Short Term Course On
Theory and Computation of Singularly Perturbed Differential Equations
December 04-08, 2017

Organised by Department of Mathematics, IIT (BHU), Varanasi
Supported by MHRD under GIAN (Global Initiative for Academic Networks)


Important Dates

  • Registration starts on:                                    October 01, 2017.
  • Last date of registration (if seats available): November 24, 2017
  • Course duration:                                             December 04-08, 2017

Course Overview

Singularly perturbed problems in ordinary and partial differential equations arise as mathematical models in various physical phenomena.  For example, mathematical models of liquid crystal, the equations governing flow in porous media, the Navier-Stokes equations of fluid flow at high Reynolds number, and the drift-diffusion equations of semiconductor device, all are singularly perturbed. In general, the solutions to singularly perturbed problems exhibit boundary and/or interior layers (narrow regions where the solution changes drastically) due to the presence of small perturbation parameter. Although the layer regions are small, their influence on the overall solution is very significant. Due to layer behavior of the solution, classical numerical approaches are not adequate for solving singularly perturbed problems, as they require prohibitively large numbers of mesh points to produce satisfactory approximations. This leads to the development of so-called parameter-robust or uniformly convergent numerical methods for singularly perturbed problems.

The principal goal of this course is to present a variety of non-classical approaches based on finite differences and finite elements for the construction of robust numerical methods for singularly perturbed problems. Further, stability, consistency and convergence of numerical methods for singularly perturbed problems will be discussed and analyzed. Along with the theory, the development of robust implementations of novel numerical methods using widespread conventional languages of scientific programming will be presented, leading to a deeper understanding of practical aspects of these methods, and providing a framework for developing an intuitive understanding of them. To conclude, some open problems will be outlined, and challenges involved in solving them will be discussed, motivating M.Sc. and PhD students to engage in research problems in this rapidly developing area of mathematical research.

Main Topics

  • Introduction to singularly perturbed problems, Regular perturbation methods, Singular perturbation methods, Numerical methods and uniform convergence.
  • Finite difference methods and their analysis for singularly perturbed problems, Coupled systems of singularly perturbed problems.
  • Singularly perturbed parabolic problems in 1D, High order numerical methods for singularly perturbed problems.
  • Finite element methods and their analysis, Finite elements in two and three dimensions, Multigrid and sparse grid methods.
  • Singularly perturbed parabolic problems in 2D, Moving mesh methods for singularly perturbed problems.

Who can Attend

  • M.Sc./B.Tech./M.Tech./Ph.D. students from various institutes, universities and research   organizations across the country.

  • Faculty/Researchers/Scientist from academic/technical institutions and R&D Centre across the country.

About the Faculty

Dr Niall Madden 
School of Mathematics, Statistics, and Applied Mathematics
National University of Ireland, Galway, Ireland 

Dr. Niall Madden is lecturer in the School of Mathematics, Statistics, and Applied Mathematics at the National University of Ireland, Galway, Ireland. He earned his masters (1996) from University College Cork and Ph.D. (2000) from National University of Ireland, Cork. He is author of more than 33 publications in international journals of repute. His current research interests are in Finite Element and Finite Difference Methods, Preconditioning and Fast Multigrid Solvers, Sparse Grid Methods, and ADI Techniques. He has organized several conferences and workshops. He is also member of the editorial board of Numerical Algorithms.

Dr. Sunil Kumar
Department of mathematical Sciences, Indian Institute of Technology (BHU), Varanasi
Uttar Pradesh-221005, India

Dr. Sunil Kumar is Assistant Professor in the Department of Mathematical Sciences, IIT (BHU), Varanasi, India. He earned his masters degree from IIT Roorkee and doctorate degree from IIT Delhi. He carried out his postdoctoral research at IISc Bangalore (2012) and University of Coimbra, Portugal (2012-2014). He was then a research scientist at Max Planck Institute for Solar System Research, Germany (2014-2015). He also served as Assistant Professor at NIT Delhi (2015-2016). His research interests are in Numerical Analysis of Partial Differential Equations, Domain Decomposition Methods, Singular Perturbation Problems, and Mathematical Image Processing.

