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Some properties of the discrete Hamiltonian method

Authors
Journal
Physica D Nonlinear Phenomena
0167-2789
Publisher
Elsevier
Publication Date
Volume
11
Identifiers
DOI: 10.1016/0167-2789(84)90438-x

Abstract

Abstract A method for approximating a large class of Hamiltonian ordinary equations by area-preserving discrete mapping equations is described. The time-steps can be quite large compared to conventional approaches. It is shown that, in general, the mapping equations are implicit, and the conditions under which a unique solution can be found are determined. Under these conditions, Newton's method is rapidly convergent. Numerical examples are studied, and the appropriateness of these methods for use in plasma simulations is explored.

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