The simulation of complex systems can be made more efficient by splitting the system into several, weakly interacting subsystems, and then integrating their equations separately. The paper discusses the required extension to the Modelica language, as well as the corresponding integration algorithms. Possible applications include real-time integration of large systems, distributed simulation, an...

Abstract. In this paper, we consider linear ordinary differential equations originating in electronic engineering, which exhibit exceedingly rapid oscillation. Moreover, the oscillation model is completely different from the familiar framework of asymptotic analysis of highly oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into asymptotic series, and this allow...

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...

The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computa...

All of the numerical methods that we have developed for solving initial value problems are onestep methods, because they only use information about the solution at time tn to approximate the solution at time tn+1. As n increases, that means that there are additional values of the solution, at previous times, that could be helpful, but are unused. Multistep methods are time-stepping methods that...

Leaping methods provide for efficient and approximate time stepping of chemical reaction systems modeled by continuous time discrete state stochastic dynamics. We investigate the application of leaping methods for ‘‘small number and stiff’’ systems, i.e. systems whose dynamics involve different time scales and have some molecular species present in very small numbers, specifically in the range ...

5 The Maxwell-Klein-Gordon equation describes the interaction of a charged particle with 6 an electromagnetic field. Solving this equation in the non-relativistic limit regime, i.e. 7 the speed of light c formally tending to infinity, is numerically very delicate as the so8 lution becomes highly-oscillatory in time. In order to resolve the oscillations, standard 9 numerical time integration sch...

We increase the efficiency of a recently proposed time integration scheme for time dependent quantum transport by using the Lanczos method for time evolution. We illustrate our modified scheme in terms of a simple one dimensional model. Our results show that the Lanczos-adapted scheme gives a large increase in numerical efficiency, and is an advantageous route for numerical time integration in ...

Solving wave propagation problems within heterogeneous media has been of great interest and has a wide range of applications in physics and engineering. The design of numerical methods for such general wave propagation problems is challenging because the energy conserving property has to be incorporated in the numerical algorithms in order to minimize the phase or shape errors after long time i...

Weak coupling of an explicit spectral/hp finite element ALE fluid solver with a Chebyshev collocation structural solver for fluid–structure interaction problems is addressed. When attempting to couple high-order spatial discretizations of both fluid and structural phenomena, we are required to consider first principles in order to answer two important questions: (1) What information (e.g. force...