0

(

ratings

)

2

students

Created by:

Profile Photo

Last updated:

September 23, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Numerical Methods of Ordinary and Partial Differential Equations. Instructor: Dr. G. P. Raja Sekhar, Department of Mathematics, IIT Kharagpur.

Ordinary Differential Equations: Initial Value Problems (IVP) and existence theorem. Truncation error, deriving finite difference equations. Single step methods for IVPs - Taylor series method, Euler's method, Runge Kutta Methods. Stability of single step methods. Multi step methods for IVPs - Predictor-Corrector method, Euler PC method, Milne and Adams Moulton PC method. System of first order ODE, higher order IVPs. Stability of multistep methods, root condition. Linear Boundary Value Problems (BVP), finite difference methods, shooting methods, stability, error and convergence analysis. Nonlinear BVP, higher order BVP.

Partial Differential Equations: Classification of PDEs, Finite difference approximations to partial derivatives. Solution of one dimensional heat conduction equation by Explicit and Implicit schemes (Schmidt and Crank Nicolson methods ), stability and convergence criteria. Laplace equation using standard five point formula and diagonal five point formula, Iterative methods for solving the linear systems. Hyperbolic equation, explicit/implicit schemes, method of characteristics. Solution of wave equation. Solution of first order Hyperbolic equation. (from nptel.ac.in)

Course Curriculum

    • Lecture 01 – Motivation with Few Examples Unlimited
    • Lecture 02 – Single Step Methods for Initial Value Problems: Taylor Series Method Unlimited
    • Lecture 03 – Analysis of Single Step Methods: Euler’s Method Unlimited
    • Lecture 04 – Runge-Kutta Methods for Initial Value Problems Unlimited
    • Lecture 05 – Higher Order Runge-Kutta Methods, Higher Order Equations Unlimited
    • Lecture 06 – Error-Stability-Convergence of Single Step Methods Unlimited
    • Lecture 07 – Tutorial I: Single Step Methods Unlimited
    • Lecture 08 – Tutorial II: Single Step Methods Unlimited
    • Lecture 09 – Multistep Methods (Explicit) Unlimited
    • Lecture 10 – Multistep Methods (Implicit) Unlimited
    • Lecture 11 – Convergence and Stability of Multistep Methods Unlimited
    • Lecture 12 – General Methods for Absolute Stability Unlimited
    • Lecture 13 – Stability Analysis of Multistep Methods Unlimited
    • Lecture 14 – Predictor-Corrector Methods Unlimited
    • Lecture 15 – Some Comments on Multistep Methods Unlimited
    • Lecture 16 – Finite Difference Methods – Linear Boundary Value Problems Unlimited
    • Lecture 17 – Linear/Nonlinear Second Order Boundary Value Problems Unlimited
    • Lecture 18 – Boundary Value Problems – Derivative Boundary Conditions Unlimited
    • Lecture 19 – Higher Order Boundary Value Problems Unlimited
    • Lecture 20 – Shooting Method – Boundary Value Problems Unlimited
    • Lecture 21 – Tutorial III: Boundary Value Problems Unlimited
    • Lecture 22 – Introduction to First Order Partial Differential Equations Unlimited
    • Lecture 23 – Introduction to Second Order Partial Differential Equations Unlimited
    • Lecture 24 – Finite Difference Approximations to Parabolic Partial Differential Equations Unlimited
    • Lecture 25 – Implicit Methods for Parabolic Partial Differential Equations Unlimited
    • Lecture 26 – Consistency, Stability and Convergence Unlimited
    • Lecture 27 – Other Numerical Methods for Parabolic Partial Differential Equations Unlimited
    • Lecture 28 – Tutorial IV: Explicit, Implicit and Derivative Boundary Conditions Unlimited
    • Lecture 29 – Matrix Stability Analysis of Finite Difference Scheme Unlimited
    • Lecture 30 – Fourier Series Stability Analysis of Finite Difference Scheme Unlimited
    • Lecture 31 – Finite Difference Approximations to Elliptic PDEs I Unlimited
    • Lecture 32 – Finite Difference Approximations to Elliptic PDEs II Unlimited
    • Lecture 33 – Finite Difference Approximations to Elliptic PDEs III Unlimited
    • Lecture 34 – Finite Difference Approximations to Elliptic PDEs IV Unlimited
    • Lecture 35 – Finite Difference Approximations to Hyperbolic PDEs I Unlimited
    • Lecture 36 – Finite Difference Approximations to Hyperbolic PDEs II Unlimited
    • Lecture 37 – Method of Characteristics for Hyperbolic PDEs I Unlimited
    • Lecture 38 – Method of Characteristics for Hyperbolic PDEs II Unlimited
    • Lecture 39 – Finite Difference Approximations for First Order Hyperbolic PDEs Unlimited
    • Lecture 40 – Summary Unlimited

About the instructor

5 5

Instructor Rating

6

Reviews

4637

Courses

24151

Students

Profile Photo
OpenCoursa
We are an educational and skills marketplace to accommodate the needs of skills enhancement and free equal education across the globe to the millions. We are bringing courses and trainings every single day for our users. We welcome everyone woth all ages, all background to learn. There is so much available to learn and deliver to the people.