| Popis: |
In this article, we look at a class of two point nonlinear boundary value problems and transforms this into derivative dependent Fredholm-Hammerstein integral equations i.e., the integral equation, where the kernel is of Green's type and nonlinear function inside the integral is dependent on the derivative. We obtain the error analysis by replacing all the integrals in Galerkin method by numerical integrations. We propose the discrete Galerkin and iterated discrete Galerkin methods by piecewise polynomials to obtain the convergence analysis of these type of derivative dependent Fredholm-Hammerstein integral equations. By choosing the numerical quadrature rule appropriately, the convergence rates in Galerkin and iterated Galerkin methods are preserved. We show that the iterated discrete Galerkin method improves on the discrete Galerkin method in terms of order of convergence. To demonstrate the theoretical results, several numerical examples are provided. |
