Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations in two-dimensional spaces based on Block Pulse functions

In this paper, the numerical technique based on Block Pulse functions (BPFs) has been developed to approximate the solutions of nonlinear Volterra-Fredholm-Hammerstein integral equations in two-dimensional spaces. These functions are orthogonal and have compact support on [0,1]. The proposed method reduces the integral equations to a system of nonlinear algebraic equations that can be easily solved by any numerical method. Also, the convergence of the proposed approach is discussed. Furthermore, in order to show the accuracy and reliability of the above-mentioned algorithm, the new approach is verified through some numerical examples.