Solving mixed singular integro-differential equation (IDE) using the finite elements method

Iranian Journal of Numerical Analysis and Optimization

مقاله 2، دوره 15، Issue 2 - شماره پیاپی 33، شهریور 2025، صفحه 457-474   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.89654.1503

نویسندگان

M. Erfanian^{* 1}؛ H. Zeidabadi²؛ M.S. Hussein³

¹Department of Science, School of Mathematical Sciences,University of Zabol, Zabol, Iran.

²Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.

³Department of Mathematics College of Science University of Baghdad.

چکیده

In this work, we describe a new method for the calculation of the numerical solution of the mixed singular integro-differential equation. The method is mainly based on a finite element approximation. For this purpose, we obtain the variational form of the problem under consideration. The result-ing system has been approximated numerically by linear B-spline function. The method of convergence and its order of convergence are established. Finally, to investigate the accuracy of the proposed method some test ex-amples are presented. The numerically obtained results are compared with another method for the validity of our results and shown by some tables and figures.

کلیدواژه‌ها

Singular integro-differential equation؛ finite element approxima-tion؛ Convergence؛ Error analysis

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