Abstract
In this paper, we discuss a paradigm for the integration in time of parabolic partial differential equations with time-dependent boundary conditions by fractional step (locally one-dimensional or LOD) methods. The original results, communicated in [8], offered the possibility that for fixed spatial mesh of size h, one particular LOD scheme which was second-order accurate with respect to the time-step k could remain second-order accurate for problems with time-dependent boundary conditions. We now extend the analysis to a particular class of L-acceptable methods, and some other fractional step splittings. The problem of maintaining accuracy in LOD methods in the neighborhood of time-dependent boundary conditions has persisted from at least [9] when accuracy limitations to 0(k0.25) were conjectured to many examples in the current (circa 1985–87) literature.
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© 1988 Springer Basel AG
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Swayne, D.A. (1988). Time-Dependent Dirichlet Boundary Conditions and Fractional Step Methods. In: Agarwal, R.P., Chow, Y.M., Wilson, S.J. (eds) Numerical Mathematics Singapore 1988. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 86. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6303-2_36
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DOI: https://doi.org/10.1007/978-3-0348-6303-2_36
Publisher Name: Birkhäuser, Basel
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