This paper derives a new family of implicit–explicit time-marching methods for PDEs with the
second-order derivative in time. The present implicit method is based on the two-derivative …

In this article, we have developed a new time-marching method to simulate sound and
soliton propagation in homogeneous and heterogeneous media. The proposed time …

This study presents an energy preserving partially implicit scheme for the simulation of wave
propagation in homogeneous and heterogeneous mediums. Despite its implicit nature, the …

We are concerned with the numerical simulation of wave motion in arbitrarily
heterogeneous, elastic, perfectly‐matched‐layer‐(PML)‐truncated media. We extend in …

Time discretization is an important issue for time-dependent partial differential equations
(PDEs). For the k-th (k≥ 2) order PDEs, the explicit time-marching method may suffer from a …

This paper proposes an adaptive hybrid approach to explicitly analyse hyperbolic models.
The new methodology considers the combination of simple and enhanced explicit time …

In this study, we introduce a staggered time integrator with the Fourier pseudospectral
method to solve the first-order linear wave equation, which is accelerated by using the …

In this chapter, we develop the linearized generalized FDTD implicit scheme for solving time-
dependent nonlinear Schrödinger equations in 1D. Using the discrete energy method, the G …

In this paper, we develop a new nearly analytic symplectically partitioned Runge–Kutta
(NSPRK) method for numerically solving elastic wave equations. In this method, we first …

In this thesis, several novel numerical methods are developed to solve two important
systems, Maxwell's equations and the acoustic equations. These methods belong to two …