# ISL Numerical Analysis (2014)

Venue: |
Department of Mathematics, Panjab University, Chandigarh |

Dates: |
9th – 28thJune, 2014 |

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

Name |
Prof. S K Tomar | Prof. G D Veerappa Gowda |
Dr Anuj Sharma |

Mailing Address |
Panjab University, Chandigarh | TIFR, Bengaluru |
Panjab University, Chandigarh |

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 HK |
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 RCM |
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**

**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.

**Acknowledgements**

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.