A compact discretization of the boundary value problems of the nonlinear Fredholm integro-differential equations
Publish place: Journal of Mathematical Modeling، Vol: 12، Issue: 2
Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JMMO-12-2_003
تاریخ نمایه سازی: 18 تیر 1403
Abstract:
In this paper, we propose a fourth-order compact discretization method for solving a second-order boundary value problem governed by the nonlinear Fredholm integro-differential equations. Using an efficient approximate polynomial, a compact numerical integration method is first designed. Then by applying the derived numerical integration formulas, the original problem is converted into a nonlinear system of algebraic equations. It is shown that the proposed method is easy to implement and has the third order of accuracy in the infinity norm. Some numerical examples are presented to demonstrate its approximation accuracy and computational efficiency, as well as to compare the derived results with those obtained in the literature.
Keywords:
Fredholm integro-differential equation , compact discretization method , Boundary value problem , fourth order of accuracy , convergence order
Authors
Sadegh Amiri
Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, P.O. Box: ۱۳۸۴۶-۶۳۱۱۳, Tehran, Iran
Mojtaba Hajipour
Department of Mathematics, Sahand University of Technology, P.O. Box: ۵۱۳۳۵-۱۹۹۶, Tabriz, Iran