Numerical Solution: Ordinary & Partial Differential Equation

Numerical Solution: Ordinary & Partial Differential Equation, available at $44.99, has an average rating of 4.95, with 39 lectures, 15 quizzes, based on 64 reviews, and has 548 subscribers.

You will learn about Basic numerical solution techniques for solving ordinary and partial differential equations. This course is ideal for individuals who are STEM students interested in learning fundamental numerical techniques for the solution of ordinary and partial differential equations. It is particularly useful for STEM students interested in learning fundamental numerical techniques for the solution of ordinary and partial differential equations.

Enroll now: Numerical Solution: Ordinary & Partial Differential Equation

Summary

Title: Numerical Solution: Ordinary & Partial Differential Equation

Price: $44.99

Average Rating: 4.95

Number of Lectures: 39

Number of Quizzes: 15

Number of Published Lectures: 39

Number of Published Quizzes: 15

Number of Curriculum Items: 59

Number of Published Curriculum Objects: 59

Original Price: $24.99

Quality Status: approved

Status: Live

What You Will Learn

Basic numerical solution techniques for solving ordinary and partial differential equations.

Who Should Attend

STEM students interested in learning fundamental numerical techniques for the solution of ordinary and partial differential equations.

Target Audiences

STEM students interested in learning fundamental numerical techniques for the solution of ordinary and partial differential equations.

The course provides an introduction to the numerical solution of ordinary and partial differential equations and is at a level appropriate for undergraduate-level STEM students. Prior knowledge of numerical methods is helpful but not necessary as (most) prerequisite material is introduced on an as-needed basis. Knowledge of a scientific programming language is necessary for those wishing to write their own codes. All codes used to demonstrate methods and solve example problems (primarily in both Fortran and Python) are available for downloading, as are the class notes. For the ordinary differential equations, we will study numerical techniques to solve:

1) Initial value (or propagation) problems

2) Boundary value (or equilibrium) problems

3) Eigenvalue (or characteristic value) problems

In terms of partial differential equations, we will concentrate on finite-difference approaches to solve second-order partial differential equations.

These equations may be classified as elliptic, parabolic, or hyperbolic. The classification helps determine the best approach to obtain a numerical solution. We will focus on elliptic and parabolic partial differential equations.

The primary course sections are:

SECTION 2: ODE’s: INITIAL VALUE PROBLEMS

SECTION 3: ODE’s: BOUNDARY VALUE PROBLEMS

SECTION 4: ODE’s: EIGENVALUE PROBLEMS

SECTION 5: ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

SECTION 6: PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

Course Curriculum

Chapter 1: Introduction and Course Content

Lecture 1: Introductory Material

Chapter 2: Ordinary Differential Equations: Initial Value Problems

Lecture 1: Introduction to IVP's

Lecture 2: Implicit and Explicit Euler's Method

Lecture 3: Example Using Explicit and Implicit Euler Approaches

Lecture 4: Truncation Error for Euler's Method

Lecture 5: Modified Euler and Midpoint Methods

Lecture 6: General Runge-Kutta Methods

Lecture 7: Example Using the Modified Euler Method

Lecture 8: Fourth-Order Runge-Kutta Method

Lecture 9: Example Using Adams-Bashforth Multi-Step Method

Lecture 10: Multi-Step Methods

Lecture 11: Higher-Order Equations

Lecture 12: Example Higher-Order System Solution

Chapter 3: Ordinary Differential Equations: Boundary Value Problems

Lecture 1: Introduction to BVP's

Lecture 2: Shooting Method for BVP's

Lecture 3: Shooting Method Example Code

Lecture 4: Shooting Method Example Results

Lecture 5: Basic Finite-Difference Approximations

Lecture 6: Finite-DIfference Methods for BVP's

Lecture 7: The Tridiagonal Matrix Algorithm

Lecture 8: Derivative Boundary Conditions

Chapter 4: Ordinary Differential Equations: Eigenvalue Problems

Lecture 1: Introduction

Lecture 2: Eigenvalues Using the Polynomial Method

Lecture 3: Power Method

Chapter 5: Elliptic Partial Differential Equations

Lecture 1: Introduction

Lecture 2: Finite-Difference Approach

Lecture 3: Elliptic Equation Solver for Rectangular Domains Using SOR

Lecture 4: Code to Solve Laplace Equation on Rectangular Meshes

Lecture 5: Compute the Stream Function About a Cylinder

Lecture 6: ParaView Visualization Results for Cylinder Flow

Lecture 7: Derivative Boundary Conditions

Lecture 8: ParaView Derivative Bondary Conditon Results for Cylinder Flow

Lecture 9: Line Relaxation

Chapter 6: Solving Parabolic Partial Differential Equations

Lecture 1: Explicit Time Advance

Lecture 2: Code For Explicit Time Advance

Lecture 3: Implicit Time Advance

Lecture 4: Crank-Nicolson Time Advance

Lecture 5: Parabolic Equations in Two Spatial Dimensions

Lecture 6: Non-dimensionalization of Differential Equations

Instructors

Robert Spall
Mechanical and Aerospace Engineering

Rating Distribution

1 stars: 0 votes
2 stars: 2 votes
3 stars: 12 votes
4 stars: 17 votes
5 stars: 33 votes

Frequently Asked Questions

How long do I have access to the course materials?

You can view and review the lecture materials indefinitely, like an on-demand channel.

Can I take my courses with me wherever I go?

Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don’t have an internet connection, some instructors also let their students download course lectures. That’s up to the instructor though, so make sure you get on their good side!

Menu