In this paper, a geometric approach is proposed to the integration of the
system of Volterra integro-differential equations (IDEs). To do this, the
equivalent system of ordinary differential equations of IDEs are obtained
and converted into a Lie type augmented dynamical system. Then we construct
the group preserving scheme (GPS) on the system of Volterra IDEs
which is formulated by an exponential mapping to keep the group properties
of SOo(n, 1). Some linear and nonlinear examples are solved as a
description for the power and efficiency of GPS. Finally, in order to demonstrate
the validity and efficiency of the present method, the convergency
is numerically discussed and accuracy of results are compared with the
reported results in the literature.