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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)
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)
CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ABSTRACT 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(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)
In many applications of atmospheric transport-chemistry problems, a major task is the numerical integration of the stii systems of ordinary diierential equations describing the chemical transformations. This paper presents a comprehensive numerical comparison between ve dedicated explicit and four implicit solvers for a set of seven benchmark problems from(More)
This paper deals with the convergence analysis of implicit Runge-Kutta methods as applied to stiff, semilinear systems of the form $$\dot U$$ (t)=QU(t)+g(t, U(t)). A criterion is developed which determines whether the order of optimalB-convergence is at least equal to the stage order or one order higher. This criterion is studied for a number of interesting(More)
In the operator splitting solution of atmospheric transport-chemistry problems modeling air pollution, a major task is the numerical integration of the stii ODE systems describing the chemical transformations. In this note a numerical comparison is presented between two special purpose solvers developed for this task. Note: This report is one of a series on(More)