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 Numerical Methods - Ordinary Differential Equations made available by Holistic Numerical Methods Institute, University of South Florida under the Creative Commons BY-NC-SA license.
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.
Reading Material
1. Numerical Methods with Applications - Chapter 8Author: 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 Equation2. 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
