Modification of Collocation Methods for the Numerical Solution of Functional Differential Equations - Samulevich, Stepan (Computer Tools in Education, 2025)
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.