Hybrid Legendre Block-Pulse functions for the numerical solutions of system of nonlinear Fredholm–Hammerstein integral equations

In this paper, the numerical technique based on hybrid Legendre-Block-Pulse function has been developed to approximate the solution of system of nonlinear Fredholm–Hammerstein integral equations. These functions are formed by the hybridization of Legendre polynomials and Block-Pulse functions. These functions are orthonormal and have compact support on [0,1]. The proposed method reduces the system of integral equations to a system of nonlinear algebraic equations that can be solved easily by any usual numerical method. The numerical results obtained by the presented method have been compared with those obtained by Legendre wavelet method (LWM). Numerical examples are presented to illustrate the accuracy of the method.