Modification of Collocation Methods for the Numerical Solution of Functional Differential Equations
Abstract
This paper presents a generalization of collocation methods for numerical integration to the case of first- and second-order functional-differential equations. The integration schemes for collocation methods are derived using Newton’s polynomial interpolation on Lobatto partitions applied to the right-hand sides of the functional-differential equations. The effectiveness of the modified collocation methods is illustrated using a planar model of the Moon’s motion with tidal effects determined by the Moon’s position on a shifted time scale with a delay. Numerical experiments show that the modified collocation method provides accuracy comparable to the generalized Adams method, with a significantly larger integration step and, accordingly, a smaller computational effort.
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