An operational collocation based on the Bell polynomials for solving high order Volterra integro-differential equations

In this paper, an operational matrix method based on the Bell polynomials  has been presented to find approximate solutions of high-order Volterra integro-differential equations. This method  uses a simple computational manner to obtain a quite acceptable approximate solution. The main characteristic behind this method lies in the fact that on the one hand, the problem will be reduced to a system of algebraic equations and on the other hand, the efficiency and accuracy of the Bell polynomials  for solving these equations are acceptable. The convergence analysis of  this method will be shown by preparing some theorems. Moreover, we will obtain an estimation of the error bound for this algorithm. Finally, some examples are presented to illustrate the applicability, efficiency and accuracy of this  scheme in comparison with some  other well-known methods such as Legendre, Bernoulli, Taylor and Bessel polynomial algorithms