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Modified differential equations

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P. Chartier, E. Hairer, and G. Vilmart

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Abstract. Motivated by the theory of modified differential equations (backward error analysis) an approach for the construction of high order numerical integrators that preserve geometric properties of the exact flow is developed. This summarises a talk presented in honour of Michel Crouzeix.

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Key Words. Geometric numerical integration, modified differential equation, backward error analysis, modifying integrator, rigid body integrator.

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