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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 – PredatorPrey 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 infinitedimensional space of functions Numerical solution of differential equations is based on finitedimensional 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 highestorder derivative of solution function appearing in ODE ODE with higherorder derivatives can be transformed into equivalent firstorder system We will discuss numerical solution methods only for...
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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.
 Spring '08
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