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Symmetric projection methods for differential equations on manifolds

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Ernst Hairer

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Abstract. Projection methods are a standard approach for the numerical solution of differential equations on manifolds. It is known that geometric properties (such as symplecticity or reversibility) are usually destroyed by such a discretization, even when the basic method is symplectic or symmetric. In this article, we introduce a new kind of projection methods, which allows us to recover the time-reversibility, an important property for long-time integrations.

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Key Words. Differential equations on manifolds, symmetric Runge-Kutta methods, projection methods, numerical geometric integration, long-time integration.

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