Deep Learning in Scientific Computing LNMIT Jaipur LNMIT Jaipur Attendee Faculty Development Programmes
Honors and Awards
Name of the Award Awarding Body Award Category Level Award Date
Best Paper Award Indian Mathematical Society Research National 23-12-2011
Best Paper Award Panjab University Research State/University Level 28-02-2011
Talk Poster Presented
Name of the Activity Role Date of Activity
Singular Perturbation Problem: An Overview Invited Talk 15-11-2021
Fitted Mesh Finite Difference Scheme for Singularly Perturbed Delay Differential Equations Invited Talk 26-10-2021
Scientific Research and Various Research Tools Invited Talk 09-10-2020
Numerical Analysis of a class of Singularly Perturbed Parabolic Turning Point Problem Invited Talk 28-08-2020
An epsilon Uniformly convergent hybrid scheme for a singularly perturbed parabolic turning point problem Oral Presentation 17-07-2019
Numerical Solution of Singularly Perturbed Delay- Differential Turning Point Problems Oral Presentation 26-06-2019
Singularly Perturbed Delay Differential Equations with boundary and Interior Layer Invited Talk 22-01-2019
A Higher Order epsilon Uniform method for Singularly Perturbed parabolic Turning Point Problems Invited Talk 02-12-2018
Robust Numerical Schemes for Singularly Perturbed Turning Point Problems Invited Talk 03-12-2017
Numerical Approximation of Singularly Perturbed Delay Differential Equations Invited Talk 08-12-2017
Fitted Operator finite Difference Scheme for Singularly Perturbed Delay Differential Equation With Turning Point Invited Talk 06-12-2016
Singularly Perturbed Turning Point Problems Oral Presentation 15-03-2022
Fitted operator finite difference scheme for a class of singularly perturbed differential- difference turning point problems exhibiting interior layers Oral Presentation 03-04-2015
An epsilon-Uniform Fitted Operator Method for Singularly Perturbed Delay Differential Turning Point Problem Oral Presentation 14-12-2014
A uniformly convergent finite difference scheme for singularly perturbed differential difference turning point problems Oral Presentation 16-12-2012
epsilon uniformly convergent finite difference scheme for singularly perturbed delay differential equations with twin boundary layer Oral Presentation 30-12-2012
The numerical study of singularly perturbed delay differential turning point problems Oral Presentation 07-09-2011
A uniformly convergent numerical method for singularly perturbed delay differential equation with turning point Oral Presentation 28-02-2011
Higher-Order Schemes for 1D Parabolic Singularly Perturbed Delay Differential Equations with Turning Point Speaker 29-11-2024
Singularly perturbed problems: Numerical Challenges and their solution” Speaker 14-02-2025
Seminar / Conference Details / Workshops
Type of Activity Name of The Event Role Duration
Workshops National Workshop cum FDP on Deep Learning in Scientific Computing Workshops 24-03-2025 To 28-03-2025 (4 days)
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