1 / 12

Introduction to Numerical Analysis I

Introduction to Numerical Analysis I. Ordinary Differential Equations. MATH/CMPSC 455. Model Problem. Euler’s Method. Example. Example. Taylor Series Method. Idea: keep more terms in the Taylor expansion. A Example (keep second order term). Example. Runge-Kutta Methods.

candice-chaney
Télécharger la présentation

Introduction to Numerical Analysis I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Numerical Analysis I Ordinary Differential Equations MATH/CMPSC 455

  2. Model Problem

  3. Euler’s Method

  4. Example Example

  5. Taylor Series Method Idea: keep more terms in the Taylor expansion A Example (keep second order term)

  6. Example

  7. Runge-Kutta Methods A drawback of Taylor Series Method is that it involves derivatives of Idea: use to express derivatives 2nd order Runge-Kutta Methods:

  8. 4th order Runge-Kutta Methods:

  9. Backward Euler Method Backward Euler Method: • Differences: • Implicit • Need to solve an equation (maybe expensive)

  10. Comparison (from FPI point of view) Example:

  11. Comparison (from STABILITY point of view) Example:

  12. How to Solve the Extra Equation Example:

More Related