In this paper we consider a sub-diffusion problem where the fractional time derivative is
approximated either by the L1 scheme or by Convolution Quadrature. We propose new …

This work investigates the discrete L 1 remainder stability of first and second order schemes
for a Volterra integro-differential equation, where the backward Euler and backward …

A focused summary of one-and two-dimensional models for linear and nonlinear wave
propagation in fractional media is given. The basic models, which represent fractional …

We consider 2D transient linear wave propagation problems defined in the exterior of
bounded domains. In particular, we first consider the problem represented by the classical …

We present a novel generalized convolution quadrature method that accurately
approximates convolution integrals. During the late 1980s, Lubich introduced convolution …

We develop a numerical method for the Westervelt equation, an important equation in
nonlinear acoustics, in the form where the attenuation is represented by a class of nonlocal …

This paper studies time-dependent electromagnetic scattering from obstacles that are
described by dispersive material laws. We consider the numerical treatment of a scattering …

An error analysis of Runge–Kutta convolution quadrature based on Gauss methods applied
to hyperbolic operators is given. Order reduction is observed, with the order of convergence …

In this work, we introduce new integral formulations based on the convolution quadrature
method for the time-domain modeling of perfectly electrically conducting scatterers that …

This paper is devoted to explore the convolution quadrature based on a class of two-point
Hermite collocation methods. Incorporating derivatives into the numerical scheme enhances …