A Monotone Second-Order Numerical Method for Fredholm Integro-Differential Equation

The purpose of this study is to present a monotone type numerical method for solving Fredholm integro-differential equations. To solve this problem numerically, we have established a finite difference scheme on a uniform mesh using the composite trapezoidal formula. Furthermore, it has been proven t...

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Bibliographic Details
Published in:	Mediterranean journal of mathematics Vol. 21; no. 7
Main Authors:	Amirali, Ilhame, Durmaz, Muhammet Enes, Amiraliyev, Gabil M.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-11-2024 Springer Nature B.V
Subjects:	Differential equations Finite difference method Mathematics Mathematics and Statistics Numerical methods Fredholm integro-differential equation error estimate 65R20 uniform convergence 65L20 45J05 65L12 finite difference method 65L11
Online Access:	Get full text
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Summary:	The purpose of this study is to present a monotone type numerical method for solving Fredholm integro-differential equations. To solve this problem numerically, we have established a finite difference scheme on a uniform mesh using the composite trapezoidal formula. Furthermore, it has been proven that this presented method is second-order convergent in the discrete maximum norm. To support the theoretical basis of this proposed approach, numerical results are presented.
ISSN:	1660-5446 1660-5454
DOI:	10.1007/s00009-024-02746-6