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

Lecture 13 - Elliptic Equations: Solution of Poisson Equation

This lecture represents the solution of Poisson equation by replacing the partial derivatives using finite difference formulas with example.

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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.)