lecture38 - CMPSC/MATH 451 Numerical Computations Lecture...

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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 38 Nov 30, 2011 Prof. Kamesh Madduri Class Overview ODEs: Existence of Solution, Uniqueness Lipschitz theorem Stability Slides from textbook follow. 2 Ordinary Differential Equations Numerical Solution of ODEs Additional Numerical Methods Differential Equations Initial Value Problems Stability Stability of Solutions Solution of ODE is Stable if solutions resulting from perturbations of initial value remain close to original solution Asymptotically stable if solutions resulting from perturbations converge back to original solution Unstable if solutions resulting from perturbations diverge away from original solution without bound Michael T. Heath Scientific Computing 13 / 84 Ordinary Differential Equations Numerical Solution of ODEs Additional Numerical Methods Differential Equations Initial Value Problems Stability Example: Stable Solutions Family of solutions for ODE y = 1 2 Michael T. Heath Scientific Computing 14 / 84 Ordinary Differential Equations...
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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 Pennsylvania State University, University Park.

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lecture38 - CMPSC/MATH 451 Numerical Computations Lecture...

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