Hosoya polynomial based matrix method for higher order linear generalized pantograph differential equations

In this study, a matrix collocation method based on Hosoya polynomials is developed to obtain approximate solutions of higher-order linear generalized pantograph differential equations under mixed conditions including initial and/or boundary conditions. The Hosoya polynomial based matrix collocation method for approximate solutions of such equations is introduced for the first time in the literature by us, and the relevant solution approach is detailed. In this method, solutions are obtained according to equally spaced collocation points and Chebyshev-Lobatto collocation points. Various example problems are considered to evaluate the effectiveness and applicability of the proposed method, and numerical calculations related to these problems are performed. According to the results obtained, the proposed method is shown to be fast and efficient in terms of both accuracy and computation, and this is supported by the comparative tables and graphs presented.