Integration Methods Based on Rigid Frames
نویسندگان
چکیده
We consider numerical integration methods for differentiable manifolds as proposed by Crouch and Grossman. The differential system is phrased by means of a system of frame vector fields on the manifold. The numerical approximation is obtained by composition of flows of vector fields in the linear span of . The methods reduce to traditional Runge-Kutta methods if the frame vector fields are chosen as the standard basis of euclidean . A complete theory for the order conditions involving ordered rooted trees is developed. Examples of explicit and diagonal implicit methods are presented, along with some numerical results. AMS Subject Classification: 65L06, 34A50
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