Abstract

This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

Keywords

Dynamical systems theoryNumerical analysisHamiltonian systemDissipative systemNumerical stabilityAttractorConvergence (economics)MathematicsApplied mathematicsStability (learning theory)Dynamical system (definition)Projected dynamical systemLinear dynamical systemComputer scienceMathematical analysisPhysicsRandom dynamical system

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Publication Info

Year
1996
Type
book
Citations
633
Access
Closed

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Andrew M. Stuart, A. R. Humphries (1996). Dynamical systems and numerical analysis. The Caltech Institute Archives (California Institute of Technology) .