Lectures (Video)

- 1. Euler's Method of Solving ODEs: Derivation
- 2. Euler's Method of Solving ODEs: Example
- 3. Euler's Method of Estimating Integrals: Theory
- 4. Euler's Method of Estimating Integrals: Example
- 5. Runge-Kutta 2nd Order Method: Background
- 6. Runge-Kutta 2nd Order Method: Formulas
- 7. Runge-Kutta 2nd Order Method: Heun's Method
- 8. Runge-Kutta 2nd Order Method: Midpoint Method
- 9. Runge-Kutta 2nd Order Method: Ralston's Method Part 1
- 10. Runge-Kutta 2nd Order Method: Ralston's Method Part 2
- 11. Runge-Kutta 2nd Order Method: Derivation Part 1
- 12. Runge-Kutta 2nd Order Method: Derivation Part 2
- 13. Runge Kutta 4th Order Method: Formulas
- 14. Runge Kutta 4th Order Method Example: Part 1
- 15. Runge Kutta 4th Order Method Example: Part 2
- 16. Shooting Method: Background
- 17. Shooting Method: The Method
- 18. Shooting Method Example: Part 1
- 19. Shooting Method Example: Part 2
- 20. Shooting Method Example: Part 3
- 21. Shooting Method Example: Part 4
- 22. Finite Difference Method: Background Part 1
- 23. Finite Difference Method: Background Part 2
- 24. Finite Difference Method: Example Beam - Part 1
- 25. Finite Difference Method: Example Beam - Part 2
- 26. Finite Difference Method: Example Pressure Vessel - Part 1
- 27. Finite Difference Method: Example Pressure Vessel - Part 2

## Numerical Methods VII

### Course Summary

This course is based on

This is a course on the basics of numerical methods and how they are used to solve scientific and engineering problems. It is accompanied by a comprehensive set of video lectures, presentation slides, textbook notes, worksheets and application examples. The lectures are in short segments of less than 10 minutes. Part VII covers the numerical methods used for solving ordinary differential equations including Euler's method, Runge-Kutta methods and Finite Difference method.
*Numerical Methods - Ordinary Differential Equations*made available by*Holistic Numerical Methods Institute, University of South Florida*under the*Creative Commons BY-NC-SA*license.### Reading Material

1.**Numerical Methods with Applications - Chapter 8**

Author: Autar Kaw et al.

Publisher: http://www.autarkaw.com

Published: May 4, 2010

ISBN: 978-0-578-05765-1

2.

**What are Ordinary Differential Equations?**

3.

**A Primer on Ordinary Differential Equations**

### Course Material

1.**Test Your Knowledge of Background of Ordinary Differential Equation**

2.

**Physical Problem**

Contracting a cylinder to shrink fit in to a hub.

3.

**On Solving Higher Order and Coupled Ordinary Differential Equations**

4.

**Historical Notes - Runge**

5.

**Historical Notes - Kutta**

6.

**Examples on Euler's Method**

Chemical Engineering

Civil Engineering

Computer Engineering

Electrical Engineering

Industrial Engineering

Mechanical Engineering

7.

**Examples of Runge-Kutta 2nd Order Method**

Chemical Engineering

Civil Engineering

Computer Engineering

Electrical Engineering

Industrial Engineering

Mechanical Engineering

8.

**Examples of Runge-Kutta 4th Order Method**

Chemical Engineering

Civil Engineering

Computer Engineering

Electrical Engineering

Industrial Engineering

Mechanical Engineering

9.

**Sample Tests**

Euler's Method

Runge-Kutta 2nd Order Method

Runge-Kutta 4th Order Method

Shooting Method

Finite Difference Method