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

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

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