Efficient spectral-collocation methods for a class of linear Fredholm integro-differential equations on the half-line

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:377

Article

Benyoussef, Soufiane¹  Rahmoune, Azedine² 

[1] Univ Msila, Dept Math, Msila 28000, Algeria

[2] Univ Bordj Bou Arreridj, Dept Math, El Anasser 34030, Algeria

关键词: Fredholm integro-differential equations;    Mapped Legendre;    Half-line;    Function approximation;   

DOI  :  10.1016/j.cam.2020.112894

来源: Elsevier

【 摘 要 】

In this paper, an extension of the Legendre spectral collocation method has been proposed for the numerical solution of a class of linear Fredholm integro-differential equation on the half-line. The properties of mapped Legendre functions are first presented. These properties together with the Legendre-Gauss points are then utilized to reform the Fredholm integro-differential equation in semi-infinite interval into a singular equation in finite interval and to reduce it to the solution of a simple matrix equation. Besides, in order to show the efficiency and accuracy of the proposed method, some numerical examples are considered and solved through a survey of three approaches, namely: Exponential, rational and logarithmic Legendre functions collocation methods. Furthermore, a comparison of the results, shows that using exponential functions, leads to more accurate results and faster convergence. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free