Iterative Numerical Methods for a Fredholm–Hammerstein Integral Equation with Modified Argument

Abstract

Iterative processes are a powerful tool for providing numerical methods for integral equations of the second kind. Integral equations with symmetric kernels are extensively used to model problems, e.g., optimization, electronic and optic problems. We analyze iterative methods for Fredholm–Hammerstein integral equations with modified argument. The approximation consists of two parts, a fixed point result and a quadrature formula. We derive a method that uses a Picard iterative process and the trapezium numerical integration formula, for which we prove convergence and give error estimates. Numerical experiments show the applicability of the method and the agreement with the theoretical results.

Keywords

• Fredholm integral equations
• modified argument
• Picard iteration
• numerical integration