The Numerical Solution of Hammerstein-Fredholm Second Kind - Integral Equations by using the Block Method

The Fredholm–Hammerstein integral equations appear in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electromagnetic fluid dynamics, antenna synthesis problem, communication theory, mathematical economics, population genetics, radiation, the particle transport problems of astrophysics and reactor theory, fluid mechanics. The purpose of this research is to extend a numerical method for solving a special type of integral equations, which is known as the block method. In this work, a new algorithm has been developed for the first time to treat the Hammerstein Fredholm-second kind integral equation (HFSKIE), and that method consists of three blocks. The resulting nonlinear equations from this method are solved by the Newton-Raphson method.