Differential equations that have highly oscillatory solutions arise in a variety of fields in
science and engineering such as astrophysics, classical and quantum physics, and …

In this paper we study space discretizations of a general class of first-and second-order
quasilinear wave-type problems. We present a rigorous error analysis based on a …

This paper analyses the long-time behaviour of one-stage symplectic or symmetric
trigonometric integrators when applied to nonlinear wave equations. It is shown that energy …

The Kuznetsov equation is a classical wave model of acoustics that incorporates quadratic
gradient nonlinearities. When its strong damping vanishes, it undergoes a singular behavior …

In the present paper, we consider a class of quasilinear wave equations on a smooth,
bounded domain. We discretize it in space with isoparametric finite elements and apply a …

This paper analyzes global error bounds of one-stage explicit extended Runge–Kutta–
Nyström integrators for semilinear wave equations. The analysis is presented by using …

In this paper we introduce a class of second-order exponential schemes for the time
integration of semilinear wave equations. They are constructed such that the established …

A new algorithm is derived for computing the action f(tA)B, where A is an n*n matrix, B is
n*n_0 with n_0≪n, and f is cosine, sinc, sine, hyperbolic cosine, hyperbolic sinc, or …

We study the full discretization of a general class of first-and second-order quasilinear wave-
type problems with the implicit midpoint rule and a linearized variant thereof. Based on a …

It is known that wave equations have physically very important properties which should be
respected by numerical schemes in order to predict correctly the solution over a long time …