# AIS Numerical Analysis (2012)

 Venue: DEPARTMENT OF MATHEMATICSHANS RAJ  GUPTA  HALLPANJAB UNIVERSITYCHANDIGARH (UT) Dates: 18th June - 7th July 2012

 School Convener(s) Name S. K. Tomar G. D. Veerappa Gowda Mailing Address Department of Mathematics,Panjab University, Sector-14Chandigarh -160014 Tata Institute of Fundamental Research, Center for Applicable Mathematics, Bangalore

While dealing with the realistic problems of physical and experimental importance in various fields like Fluid Dynamics, Electrodynamics, Elasticity, Chaotic dynamics, Biological sciences, Information sciences etc., Mathematics plays a key role in finding their solutions. Very frequently, we come across various types of equations, e.g., non-linear equations, ordinary differential equations, partial differential equations, functional differential equations and Integro-differential equations. Many times, it is not possible to find their analytical solutions. In order to find the approximate solutions of these equations, one has to adopt numerical techniques. The numerical solutions so obtained may suffer numerical instability or may contain large errors. In order to control these implications, the correct mathematical methods in correct situation need to be analyzed. This is where one cannot go ahead without mathematical help. At the same time, one should not rely blindly on the solutions provided by the mathematical software available today. It is emphasized that before going to solve the related mathematical problems on the available software, the mathematical well-posedness and the existence of solution space should be analyzed properly. Keeping in view the need and importance of classical and advances numerical methods, it will be highly useful to hold an Advanced Instructional School on this topic. This course will be of great importance to the research scholars dealing with numerical analysis and will provide impetus to their further research.

 Speakers and Syllabus

 Speaker Number of Lectures Detailed Syllabus Speaker 1 KKS(2) VK(4) 6 Root Finding for Nonlinear Equations (Bisection, Newton’s method, Secant and Muller’ method);  Approximation of Functions (Weierstrass, Tyalor’ theorem, Minimax and least square Approximation), Numerical Integration. Speaker 2RCM(6) 6 Linear multistep method: Introduction to general linear multistep methods, derivation of multistep methods through Taylor’s expansion, numerical integration and interpolation, stability and convergence analysis, Runge-Kutta methods, classical and higher order Runge-Kutta methods, stability and convergence analysis. Speaker 3KB(6) 6 Numerical Analysis of ordinary differential equations: Rayleigh – Ritz, Galerkin, Differential quadrature, Shooting, Finite Difference and Finite element methods. Speaker 4KB(6) 6 Parabolic partial differential equations:Explicit, Implicit, Three time level schemes, ADI and LOD methods, their stability and convergence analysis Speaker 5GDV(6) 6 Hyperbolic partial differential equation in one space dimension: Upwind, Lax-Wendroff, Box, Le-Frog Schemes and their stability and convergence analysis. Finite volume method for conservation laws. Speaker 6RKM(6) 6 Elliptic partial differential equation: Finite difference method, variational formulation of elliptic partial differential equation and Finite element method.

Abbreviations used:

VK- Vinay Kanwar (PU, Chandigarh) , RCM- R C Mittal (IITR, Roorkee), RKM- R K Mohanty (DU Delhi), KB- M K Kadalbajoo (IIT, Kanpur) , GDV- G D Veerappa Gowda (TIFR, Bangalore), KKS-Kapil Kumar Sharma (PU, Chandigarh).

Time-Table

 Lecture 1 Tea Lecture 2 Lunch Tutorial or Tea & Guest lecture Snacks Day Date 9.00-10.30 11.00 -12.30 2.00 - 4.00 Week 1 1 18/6/12 RKM RCM RKM+AS+RD 2 19/6/12 RKM RCM RKM+AS+RD 3 20/6/12 RKM RCM RKM+AS+RD 4 21/6/12 RKM RCM RCM+SG+AK 5 22/6/12 RKM RCM RCM+SG+AK 6 23/6/12 RKM RCM RKM+SG+AK Week 2 1 25/6/12 GDV GDV GDV+AK+SG 2 26/6/12 GDV GDV GDV+AK+SG 3 27/6/12 GDV VK VK+AK+SG 4 28/6/12 GDV VK VK+AK+SG 5 29/6/12 GDV KKS Special Lecture 6 30/6/12 GDV KKS KKS*+RD+AS Week 3 1 02/7/12 KB KB KB+RD+AS 2 03/7/12 KB KB KB+RD+AS 3 04/7/12 KB KB KB+RD+AS 4 05/7/12 KB KB KB+AK+AS 5 06/7/12 KB KB RD+AK+KB 6 07/7/12 KB KB RD+AK+KB

Abbreviations used:

VK- Vinay Kanwar (PU, Chandigarh) , RCM- R C Mittal (IITR Roorkee), RKM- R K Mohanty (DU Delhi), KB- M K Kadalbajoo (IIT, Kanpur) , GDV- G D Veerappa Gowda (TIFR, Bangalore), KKS- K K Sharma (PU, Chandigarh),AK= Arti Khurana (DAV, Chandigarh), SG-Suraj Goyel (PU Chandigarh), RD- Raman Deep(PU Chandigarh), AS-Anuj Sharma(PU Chandigarh).

 Selected Applicants
• The selected participants are requested to confirm their participation by 10th May 2012 for booking accommodation.
• Confirmation mail should be sent to sktomar66 at gmail.com
• Travel by 3rd AC Train fare is allowed to the participants