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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.

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Introduction to Numerical Analysis I

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  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:

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