Approximation methods for system of nonlinear Fredholm–Hammerstein integral equations

Abstract

In this article, we apply projection methods and their iterated versions to approximate the solution of system of Fredholm-Hammerstein integral equations with both smooth and weakly singular kernels of algebraic and logarithmic type using the piecewise polynomial basis functions. We show that the iterated Galerkin approximate solution converges to the exact solution faster than the Galerkin approximate solution for both smooth and weakly singular algebraic and logarithmic type kernels. We improve these results further in iterated multi-Galerkin method. Numerical results are provided for the illustration of the theoretical results. KeywordsSystem of Fredholm-Hammerstein integral equations • Galerkin method • Multi-Galerkin method • Smooth kernels • Weakly singular kernels • Superconvergence results Mathematics Subject Classification 45G15 • 45B05 • 65R20 B Samiran Chakraborty