Approximate solutions for mixed nonlinear Volterra–Fredholm type integral equations via modified block-pulse functions

In this article a robust approach for solving mixed nonlinear Volterra–Fredholm type integral equations of the first kind is investigated. By using the modified two-dimensional block-pulse functions (M2D-BFs) and their operational matrix of integration, first kind mixed nonlinear Volterra–Fredholm type integral equations can by reduced to a nonlinear system of equations. The coefficients matrix of this system is a block matrix with lower triangular blocks. Some theorems are included to show the convergence and advantage of this method. Numerical results show that the approximate solutions have a good degree of accuracy.