Modified Galerkin Method for Derivative Dependent Fredholm–Hammerstein Integral Equations of Second Kind (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, we consider modified Galerkin and iterated modified Galerkinmethods for solving a class of two point boundary value problems. The methods areapplied after constructing the equivalent derivative dependent Fredholm-Hammersteinintegral equations to the boundary value problem. Existence and convergence of theapproximate solutions to the actual solution is discussed and the rates of convergenceare obtained. Superconvergence results for the approximate and iterated approximatesolutions of piecewise polynomial based modified Galerkin method in infinity normare given. We have also established that iterated modified Galerkin approximationimproves over the modified Galerkin solution. Numerical examples are presented toillustrate the theoretical results.