A Reproducing Kernel Method for Solving Nonlocal Functional Differential Equations with Delayed or Advanced Arguments

Rasekhinezhad, Hajar; Abbasbandy, Saeid; Allahviranloo, Tofigh; Babolian, Esmail

doi:10.22034/cmde.2025.63743.2850

A Reproducing Kernel Method for Solving Nonlocal Functional Differential Equations with Delayed or Advanced Arguments

Articles in Press

Document Type : Research Paper

Authors

¹ Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

² Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.

³ Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey.

⁴ Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.

10.22034/cmde.2025.63743.2850

Abstract

This paper discusses an effective approach for solving non-local functional differential equations with delayed or advanced arguments. The reproducing kernel method is utilized to avoid the need for an orthogonalization process. The main objective of this technique is to successfully apply this method to solve singular multi-point boundary value problems with non-local conditions, resulting in an accurate approximate solution and a valid error analysis. This method greatly improves the accuracy of the solutions obtained.

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