Introduction to Numerical Analysis I
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Introduction to Numerical Analysis I MATH/CMPSC 455 Ordinary Differential Equations
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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. - PowerPoint PPT Presentation
Transcript of Introduction to Numerical Analysis I
Introduction to Numerical Analysis I
MATH/CMPSC 455
Ordinary Differential Equations
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
A drawback of Taylor Series Method is that it involves derivatives of
Idea: use to express derivatives
2nd order Runge-Kutta Methods:
4th order Runge-Kutta Methods:
BACKWARD EULER METHOD
Backward Euler Method:
Differences:• Implicit• Need to solve an equation (maybe
expensive)
COMPARISON (FROM FPI POINT OF VIEW)
Example:
COMPARISON (FROM STABILITY POINT OF VIEW)
Example:
HOW TO SOLVE THE EXTRA EQUATION
Example:
