Abstract
In this paper, the solving of a class of both linear and nonlinear Volterra integral equations of the first kind is investigated. Here, by converting integral equation of the first kind to a linear equation of the second kind and the ordinary differential equation to integral equation we are going to solve the equation easily. The method of successive approximations (Neumann’s series) is applied to solve linear and nonlinear Volterra integral equation of the second kind. Some examples are presented to illustrate methods.
Highlights
The integral equation originates from the conversion of a boundary-value problem or an initial-value problem associated with a partial or an ordinary differential equation, but many problems lead directly to integral equations and cannot be formulated in terms of differential equations [7], [10] & [11]
An integral equation is an equation in which the unknown function ( ) to be determined appears under the integral sign [3] & [7].A typical form of an integral equation in
The theory and application of integral equations is an important subject within applied mathematics, physics, and engineering
Summary
The integral equation originates from the conversion of a boundary-value problem or an initial-value problem associated with a partial or an ordinary differential equation, but many problems lead directly to integral equations and cannot be formulated in terms of differential equations [7], [10] & [11]. The prime objective of this paper is to determine the unknown function f(x)that will satisfy equation (1) using a number of Numerical techniques. It needs considerable efforts in exploring these methods to find solutions of the unknown function. The theory and application of integral equations is an important subject within applied mathematics, physics, and engineering. They are widely used in mechanics, geophysics, electricity and magnetism, kinetic theory of gases, hereditary phenomena in biology, quantum mechanics, mathematical economics, and queuing theory [2], [7], [8] & [11]
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