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We study the numerical time integration of Maxwell's equations from electromag-netism. Following the method of lines approach we start from a general semidiscrete Maxwell system for which a number of time-integration methods are considered. These methods have in common an explicit treatment of the curl terms. Central in our investigation is the question how… (More)

- W Hundsdorfer, B Koren, M Van Loon, J G Verwer
- 1995

1 Abstract. This paper examines a class of explicit nite-diierence advection schemes derived along the method of lines. An important application eld is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity. For the spatial discretization, attention is connned to conservative schemes using 5 points per direction. The 4-th… (More)

- J Frank, W H Hundsdorfer, J G Verwer
- 1996

- J G Verwer, M A Nl, Botchev
- 2008

Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicit – finite difference time domain scheme. In this paper we discuss… (More)

- A Sandu, J G Verwer, J G Blom, E J Spee, G R Carmichael, F A Potra
- 1997

In the numerical simulation of atmospheric transport-chemistry processes, a major task is the integration of the stii systems of ordinary diierential equations describing the chemical transformations. It is therefore of interest to systematically search for stii solvers which can be identiied as close to optimal for atmospheric applications. In this paper… (More)

A simple Gauss-Seidel technique is proposed which exploits the special form of the chemical kinetics equations. Classical Aitken extrapolation is applied to accelerate convergence. The technique is meant for implementation in stii solvers that are used in long range transport air pollution codes using operator splitting. Splitting necessarily gives rise to… (More)

- A Sandu, J G Verwer, J G Blom, E J Spee, G R Carmichael
- 1996

In the numerical simulation of atmospheric transport-chemistry processes, a major task is the integration of the stii systems of ordinary diierential equations describing the chemical transformations. It is therefore of interest to systematically search for stii solvers which can be identiied as close to optimal for atmospheric applications. In this paper… (More)

Due to the large number of chemical species and the three space dimensions, oo-the-shelf stii ODE integrators are not feasible for the numerical time integration of stii systems of advection-diffusion-reaction equations @c @t + r (uc) = r (K r c) + R (c) ; c = c(x; t); c 2 IR m ; x 2 IR 3 from the eld of air pollution modelling. This has led to the use of… (More)