Numerical Inversion of the Abel Integral Equation using Homotopy Perturbation Method

A HOMOTOPY PERTURBATION ALGORITHM AND TAYLOR SERIES EXPANSION METHOD TO SOLVE A SYSTEM OF SECOND KIND FREDHOLM INTEGRAL EQUATIONS

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

A Method to Approximate Solution of the First Kind Abel Integral Equation Using Navot's Quadrature and Simpson's Rule

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

Generalized Abel Inversion Using Homotopy Perturbation Method

Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. Obtaining the physically relevant quantity from the measured one requires, therefore ...

Homotopy approximation technique for solving nonlinear‎ ‎Volterra-Fredholm integral equations of the first kind

In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...