Discretization And Weak Invariants

We consider the preservation of weak solution invariants in the time integration of ordinary diier-ential equations (ODEs). Recent research has concentrated on obtaining symplectic discretizations of Hamiltonian systems and schemes that preserve certain rst integrals (i.e. strong invariants). In this article, we examine the connection between constrained systems and ODEs with weak invariants for both Hamiltonian and non-Hamiltonian systems. Runge-Kutta and partitioned Runge-Kutta methods are considered, and suucient conditions are derived for preservation of a class of weak invariants. AMS(MOS) subject classiications. 65L05

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