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Numerical Methods: Finite Difference Approach

Numerical Methods: Finite Difference Approach. Instructor: Dr. Ameeya Kumar Nayak, Department of Mathematics, IIT Roorkee. This course is an advanced course offered to UG/PG student of Engineering/Science background. It contains solution methods for different class of partial differential equations. The convergence and stability analysis of the solution methods is also included. It plays an important role for solving various engineering and sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences. (from nptel.ac.in)

Lecture 05 - Polynomial Fitting and One-sided Approximation

This lecture deals with the order of approximation and polynomial fitting for first and second order partial derivatives.

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Lecture 01 - Introduction to Numerical Solutions

Lecture 02 - Numerical Solution of Ordinary Differential Equations

Lecture 03 - Numerical Solution of Partial Differential Equations

Lecture 04 - Finite Differences using Taylor Series Expansion

Lecture 05 - Polynomial Fitting and One-sided Approximation

Lecture 06 - Solution of Parabolic Equations

Lecture 07 - Implicit and Crank-Nicolson Method for Solving 1D Parabolic Equations

Lecture 08 - Compatibility, Stability and Convergence of Numerical Methods

Lecture 09 - Stability Analysis of Crank-Nicolson Method

Lecture 10 - Approximation of Derivative Boundary Conditions

Lecture 11 - Solution of Two Dimensional Parabolic Equations

Lecture 12 - Solution of 2D Parabolic Equations using ADI Method

Lecture 13 - Elliptic Equations: Solution of Poisson Equation

Lecture 14 - Solution of Poisson Equation using Successive over Relaxation (SOR) Method

Lecture 15 - Solution of Poisson Equation using ADI Method

Lecture 16 - Solution of Hyperbolic Equations

Lecture 17 - Stability Analysis of Hyperbolic Equations

Lecture 18 - Characteristics of PDEs and Solution of Hyperbolic Equations

Lecture 19 - Lax-Wendroff Method

Lecture 20 - Lax-Wendroff Method (cont.)