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

In this paper, the Modied 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 M2D-BFs are determined and an operational matrix for integration obtained. M2D-BFs are used to solve nonlinear two-dimensional Volterra integral equations of the rst kind. Some theorems are included to show convergence and advantage of the method. Finally, numerical example is presented to show the efciency and accuracy of the method.