A simple algorithm for solving the Volterra integral equation featuring a weakly singular kernel

Document Type: research paper

Authors

Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Abstract

There are many methods for numerical solutions of integral equations. In various branches of science and engineering, chemistry and biology, and physics applications integral equation is provided by many other authors. In this paper, a simple numerical method using a fuzzy, for the numerical solution of the integral equation with the weak singular kernel is provided. Finally, by providing three examples of the effectiveness of the proposed method was evaluated. In all the calculations and diagrams of the software, Mathematica is used.
The advantage of the proposed method is that the algorithm is simple, appropriate and consistent with the exact solution provides a numerical answer. Examples and results presented in the previous section suggest this claim. A fast algorithm for the numerical solution for converting n fuzzy partition is also provided. The speed and simplicity of the algorithm allow any author to obtain a numerical answer with the help of this method it used to take.

Keywords


Article Title [Persian]

الگوریتمی ساده برای حل عددی معادله انتگرال ولترا با هسته منفرد ضعیف

Authors [Persian]

  • محمد ادبی تبار فیروزجاء
  • بهرام عاقلی
گروه ریاضی، دانشگاه آزاد اسلامی، واحد قائمشهر، قائمشهر، ایران
Abstract [Persian]

روش‌های زیادی برای حل عددی معادلات انتگرال وجود دارد. در این مقاله یک روش عددی ساده با استفاده از تبدیل فازی، برای حل عددی معادله انتگرال با هسته منفرد ضعیف ارائه شده است. در پایان نیز با ارائه سه مثال موثر بودن روش پیشنهادی بررسی گردید. در تمامی محاسبات و نمودارها از نرم افزار متمتیکا استفاده شده است.

Keywords [Persian]

  • معادله انتگرال ولترا با هسته منفرد ضعیف
  • تبدیل فازی
  • توابع پایه‌ای