The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind

Abstract

Abstract:In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying the regularization method. Then the homotopy perturbation method is employed to the resulting second kind of equation to obtain a solution. A few examples including linear and nonlinear equations are provided to show the validity and applicability of this approach.

Regularization method for solving dual series equations involving heat equation with mixed boundary conditions

“…In similar manner ,separate variables in (1), then use the mixed conditions (15), (16) in L-transform , we obtain a DSE for determinationC n (λ n , s)…”

“…In this section, we will use the regularization method for solving the resulting Fredholm integral equation of the previous section. Regularization method is an effect tool for solving a first kind Fredholm integral equations [10,18,2,12,17,1]. Firstly, integral equation (13) can be written as…”

Efficient Numerical Algorithm for the Solution of Nonlinear Two-Dimensional Volterra Integral Equation Arising from Torsion Problem

“…Authors, in [12], solved twodimensional integral equation of the first kind by a multistep method. Alturk, in [13], solved two-dimensional Fredholm integral equations of the first kind using regularization-homotopy method. In this work, effective numerical methods are proposed to obtain the solution of nonlinear two-dimensional Volterra integral equations of the second kind and study the values of absolute errors.…”

Intelligent Object-Oriented Approach to Dynamic Energy Systems’ Modelling

“…The particular case of such equations is the Fredholm integral equations of the 1-st kind [11][12][13][14], which have many important applications, for example, the signal restoration problem. This problem is commonly formulated in the following way: to obtain a required signal from experimental data by means of solving an operator equation…”