Abstract:
This paper concerns a family of generalized collocation multistep methods that evolves the numerical
solution of ordinary differential equations on configuration spaces formulated as homogeneous
manifolds. Collocating the general linear method at x x for k s n k = = 0,1,... + , we obtain the discrete
scheme which can be adapted to homogeneous spaces. Varying the values of k in the collocation
process, the standard Munthe-Kass (k = 1) and the linear multistep methods (k = s) are recovered. Any
classical multistep methods may be employed as an invariant method and the order of the invariant
method is as high as in the classical setting. In this paper an implicit algorithm was formulated and two
approaches presented for its implementation.
