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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Explicit canonical methods for Hamiltonian systems

Authors: Daniel Okunbor and Robert D. Skeel
Journal: Math. Comp. 59 (1992), 439-455
MSC: Primary 70-08; Secondary 65L06, 70H05
MathSciNet review: 1136225
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Abstract: We consider canonical partitioned Runge-Kutta methods for separable Hamiltonians $ H = T(p) + V(q)$ and canonical Runge-Kutta-Nyström methods for Hamiltonians of the form $ H = \frac{1}{2}{p^{\text{T}}}{M^{ - 1}}p + V(q)$ with M a diagonal matrix. We show that for explicit methods there is great simplification in their structure. Canonical methods of orders one through four are constructed. Numerical experiments indicate the suitability of canonical numerical schemes for long-time integrations.

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Keywords: Hamiltonian systems, canonical methods, Runge-Kutta methods, adjoint methods, Runge-Kutta-Nyström methods
Article copyright: © Copyright 1992 American Mathematical Society