A numerical solution of the arbitrary order weakly singular integral using block-pulse functions and applications

The purpose of this paper is to obtain the approximation of the arbitrary order weakly singular integral using Block-Pulse functions. The obtained results can be used to solve the numerical solution of higher order linear and nonlinear weakly singular Volterra integral equation of the second kind. Furthermore, the initial equations are transformed into a system of algebraic equations. Finally, some examples are given to demonstrate the validity and applicability of this approach, results of these examples show that this new method is an efficient algorithm.