Analysis of the Transient Behaviour in the Numerical Solution of Volterra Integral Equations

Abstract

In this paper, the asymptotic behaviour of the numerical solution to the Volterra integral equations is studied. In particular, a technique based on an appropriate splitting of the kernel is introduced, which allows one to obtain vanishing asymptotic (transient) behaviour in the numerical solution, consistently with the properties of the analytical solution, without having to operate restrictions on the integration steplength.

Differential Models, Numerical Simulations and Applications

“…The authors in [12] studied the asymptotic behavior of the numerical solution to the Volterra integral equations. In particular, a technique based on an appropriate splitting of the kernel is introduced, which allows one to obtain vanishing asymptotic (transient) behavior in the numerical solution, consistent with the properties of the analytical solution, without having to operate restrictions on the integration steplength.…”