Applying the three-dimensional block-pulse functions to solve system ofVolterra-Hammersteinintegral equations

In this paper, a numerical scheme is utilized to solve three-dimensional nonlinear system of Volterra-Hammerstein integrals equations, which is based on the three-dimensional block-pulse functions (3D-BPFs) and their operational matrices. Then the primary nonlinear system is transferred into a linear system of algebraic equations by applying the approximate expression and operational matrices, which can be easily solved through any numerical techniques. According to the convergence of 3D-BPFs, the new convergence analysis and error estimation theorem of the research system is detailed investigated. Lastly illustrative examples are included to demonstrate the validity and applicability of the technique.