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dc.contributor.authorFatokun, J. O-
dc.contributor.authorAjibola, I. K. O.-
dc.identifier.citationFatokun, J. O. & Ajibola, I. K. O. (2009) A collocation multistep method for integrating ordinary differential equations on manifolds. African Journal of Mathematics and Computer Science Research, 2(4), pp. 051-055.en_US
dc.description.abstractThis 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.en_US
dc.publisherAcademic Journalsen_US
dc.subjectCollocation methodsen_US
dc.subjectMultistep methodsen_US
dc.subjectDifferential equationsen_US
dc.subjectInvariant methodsen_US
dc.subjectGeometric integrationen_US
dc.titleA collocation multistep methods for integrating ordinary differential equations on manifolds.en_US
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