Numerical Methods: Finite Difference Approach (Dr. Ameeya Kumar Nayak, IIT Roorkee): Lecture 07 - Implicit and Crank-Nicolson Method for Solving 1D Parabolic Equations

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

This lecture deals with the Implicit scheme and Crank-Nicolson scheme for the solution of one dimensional parabolic equations with example. Compatibility stability and convergence of finite difference scheme is also discussed here.

Go to the Course Home or watch other lectures:

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