Using the improved Petrov–Galerkin elements k−0k−0 for solving nonlinear Hammerstein–Fredholm integral equations

In this paper, we are interested in showing how the improved continuous or discontinuous Petrov–Galerkin Lagrange type k−0k−0 elements can be used to solve Hammerstein–Fredholm integral equations. For this purpose, we present a brief summary of the improved elements.The most important feature of the improved methods is the elimination of restriction kk between 1 and 5 which exists for common Petrov–Galerkin elements. The main point in removing this restriction is the application of Chebyshev polynomials. Finally, numerical results of some relevant counterexamples will demonstrate accuracy and efficiency of the suggested methods.