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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 دی 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.89654.1503

نویسندگان

Majid Erfanian^{* 1}؛ Hamed 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, Iraq.

چکیده

‎In this work, we describe a new method for the calculation of the numerical solution of the mixed singular integro-differential equation (MSIDE). The method is mainly based on finite element approximation. For this purpose, we obtain the variational form of the problem under consideration. The resulting 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 examples 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 approximation؛ Convergence؛ Error analysis