  In this paper we will consider the peridynamic equation of motion which is
described by a second order in time partial integro-differential equation. This
equation has recently received great attention in several fields of Engineering
because seems to provide an effective approach to modeling mechanical systems
avoiding spatial discontinuous derivatives and body singularities. In
particular, we will consider the linear model of peridynamics in a
one-dimensional spatial domain. Here we will review some numerical techniques
to solve this equation and propose some new computational methods of higher
order in space; moreover we will see how to apply the methods studied for the
linear model to the nonlinear one. Also a spectral method for the spatial
discretization of the linear problem will be discussed. Several numerical tests
will be given in order to validate our results.
