Abstract
For many PDE problems in higher space dimension, such as the advection-diffusion-reaction system
it is in general inefficient or infeasible to apply one and the same integration formula to the different parts of the system. For example, the chemistry can be very stiff, which calls for an implicit ODE method. On the other hand, if the advection is discretized in space using a limiter, then explicit methods are often much more suitable for that part of the equation. Moreover, use of a single implicit integration formula for the whole problem readily leads to a nonlinear algebraic system too large to handle due to the simultaneous coupling over the species and over space. In such cases a more tuned approach based on an appropriate form of splitting is advocated. The general idea behind splitting is breaking down a complicated problem into smaller parts for the sake of time stepping, such that the different parts can be solved efficiently with suitable integration formulas.
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© 2003 Springer-Verlag Berlin Heidelberg
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Hundsdorfer, W., Verwer, J. (2003). Splitting Methods. In: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer Series in Computational Mathematics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09017-6_4
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DOI: https://doi.org/10.1007/978-3-662-09017-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05707-6
Online ISBN: 978-3-662-09017-6
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