Application of 2D-BPFs to nonlinear integral equations

Abstract

In this study, an efficient method is presented for solving nonlinear two-dimensional Volterra integral equations (VIEs). Using piecewise constant two-dimensional block-pulse functions (2D-BPFs) and their operational matrix of integration, two-dimensional first kind integral equations reduce to a lower triangular system. The rate of convergence and error analysis are given and numerical examples illustrate efficiency and accuracy of the proposed method.