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On the Qualitative Behaviour of Symplectic Integrators. Part II. Integrable Systems

✍ Scribed by Daniel Stoffer

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
226 KB
Volume
217
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper the numerical integration of integrable Hamiltonian systems is considered. Symplectic one-step methods are used. The discrete system is shown to be integrable up to a remainder which is exponentially small with respect to the step size of the one-step method. As a consequence it is shown that the global error grows linearly for exponentially long times.

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## Abstract The asymptotic behaviour of solutions of nonlinear VOLTERRA integral equations is studied in a real BANACH spaces. The nonlinear operator is assumed to satisfy some accretivity‐type conditions.