Dynamical Systems and Numerical Analysis, Volumen 8Cambridge University Press, 28 nov 1998 - 685 páginas 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. |
Índice
Ordinary Differential Equations | 100 |
Numerical Methods for Initial Value Problems | 212 |
Numerical Methods as Dynamical Systems | 269 |
Global Stability | 355 |
Convergence of Invariant Sets 428 | 430 |
Global Properties and Attractors Under Discretiza | 497 |
Equations | 506 |
7 | 550 |
8 | 557 |
9 | 571 |
3 | 591 |
5 | 606 |
7 | 627 |
8 | 638 |
Bibliography | 660 |
Otras ediciones - Ver todo
Dynamical Systems and Numerical Analysis Andrew Stuart,A. R. Humphries No hay ninguna vista previa disponible - 1996 |
Términos y frases comunes
A-stable absorbing set algebraically stable approximation assume Assumption asymptotically stable backward Euler method behaviour bifurcation bounded set Chapter Consider the equation Consider the map convergence Corollary deduce defines a dynamical Definition denote dissipative eigenvalues equilibrium point Exercise exists explicit follows generalised dynamical system given global attractor gradient system Hence hyperbolic implies initial conditions initial data invariant manifold invariant sets iteration Lemma limit sets linear multistep method Lipschitz continuity locally Lipschitz Lyapunov function map Un+1 matrix multistep method 3.3.1 nonlinear problems norm Note numerical method one-leg method one-sided Lipschitz condition one-stage theta method orbit period two solution periodic solution positively invariant Proof properties prove result Runge-Kutta method satisfies Section semigroup solution of 2.1.1 solution sequence subspace sufficiently small system on RP Theorem theory two-stage theta method unstable manifold vector w-limit set zero-stable
Referencias a este libro
Computer Methods for Ordinary Differential Equations and Differential ... Uri M. Ascher,Linda R. Petzold No hay ninguna vista previa disponible - 1998 |