Abstract
There is a duality between the use of node functions and that of cell functions in finite difference methods. From the same extremum principle they give bounds in opposite directions for a domain functional. — A difference scheme is called coherent if the equations relative to successive mesh sizes don’t contradict each other. Such coherent schemes give the exact solutions in very elementary problems. In general they yield especially good approximations. — Not only in symmetric domains, also in the case of “generali zed symmetry” the number of unknowns can be reduced by splitting the problem. Not the domain itself, but the set of admissible functions in it has a certain symmetry.
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© 1983 Springer Basel AG
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Hersch, J. (1983). Zellenfunktionen, Kohaerenz und Erweiterte Symmetrien bei Differenzenmethoden. In: Collatz, L., Meinardus, G., Wetterling, W. (eds) Differential-Difference Equations/Differential-Differenzengleichungen. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 62. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6767-2_9
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DOI: https://doi.org/10.1007/978-3-0348-6767-2_9
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