Prof. L. P. Singh
Department of mathematical Sciences, Indian Institute of Technology (BHU), Varanasi
Uttar Pradesh-221005, India

Dr. L. P. Singh is Professor in Department of Mathematical Sciences, IIT (BHU), Varanasi, India. He has done his masters and Ph.D. from BHU, Varanasi. His research interests are in Non-linear waves and Computational Fluid Dynamics.

Registration Process

Registration to this course is a two step process.

Step 1: One-time Registration on GIAN portal (if already registered, go to Step 2 for details regarding institute registration for this course)

 Web link:

Note that registration to the portal is one-time affair and will be valid for lifetime of GIAN. Once registered in the portal, an applicant will be able to apply for any number of GIAN courses as and when necessary. Please also note that mere registration to the portal will not ensure participation in the course. Please do not confuse GIAN portal registration with course registration. The course participation fee is separate.

Step 2: Institute Registration: Once registered in the portal, an applicant will be able to apply for this GIAN course titled “Isogeometric Methods using B-Splines and NURBS”. All participants are required to pay the appropriate registration fee as given below.

  • Participants from Industry/Research Organizations: Rs. 3500
  • Faculty/Scientist/Researchers from Academic/Technical Institutions: Rs. 3000
  • Students from Academic Institutions: Rs 1000
  • SC/ST Students Academic Institutions: Rs 500
  • Participants from Abroad: USD 200

The above fee entitles participants to attend all the lectures, instructional materials, computer use for tutorials and assignments, internet facility. Boarding, lodging and meal charges are not included in the fee.

Participants are requested to email the scanned copy of duly filled registration form given at the end, along with the receipt of prescribed fee submitted through State Bank Collect, on or before November 24, 2017, with the subject ‘GIAN TCSPDE 2017 Participant’ to The procedure for making the fee payment is as follows.

Payment Instructions: Access Click on SB Collect. Click Checkbox to accept ‘Terms & conditions’. Then click on ‘Proceed’. Select state as ‘Uttar Pradesh’. Select type of category as ‘Educational Institutions’. Click on ‘Go’. Select the name of institutions as ‘Indian Institute of Technology (B.H.U.), Varanasi’. Select payment category as ‘GIAN-short term course participation fee’. Fill up the form and pay the fee according to your participation category. Save the receipt for record and get SB collect reference number; you need to fill it on registration form.


The participants may be provided with accommodation at the Institute Guest House/ Hostels on nominal payment basis subject to availability. Request for accommodation has to be sent in advance. Otherwise, participants will have to make their own stay arrangement.

Address for all Correspondence

Course Coordinator
Dr. Sunil Kumar,
Assistant Professor,
Department of mathematical Sciences, IIT (BHU)
Varanasi, Uttar Pradesh-221005, India
Mobile No.: +91 7835014019


The course brochure can be downloaded here: GIAN TCSPDE Brochure.

Further Information

  • Number of participants for the course will be limited to forty.
  • List of selected participants will be available on this webpage on November 24, 2017.
  • Accommodation will be provided on first come first serve basis.
  • Bring your fee receipt, registration form, and selection confirmation to attend the course.
  • Participants will be provided registration kit and course material covering the entire course. The registration fee includes all instructional materials, computer use for tutorials and assignments, and free internet facility.
  • There will be continuous evaluation of each participant during the course on understanding of the concepts and skills. Based on the performance, winners will be announced and some prizes may be given.
  • After successful completion of the course, all participants will get participation certificate.
  • Last but not least, do not hesitate to contact the course coordinator if you have any questions or require any information about the course.

How to Reach

The city of Varanasi is well connected by road, rail and air with all the important places of India. Regular flights are there from Varanasi to Delhi, Mumbai, Chennai, Bangalore, Kolkata, Khajuraho and Lucknow. The Banaras Hindu University campus is only 10 Kms from Varanasi railway station, 20 Kms from Mughal Sarai railway station and 35 Kms from the airport. More information can be found by clicking (More Information).