ISL Numerical Analysis (2014)

Venue: Department of Mathematics, Panjab University, Chandigarh
Dates:  9th – 28thJune, 2014


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name Prof. S K Tomar Prof. G D Veerappa Gowda
Dr Anuj Sharma 
Mailing Address Panjab University, Chandigarh TIFR, Bengaluru

Panjab University, Chandigarh


Speakers and Syllabus 


Speaker Lectures Detailed Syllabus
Speaker 1 GDV 6 Finite difference methods for partial differential equations (PDE): Introduction to basics of second order wave equation, Laplace equation and heat equation with corresponding finite difference equations. Consistency, stability and convergence analysis. Equivalence between Von-Neumann stability and L2 stability, Lax equivalence theorem. Explicit and implicit schemes. Error and convergence Analysis. Finite difference methods for non-linear hyperbolic conservation laws.

Speaker 2

6 Spectral methods for differential equations:  Fourier series, Discrete Fourier Transform and Fast Fourier Transform. Galerkin and collocation method for ODE's using Chebyshev polynomials. Fourier spectral methods for Laplace, Heat and Wave equations.

Speaker 3

6 Finite Element Methods: Weak formulation (a quick introduction), Finite element method (FEM) formulation,  Construction of finite element spaces, Interpolation estimates, Error estimates for finite element solution, Implementation of FEM in MATLAB, Introduction to discontinuous Galerkin methods.
Speaker 4
6 Finite volume methods: General ideas and an example of application to conservation laws.
a) Elliptic Problems: Formulation of finite volume scheme in one - dimension. Comparison with finite difference and finite element methods. Convergence and error estimates. Structured and general meshes in higher dimensions. Existence, convergence and error estimates.
b) Parabolic problems: Error estimate for the linear parabolic equations. Finite Volume methods for nonlinear case. Convergence and error estimates.
c) Finite volume methods for scalar conservation laws in 1D and in higher dimensions and also for systems of conservation laws.
Speaker 5
6 Numerical solutions of differential equations by Haar Wavelets: Wavelets, why wavelets, multi resolution analysis, construction of orthogonal wavelets with compact support, applications of Haar wavelets, Numerical solutions of Linear ordinary differential equations Initial and Boundary Value problems by Haar wavelet, Solutions of Non-linear ODE, Quasi-linearization, Numerical Solutions linear and nonlinear initial boundary value problems (PDE).

Speaker 6

6 Numerical methods for ordinary differential equations (ODE): Introduction to basics of ODE and difference equations. Euler and Euler predictor-corrector methods, Adams-Moulton method, Runge-Kutta methods and other higher order methods to the system of first order ODE for initial value problems. Shooting method and finite difference methods for the second order  boundary value problems with error and convergence analysis.

Abbreviations used:

  • KB- M K Kadalbajoo (IIT- Kanpur)
  • RCM- R C Mittal (IITR-Roorkee)
  • HK-Harish Kumar (IIT- Delhi)
  • GDV- G D Veerappa Gowda (TIFR-Bangaluru)
  • TG – Thirupathi Gudi (IISc-Bangaluru)
  • VM- A S Vasudeva Murthy (TIFR-Bangaluru).
  • SKT- S K Tomar (PU Chandigarh)

Time Table

      Lecture 1 Tea Lecture 2 Lunch Tutorial or Guest lecture Tea & Snacks
  Day Date 9.00-10.30   11.00 -12.30   2.00 - 4.00  
Week 1 1 09/6/14 RCM   VM   VM+SG+SD  
  2 10/6/14 RCM   VM   VM+SG+SD  
  3 11/6/14 RCM   RCM   VM+SG+SS  
  4 12/6/14 AS   VM   AS+JS+AKS  
  5 13/6/14 VM   VM   AS+JS+DS  
  6 14/6/14 SKT   VM   AS+JS+AKS  
Week 2 1 16/6/14 SKT   TG   SKT+AKS+JS  
  2 17/6/14 SKT   TG   SKT+AKS+SS  
  3 18/6/14 SKT   TG   SKT+VK+JB  
  4 19/6/14 SKT   TG   TG+VK+DS  
  5 20/6/14 SKT   TG   TG+VK+DS  
  6 21/6/14 TG   TG   TG+MS+JS  
Week 3 1 23/6/14 GDV   HK   GDV+MS+JS  
  2 24/6/14 GDV   HK   GDV+MS+JS  
  3 25/6/14 GDV   HK   GDV+DS+JB  
  4 26/6/14 GDV   HK   HK+DS+JS  
  5 27/6/14 GDV   HK   HK+DS+JB  
  6 28/6/14 GDV   HK   HK+AS+SKT  

 Abbreviations used:

