Solving nonlinear mixed Volterra-Fredholm integral equations with two dimensional block-pulse functions using direct method

摘要

Few numerical methods such as projection methods, time collocation method, trapezoidal Nystrom method, Adomian decomposition method and some else are used for mixed Volterra-Fredholm integral equations. The main purpose of this paper is to use the piece-wise constant two-dimensional block-pulse functions (2D-BPFs) and their operational matrices for solving mixed nonlinear Volterra-Fredholm integral equations of the first kind (VFIE). This method leads to a linear system of equations by expanding unknown function as 2D-BPFs with unknown coefficients. The properties of 2D-BPFs are then utilized to evaluate the unknown coefficients. The error analysis and rate of convergence are given. Finally, some numerical examples show the implementation and accuracy of this method.