Time-stepping schemes for systems of Volterra integro-differential equations Original Research Article

Linear Volterra-type systems of integro-differential equations (SIDEs) with kernels in the form of sums of (complex) exponentials are considered. Such systems arise, for example, in the semi-discrete finite element model of dynamic viscoelasticity and of some dispersive wave equations, and in the representation of dynamic subsystems on interfaces. Several new families of time-stepping schemes are proposed here for the solution of this class of SIDEs. The accuracy, stability and efficiency properties of these schemes are demonstrated via both theoretical analysis, using a scalar model problem, and numerical experiments applied to first- and second-order SIDEs.