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Mathematical Methods for Boundary Value Problems

Mathematical Methods for Boundary Value Problems. Instructor: Prof. S. Bhattacharyya, Department of Mathematics, IIT Kharagpur. This course is intended to provide methods to solve linear and nonlinear boundary value problems involving ordinary as well as partial differential equations. The course will start providing mathematical tools based on integral transformation, Fourier series solution and Green's function for obtaining analytic solutions for BVPs. This course, apart from being a part of regular undergraduate/ postgraduate mathematics course, will provide a guidance to solve BVPs arising in mathematical modeling of several transport phenomena. (from nptel.ac.in)

Lecture 05 - Solutions of Linear Parabolic, Hyperbolic and Elliptic PDEs with Finite Domain by ...

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Lecture 01 - Sturm-Liouville Problems, Linear BVP

Lecture 02 - Sturm-Liouville Problems, Linear BVP (cont.)

Lecture 03 - Solution of BVPs by Eigenfunction Expansion

Lecture 04 - Solution of BVPs by Eigenfunction Expansion (cont.)

Lecture 05 - Solutions of Linear Parabolic, Hyperbolic and Elliptic PDEs with Finite Domain by Eigenfunction Expansions

Lecture 06 - Solutions of Linear Parabolic, Hyperbolic and Elliptic PDEs with Finite Domain by Eigenfunction Expansions (cont.)

Lecture 07 - Green's Function for BVP and Dirichlet Problem

Lecture 08 - Green's Function for BVP and Dirichlet Problem (cont.)

Lecture 09 - Numerical Techniques for IVP; Shooting Method for BVP

Lecture 10 - Numerical Techniques for IVP; Shooting Method for BVP (cont.)

Lecture 11 - Finite Difference Methods for Linear BVP; Thomas Algorithm

Lecture 12 - Finite Difference Methods for Linear BVP; Thomas Algorithm (cont.)

Lecture 13 - Finite Difference Method for Higher-Order BVP; Block Tridiagonal System

Lecture 14 - Finite Difference Method for Higher-Order BVP; Block Tridiagonal System (cont.)

Lecture 15 - Iterative Methods for Nonlinear BVP; Control Volume Formulation

Lecture 16 - Iterative Methods for Nonlinear BVP; Control Volume Formulation (cont.)

Lecture 17 - Implicit Scheme; Truncation Error; Crank-Nicolson Scheme

Lecture 18 - Implicit Scheme; Truncation Error; Crank-Nicolson Scheme (cont.)

Lecture 19 - Stability Analysis of Numerical Schemes

Lecture 20 - Alternating-Direction-Implicit Scheme; Successive-Over-Relaxation Technique for Poisson Equations