Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 54, pp. 1-9.

Title: Block-pulse functions and their applications to solving systems of
       higher-order nonlinear Volterra integro-differential equations

Authors: Ali Ebadian             (Urmia Univ., Urmia, Iran)
         Amir Ahmad Khajehnasiri (Urmia Univ., Urmia, Iran)

Abstract:
 The operational block-pulse functions, a well-known method for solving 
 functional  equations, is employed to solve a system of nonlinear 
 Volterra integro-differential  equations. First, we present 
 the block-pulse operational matrix of integration, then by using 
 these matrices, the nonlinear  Volterra high-order  integro-differential 
 equation is reduced to an algebraic system. The benefits of this method 
 is low cost of setting up the equations without  applying any projection 
 method such as Galerkin, collocation, etc.  The results reveal that 
 the method is very effective and convenient.

Submitted May 4, 2013. Published February 21, 2014.
Math Subject Classifications: 45G10, 45D05.
Key Words: Operational matrix; Volterra integral equations; block-pulse function.