YoVDO

Numerical Methods: Finite difference approach

Offered By: Indian Institute of Technology Roorkee via Swayam

Tags

Engineering Courses Numerical Methods Courses Stability Analysis Courses Partial Differential Equations Courses Ordinary Differential Equations Courses

Course Description

Overview

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.INTENDED AUDIENCE : UG students of technical universities/collegesPRE-REQUISITES : Numerical Methods Basic KnowledgeINDUSTRY SUPPORT : TCS, Intel, General Electric, General Motors, ABB, Nuclear Industries, etc

Syllabus

Week 1: Introduction to Numerical methods, Initial and Boundary value problems, Numerical solution of ODE, Picard’s method, Taylor’s series method, Euler’s method, ModifiedEuler’s method, Runge-Kutta method.Week 2 : Introduction of PDE, Classification of PDE: parabolic, elliptic and hyperbolic. Boundary and initial conditions, Taylor series expansion, analysis of truncation error, Finite difference method: FD, BD & CD, Higher order approximation, Order of Approximation, Polynomial fitting, One-sided approximation.Week 3 : Parabolic equation in 2D, Explicit & Crank-Nicolson method, Alternating direction Implicit method (ADI), Elliptic equations, Solution of Poisson equation with Example,Successive over Relaxation (SOR) method, Solution of Elliptic equation by using ADI method, Example.Week 4 : Hyperbolic equations, solution using Explicit method, Stability analysis of Explicit and Implicit scheme, Example, Characteristics of PDE, Solution of Hyperbolic equation by using methods of Characteristics, Hyperbolic equation of first order, Lax-Wendroff’s method, Wendroff’s method, stability analysis of method, Example.

Taught by

Ameeya Kumar Nayak

Tags

Related Courses

Differential Equations in Action
Udacity
Dynamical Modeling Methods for Systems Biology
Icahn School of Medicine at Mount Sinai via Coursera
An Introduction to Functional Analysis
École Centrale Paris via Coursera
Practical Numerical Methods with Python
George Washington University via Independent
The Finite Element Method for Problems in Physics
University of Michigan via Coursera