Direct method for solving nonlinear two-dimensional Volterra-Fredholm integro-differential equations by block-pulse functions

Subject Areas : International Journal of Information, Security and Systems Management

Elnaz Poorfattah ¹ , Akbar Jafari Shaerlar ²

1 - Department of Mathematics, Ardabil Science and Research Branch, Islamic Azad University, Ardabil, Iran
2 - Department of Mathematics, Ardabil Science and Research Branch, Islamic Azad University, Ardabil, Iran

Received: 2015-08-30 Accepted : 2015-08-30 Published : 2015-02-01

Keywords: Nonlinear equations, Two-dimensional Volterra-Fredholm integro-differential equations, Two-dimensional block-pulse functions, operational matrix,

Abstract :

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Volterra-Fredholm integro-differential equation has been reduced to an algebraic system. Some numerical examples are presented to illustrate the effectiveness and accuracy of the method