Modified Galerkin method for Volterra-Fredholm-Hammerstein integral equations

In this paper, we analyze piecewise polynomial based modified Galerkin method for a class of nonlinear Volterra-Fredholm mixed type Hammerstein integral equations with smooth kernels. Existence and convergence of the approximate and iterated approximate solutions to the actual solution is discussed and the rates of convergence are obtained. We are able to improve the existing convergence results for Galerkin method with the modified Galerkin method for nonlinear Volterra-Fredholm-Hammerstein integral equations. Also, we further obtain better convergence rates with one step iteration approximation.