ANALYTICAL SOLUTIONS FOR VOLTERRA AND ABEL INTEGRAL EQUATIONS USING A GENERALIZED POWER SERIES METHOD

G Guzeliya,A Alena

doi:10.12732/ijpam.v105i3.19

Abstract

Abstract: Even though they have a rather specialized structure, Volterra and Abel integral equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. In this paper we consider the nonlinear Volterra integral equation of second kind and Abel integral equations of first kind. Authors have been proposed a new method for constructing solutions of Abel integral equations by a generalized power series.

Highlights

The real world problems in scientific fields [1], [2] such as solid state physics, plasma physics, fluid mechanics, chemical kinetics and mathematical biology are nonlinear in general when formulated as partial differential equations or integral equations
We use the method of generalized power series, to solve linear Volterra integral equations and generalized Volterra integral equations of the first and second kind.This power series method are undetermined coefficients method, or a method based on the application of the Taylor series
The main purpose of this paper is to introduce and study the relation between Volterra integral equations and generalized power series

Summary

Introduction and Preliminary

The real world problems in scientific fields [1], [2] such as solid state physics, plasma physics, fluid mechanics, chemical kinetics and mathematical biology are nonlinear in general when formulated as partial differential equations or integral equations. Alena with integral equations and some of them are non-linear, even some problems of stochastic processes can be formulated in terms of integral equations. One of the outstanding practical problems met in the solution of Volterra integral equations is the form of power series. We use the method of generalized power series, to solve linear Volterra integral equations and generalized Volterra integral equations of the first and second kind.This power series method are undetermined coefficients method, or a method based on the application of the Taylor series. The result obtained in the form of generalized power series solution further converted to the inversion formula of the integral equation. The main purpose of this paper is to introduce and study the relation between Volterra integral equations and generalized power series

Nonlinear Volterra Integral Equations of Second Kind

Abel Integral Equation of First Kind