We analyze and implement fully discrete schemes for periodic initial value problems for a general class of dispersively modified Kuramoto–Sivashinsky equations. Time discretizations are constructed using linearly implicit schemes and spectral methods are used for the spatial discretization. The general case analyzed covers several physical applications arising in multi-phase hydrodynamics and t...

Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a second-order finite-difference time scheme. However it is often of interest to increase the order of the time-stepping scheme in order to increase the accuracy of the algorithm. This is important for instance in the case of very long simu...

In the field of strong-stability-preserving time discretizations, a number of researchers have considered using both upwind and downwind approximations for the same derivative, in order to guarantee that some strong stability condition will be preserved. The cost of computing both the upwind and downwind operator has always been assumed to be double that of computing only one of the two. Howeve...

In this paper, we propose a semi-Lagrangian discontinuous Galerkin method coupled with Runge-Kutta exponential integrators (SLDG-RKEI) for nonlinear Vlasov dynamics. The commutator-free (RK) (EI) were proposed by Celledoni, et al. (FGCS, 2003). the transport setting, RKEI can be used to decompose evolution of into composition sequence linearized resulting equations solved (SL) (DG) in Cai, (JSC...

We consider stability properties of a class of adaptive time-stepping schemes based upon the Milstein method for stochastic differential equations with a single scalar forcing. In particular we focus upon mean-square stability for a class of linear test problems with multiplicative noise. We demonstrate that highly desirable stability properties can be induced in the numerical solution by the u...

This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on accuracy considerations. Of particular interest are problems for which both the implicit and explicit parts of the ImEx splitting are stiff. Such ...

In this script, we consider some technical issues of the implementation of non-linear solvers and time-stepping schemes for the discretization of partial differential equations. The approach described below was used, for example, in the simulation software package UG (cf. [2]) and this text aims to help new developers to understand the program interfaces in this tool. Nevertheless, we omit any ...

In some situations, when an external disturbance occurs, humans can rock stably backward and forward by lifting the toe or the heel to keep the upright balance without stepping. Many control schemes have been proposed for standing balance control under external disturbances without stepping. But, in most of them researchers have only considered a flat foot phase. In this paper a framework is pr...

We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational functions r(z) e ?z which are A()-stable for suitable 2 (0; =2] and satisfy jr(1)j < 1. First and second order appr...