An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion  

作　　者：Mohsen Didgar Alireza Vahidi 

机构地区：[1]Department of Mathematics, Guilan Science and Research Branch, Islamic Azad University [2]Department of Mathematics, Rasht Branch, Islamic Azad University [3]Department of Mathematics, College of Science, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University

出　　处：《Communications in Theoretical Physics》2018年第8期145-152,共8页理论物理通讯（英文版）

摘　　要：In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.

关 键 词：systems of singular Volterra integral equations （SSVIEs） systems of generalized Abel＇s integral equations error analysis Taylor expansion 

分 类 号：O175.5[理学—数学]