Access Type

Open Access Embargo

Date of Award

1-1-2010

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics

First Advisor

ZHIMIN ZHANG

Abstract

We conduct a systematic comparison of spectral methods with some

symplectic methods in solving Hamiltonian dynamical systems. Our

main emphasis is on the non-linear problems. Numerical evidence has

demonstrated that the proposed spectral collocation method preserves

both energy and symplectic structure up to the machine error in each

time (large) step, and therefore has a better long time behavior.

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