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

Subject Areas : Statistics

M. Adabitabar Firozja ¹ , B. Agheli ²

1 - Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
2 - Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Received: 2016-09-13 Accepted : 2017-01-31 Published : 2017-02-19

Keywords: معادله انتگرال ولترا با هسته م, تبدیل فازی, توابع پایه‌ای,

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.