A class of Runge-Kutta methods for nonlinear Volterra integral equations of the second kind with singular kernels

被引：4

作者：

Lichae, Bijan Hasani ^{[1
,2
]}

Biazar, Jafar ^{[3
]}

Ayati, Zainab ^{[4
]}

机构：

[1] Islamic Azad Univ, Guilan Sci & Res Branch, Dept Math, Rasht, Iran

[2] Islamic Azad Univ, Rasht Branch, Dept Math, Rasht, Iran

[3] Univ Guilan, Fac Math Sci, Dept Appl Math, Rasht, Iran

[4] Univ Guilan, Fac Technol & Engn East Guilan, Dept Engn Sci, Rudsar Vajargah, Iran

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2018年

关键词：

Fractional order Riccati differential equations; Runge-Kutta methods; Subtraction of the singularity; Nonlinear Volterra integral equations of the second kind; Caputo fractional derivative; RICCATI DIFFERENTIAL-EQUATION; NUMERICAL-SOLUTION;

D O I：

10.1186/s13662-018-1811-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper aims to obtain an approximate solution for fractional order Riccati differential equations (FRDEs). FRDEs are equivalent to nonlinear Volterra integral equations of the second kind. In order to solve nonlinear Volterra integral equations of the second kind, a class of Runge-Kutta methods has been applied. Runge-Kutta methods have been implemented to solve nonsingular integral equations. In this work Volterra integral equations are singular. The singularity by a suitable subtraction technique will be weakened; then, this method will be applied to gain an approximate solution. Fractional derivatives are defined in the Caputo form of order 0 < alpha <= 1.

引用

页数：19

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