Using modified two-dimensional block-pulse functions for the numerical solution of nonlinear two-dimensional volterra integral equations

In this paper, the Modified two-dimensional block-pulse functions (M2D-BFs) are used as a new set of basis functions for expanding two-dimensional functions. The main properties of M2DBFs are determined and an operational matrix for integration obtained. M2D-BFs are used to solve nonlinear two-dimensional Volterra integral equations of the first kind. Some theorems are included to show convergence and advantage of the method. Finally, numerical examples is presented to show the efficiency and accuracy of the method.