In this paper, we continue our study that began in
recent papers \cite{RZQ} and \cite{HNK} concerning a simple yet
effective Taylor series expansion method to approximate  a
solution of integral equations. The method is applied to Volterra
integral equation of the second kind as well as to systems of
Volterra equations. The results obtained in this paper improve
significantly the results reported in recent papers, \cite{MA} and
\cite{RMA}. An error analysis is also provided.