Clique Collocation Method to Solve the Third-Order Multisingular (MS) Functional Differential Equations

Year 2025, Volume: 6 Issue: 1, 59 - 74, 31.01.2025

Gamze Yıldırım , Şuayip Yüzbaşı

Abstract

In this paper, a Clique collocation method is presented to numerically solve the third-order multisingular (MS) functional differential equation. This method convert this equation to a system of the algebraic equations via the collocation points and the matrix relations. Also, the error estimation technique is constituted for the third-order multisingular (MS) functional differential equation. Applications of the Clique collocation method and the error estimation technique are made for three examples. In addition, the comparison is made with another method in the literature. The obtained results are tabulated and visualized to demonstrate the effectiveness of the presented method. Applications of the method and graphics are made by using MATLAB. According to the applications, it is observed that the results have quite decent errors.

Keywords

Clique polynomials, collocation method, error estimation, functional differential equation, singular differential equation

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