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Symmetric multistep methods for constrained Hamiltonian systems

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P. Console, E. Hairer, and C. Lubich

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Abstract. A method of choice for the long-time integration of constrained Hamiltonians systems is the Rattle algorithm. It is symmetric, symplectic, and nearly preserves the Hamiltonian, but it is only of order two and thus not efficient for high accuracy requirements. In this article we prove that certain symmetric linear multistep methods have the same qualitative behavior and can achieve an arbitrarily high order with a computational cost comparable to that of the Rattle algorithm.

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Key Words. Symmetric multistep methods, constrained Hamiltonian systems, Rattle algorithm, backward error analysis, parasitic solution components.

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