This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra
integral equations (VIEs), ranging from Volterra's fundamental contributions and the …

Partial differential equations with highly oscillatory input terms are hardly ever solvable
analytically and their numerical treatment is difficult. Modulated Fourier expansion used as …

We are concerned with numerical approximation of the linear Klein–Gordon equation with
time-and space-dependent mass. We propose an asymptotic-numerical approach as a …

We introduce a new strategy for coupling the parallel in time (parareal) iterative
methodology with multiscale integrators. Following the parareal framework, the algorithm …

We present a method to compute efficiently and easily solutions of systems of linear neutral
delay differential equations with highly oscillatory forcing terms. This method is based on …

In this paper, we propose an approach of combination of asymptotic and numerical
techniques to solve highly oscillatory second-order initial value problems. An asymptotic …

Purpose The paper proposes an efficient and insightful approach for solving neutral delay
differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the …

Highly oscillatory differential equations present significant challenges in numerical
treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly …

The paper is concerned with the discretization and solution of DAEs of index 1 and subject
to a highly oscillatory forcing term. Separate asymptotic expansions in inverse powers of the …

We introduce a new parallel in time (parareal) algorithm which couples multiscale
integrators with fully resolved fine scale integration and computes highly oscillatory solutions …