相关论文: Unconditionally Stable Algorithms to Solve the Tim…

We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to…

For the recently introduced algorithms to solve the time-dependent Maxwell equations (see Phys.Rev.E Vol.64 p.066705 (2001)), we construct a variable grid implementation and an improved spatial discretization implementation that preserve…

We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…

We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast with second-order-in-time formulations, which require a CFL…

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several…

We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.

In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…

Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…

We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…

This paper focuses on the question of how unconditional stability can be achieved via multistep ImEx schemes, in practice problems where both the implicit and explicit terms are allowed to be stiff. For a class of new ImEx multistep schemes…

Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…

In this paper we consider unconditionally energy stable numerical schemes for the nonstationary 3D magneto-micropolar equations that describes the microstructure of rigid microelements in electrically conducting fluid flow under some…

This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…

In this work, we introduce a new space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable, and a modified Hilbert transformation is used. For this…

In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for…

Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…

This paper proposes an unconditionally stable numerical method for solving a nonlinear Sobolev model with distributed delay. The proposed computational approach approximates the time derivative by interpolation technique whereas the spatial…

We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…