We present a collection of recent results on the numerical approximation of Volterra integral
equations and integro-differential equations by means of collocation type methods, which …

Abstract Fractional Partial Differential equations (FPDEs) are essential for modeling complex
systems across various scientific and engineering areas. However, efficiently solving FPDEs …

This work proposes a multigrid Waveform Relaxation Method (WRMG) that uses the finite
difference method for the discretization to solve Pennes' bioheat equation. There is no …

We introduce domain decomposition methods of Schwarz waveform relaxation (WR) type for
fractional diffusion-wave equations. We show that the Dirichlet transmission conditions …

The paper provides a comparison between two relevant classes of numerical discretizations
for stiff and nonstiff problems. Such a comparison regards linearly implicit Jacobian …

The purpose of this paper is to employ graphics processing units for the numerical solution
of large systems of weakly singular Volterra Integral Equations (VIEs), by means of …

In the present paper, a parallel-in-time discretization of linear systems of Volterra equations
of type u¯(t)= u¯ 0+∫ 0 t K (ts) u¯(s) ds+ f¯(t), 0< t≤ T, is addressed. Related to the …

The purpose of this paper is to provide a parallel acceleration of peer methods for the
numerical solution of systems of Ordinary Differential Equations (ODEs) arising from the …

In this paper we compare the implicit schemes for the solution of the two-dimensional wave
equation using Singlegrid and Multigrid methods. The discretization is performed using the …

The paper is focused on the development of A-stable collocation based multivalue methods
for stiff problems. This methods are dense output extensions of discrete multivalue methods …