# InfoCoBuild

## 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 06 - Solution of Parabolic Equations

One-sided approximation for first and second order partial derivative and solution of one dimensional parabolic equation using explicit scheme with example is discussed in this lecture.

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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.)