  • HK- Harish Kumar (IIT Delhi)
  • RCM- R C Mittal (IITR Roorkee)
  • SKT- S K Tomar (PU Chandigarh)
  • GDV- G D Veerappa Gowda (TIFR Bengaluru)
  • TG -Thirupathi Gudi (IISc Bengaluru)
  • VM=Vasudeva Murthy (TIFR Bengaluru)
  • VK- Vinay Kanwar (UIET, PU Chandigarh)
  • AKS - Aditya Kaushik (UIET, PU Chandigarh)
  • SD -Saranjeet Dhawan (DAVU Jalandhar)
  • SS - Sachin Kumar (DAVU Jalandhar)
  • MS-Manu Sharma (UIET, PU Chandigarh)
  • JS- Jitender Singh (GNDU, Amritsar)
  • AS-Anuj Sharma(PU, Chandigarh)
  • DS – Dilbag Singh (PU Chandigarh)
  • JB-Jai Bhagwan (Govt. College,Chachroli)
  • SG-Suraj Goyal (PU, Chandigarh)
Selected Applicants
Sr. No. Participant Name Institute/ affiliation
1 Dr. Sanjib Sengupta Department of Mathematics, Assam University, Silchar
2 Dr. Biju Kumar Dutta Kaziranga University, Koraikhowa,
3 Dr. Arvind Patel Department of Mathematics, University of Delhi, Delhi
4 Mr. Sunil Kumar Department of Basic & Applied Sciences, BPS Women University, Sonepat (Haryana)
5 Dr. Jai Prakash Jaiswal MACT Square, Bhopal,( MP)
6 Mr. Bhimanand Pandurang Gajbhare Vaidynath College, Beed (Maharashtra).
7 Dr. Prem Prakash Mishra NIT, Chumukedima-797103, Dimapur,Nagaland.
8 Dr. Jitender Singh Department of Mathematics, GNDU, Amritsar(Pb)
9 Dr. Vikramjeet Singh DAV University Jalandhar-Pathankot National Highway- 44, Sarmastpur, Jalandhar, (Pb)
10 Mr. Vinay Arora Department of Mathematics,PURC, Hoshiarpur (Pb.)
11 Dr. Praveen Kumar Gupta Banasthali University, Banasthali-304022, Rajasthan
12 Dr. Yajuvindra Kumar M.K. Government Degree College near central jail Ninowa, Farrukhabad(UP)
13 Mr. Mohsin Islam St Xavier‟s College, Mother Teresa Sarani Kolkata (WB)
14 Mr Pandith Giri Mohan Das Department of Mathematics J.N.N.C.E Navule, Shimoga, Karnataka
15 Dr. Deep Sarmah NIT, Department of Mathematics Chumukedima, Dimapur, Nagaland.
16 Dr Sharanjeet Dhawan Department of Mathematics D.A.V.University Jalandhar (Pb)
17 Dr. Sachin Kumar DAV University, Jalandhar, (Pb)
18 Dr. Satish Kumar Department of Mathematics,PURC, Hoshiarpur (Pb.)
19 Mr. Shanti Swarup Dubey MATS University, Arang-Kharora Highway,Gullu,Arang, Chattisgarh
20 Ms. Brehmit Kaur Sri Guru Granth Sahib World University, Fatehgarh Sahib, Sirhind,( Pb)
21 Mr. Jai Bhagwan Government College, Chhachhrouli (Haryana)
22 Mr. Gurjinder Singh UIET, Panjab University, Chandigarh
23 Mr. Munish Kansal UIET, Panjab University, Chandigarh.
24 Mrs. Vanita Sharma IET, Bhaddal, Ropar,( Pb)
25 Dr. Dilbag Singh Department of Mathematics, PU, Chandigarh
26 Ms. Komal Bansal Department of Mathematics,PU, Chandigarh
27 Suraj Goyal Department of Mathematics, PU, Chandigarh
28* Jitendra Singh Department of Mathematics, Central University of Bihar, Patana (Bihar)

 Inagural Session

1) Click here to see picture

2) Click here to see picture

3) Click here for Group photo


How to reach

Chandigarh is capital of Punjab and Haryana and is a Union Territory. Chandigarh is well connected with trains, air and roads from Delhi. It is about 250 kilometers from Delhi in the north direction. It is well connected with trains and roads from Uttar Pradesh, Haryana, Himachal Pradesh and Punjab.


Organizers Comments

From the feedback of the participants, we understand that the program was a success in achieving its goals. Participants felt that local facilities are excellent, e.g. food, hospitality and AC accommodation. Also most of the participants were able to follow the course in-spite of their not so good background. According to the feedbacks teaching was excellent and rated the school overall 9 out of 10. However, in general, there are following suggestions from some of the participants:
1. Travelling allowances should be provided
2. Study materials should be provided before the start of the School.
3. Schools on Neural Networks & Applications, Solid Mechanics, Fluid
Mechanics and Nano-mechanics should also be organized in future.

The organizers wish to thank National Centre for Mathematics for financial support and the encouragement. Also, we are thankful to Panjab University for providing excellent infrastructure and full cooperation in smooth conducting the school.
Especially, we are grateful to Professor Arun Kumar Grover, Vice-Chancellor of Panjab University, Chandigarh and Professor A K Bhandari, Dean University Instructions-cum-Registrar of Panjab University, Chandigarh and faculty of Mathematics for providing full support for smooth conduct of this School.