Almost all the difficulties that arise in the numerical solution of Maxwell’s equations are due to material interfaces. In case that their geometrical features are much smaller than a typical wave length, one would like to use small space steps with large time steps. The first time stepping method which combines a very low cost per time step with unconditional stability was the ADI-FDTD method ...

Stability analysis of the numerical Method of characteristics applied to energy-preserving systems. Abstract We study numerical (in)stability of the Method of characteristics (MoC) applied to a system of non-dissipative hyperbolic partial differential equations (PDEs) with periodic boundary conditions. We consider three different solvers along the characteristics: simple Euler (SE), modified Eu...

We prove unconditional long-time stability for a particular velocity-vorticity discretization of the 2D Navier-Stokes equations. The scheme begins with a formulation that uses the Lamb vector to couple the usual velocity-pressure system to the vorticity dynamics equation, and then discretizes with the finite element method in space and implicit-explicit BDF2 in time, with the vorticity equation...

A time integration method for the equations of motion is developed based on Gauss implicit Runge-Kutta to high-accurate solving responses in structural vibration. The present possesses features unconditional stability and self-starting can achieve fourth-order accuracy displacement, velocity, acceleration simultaneously. algorithm a matrix form no need iterate calculation. convergent verified b...

The numerical simulation of the dynamics of the molecular beam epitaxy (MBE) growth is considered in this article. The governing equation is a nonlinear evolutionary equation that is of linear fourth order derivative term and nonlinear second order derivative term in space. The main purpose of this work is to construct and analyze two linearized finite difference schemes for solving the MBE mod...

Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear diffusion, with typical examples like the Cahn-Hilliard equation and the thin film type equation. The up-to-date theoretical explanation of the numerical stability relies on the assumption that the deriv...

In this paper, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formulating an unconditionally stable two-dimensional FDTD is applied. Unlike the conventional ADI algorithms, ho...

Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic–parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small L1 ∩ H3 perturbations, converging time-asymptotically to a translate of...

We present a general methodology for constructing lattice Boltzmann models of hydrodynamics with certain desired features of statistical physics and kinetic theory. We show how a methodology of linear programming theory, known as Fourier-Motzkin elimination, provides an important tool for visualizing the state space of lattice Boltzmann algorithms that conserve a given set of moments of the dis...

A high-current, wide-band transconductance amplifier is described that provides an unprecedented level of output current at high frequencies with exceptional stability. It is capable of converting a signal voltage applied to its input into a groundreferenced output rms current up to 100 A over a frequency range from dc to 100 kHz with a useable frequency extending to 1 MHz. The amplifier has a ...