lecture37

# lecture37 - CMPSC/MATH 451 Numerical Computations Lecture...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 37 Nov 28, 2011 Prof. Kamesh Madduri Class Overview • Definitions – Order of an ODE – Linear ODE – Homogenous ODE – Independent and dependent variables – IVP – Predator-Prey populations example • Slides from textbook follow. 2 Ordinary Differential Equations Numerical Solution of ODEs Additional Numerical Methods Differential Equations Initial Value Problems Stability Differential Equations Differential equations involve derivatives of unknown solution function Ordinary differential equation (ODE): all derivatives are with respect to single independent variable, often representing time Solution of differential equation is function in infinite-dimensional space of functions Numerical solution of differential equations is based on finite-dimensional approximation Differential equation is replaced by algebraic equation whose solution approximates that of given differential equation Michael T. Heath Scientific Computing 3 / 84 Ordinary Differential Equations Numerical Solution of ODEs Additional Numerical Methods Differential Equations Initial Value Problems Stability Order of ODE Order of ODE is determined by highest-order derivative of solution function appearing in ODE ODE with higher-order derivatives can be transformed into equivalent first-order system We will discuss numerical solution methods only for...
View Full Document

## This note was uploaded on 01/19/2012 for the course CMPSC 451 taught by Professor Staff during the Spring '08 term at Penn State.

### Page1 / 11

lecture37 - CMPSC/MATH 451 Numerical Computations Lecture...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online