A Collocation Method Based on Morgan-Voyce Polynomials for Approximating Solutions to Nonlinear Pantograph Differential Equations

Authors : Gözde Şahin, Özgül İlhan

Pages : 595-620

Doi:10.33484/sinopfbd.1676300

View : 52 | Download : 143

Publication Date : 2025-12-24

Article Type : Research Paper

Abstract :This study proposes a novel collocation technique based on Morgan-Voyce polynomials to obtain approximate solutions for a certain class of nonlinear pantograph differential equations that are subject to initial and boundary conditions. The method utilizes specially selected collocation points to transform the original nonlinear differential problem into an equivalent nonlinear algebraic system. The solutions of this algebraic system correspond to the unknown coefficients in the approximate solution expression. The main advantage of the proposed approach lies in its ability to reduce the complexity of solving nonlinear differential equations by converting them into manageable algebraic systems, while maintaining a high level of accuracy. To validate the accuracy and efficiency of the technique, several benchmark problems are considered. Numerical experiments are carried out, and the absolute error functions are used to analyze the performance of the method. All numerical computations and graphical illustrations presented in this paper have been conducted using a program developed in MATLAB R2022b.
Keywords : Doğrusal olmayan pantograf diferansiyel denklemler, Pantograf Denklemler, Morgan- Voyce Sıralama Yöntemi, Sıralama noktaları, Morgan-Voyce polinomları

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