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Numerical methods of Ordinary and Partial Differential Equations

Lecture 1: Mod-01 Lec-01 Motivation with few Examples

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Lecture Details :

Numerical methods of Ordinary and Partial Differential Equations by Prof. Dr. G.P. Raja Sekhar, Department of Mathematics, IITKharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

Initial Value Problems (IVP) and existence theorem. Truncation error, deriving finite difference equations - Single step methods for I order IVP- Taylor series method, Euler method, Picardís method of successive approximation - Runge Kutta Methods. Stability of single step methods - Multi step methods for I order IVP - Predictor-Corrector method, Euler PC method, Milne and Adams Moulton PC method.

Stability of multi step methods, root condition - System of first order ODE, higher order IVPs - Linear Boundary Value Problems (BVP), finite difference methods, shooting methods, stability, error and convergence analysis - Non linear BVP, higher order BVP - Classification of PDEs, Finite difference approximations to partial derivatives - Solution of one dimensional heat conduction equation by Explicit and Implicit schemes (Schmidt and Crank Nicolson methods ), stability and convergence criteria.

Laplace equation using standard five point formula and diagonal five point formula, Iterative methods for solving the linear systems - Hyperbolic equation, explicit / implicit schemes, method of characteristics. Solution of wave equation - Solution of I order Hyperbolic equation. Von Neumann stability - In hand for some topics to be revised

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