On the construction of Hermitian from Lagrangian difference approximations
Authors:
Mahmut Tanrikulu and William Prager
Journal:
Quart. Appl. Math. 24 (1967), 371-373
MSC:
Primary 65.66
DOI:
https://doi.org/10.1090/qam/218035
MathSciNet review:
218035
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Abstract: It is shown how simple finite difference approximations to the Laplace operator in two- or three-dimensions can be combined to construct Hermitian finite difference approximations to the two- or three-dimensional Poisson equation $\Delta u = f$.
- Lothar Collatz, Numerische Behandlung von Differentialgleichungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Band LX, Springer-Verlag, Berlin, Göttingen, Heidelberg, 1951 (German). MR 0043563
- Bernd Meister and William Prager, On the construction of symmetric difference operators for square and cubic lattices, Z. Angew. Math. Phys. 16 (1965), 403–410 (English, with German summary). MR 186955, DOI https://doi.org/10.1007/BF01591920
- J. Albrecht, Taylor-Entwicklungen und finite Ausdrücke für $\Delta u$ and $\Delta \Delta u$, Z. Angew. Math. Mech. 33 (1953), 41–48 (German, with English, French and Russian summaries). MR 54343, DOI https://doi.org/10.1002/zamm.19530330105
L. Collatz, Numerische Behandlung von Differentialgleichungen, Springer, Berlin, 1951; see also Das Mehrstellenverfahren bei Plattenaufgaben, Z. Angew. Math. Mech. 30, 385-388, and Einige neuere Forschungen über numerische Behandlung von Differentialgleichungen, Z. Angew. Math. Mech. 31, 230-236 (1951)
B. Meister and W. Prager, On the construction of symmetric difference operators for square and cubic lattices, Z. Angew. Math. Phys. 16, 403-410 (1965)
J. Albrecht, Taylor-Entwicklungen und finite Ausdrücke für $\Delta u$ u und $\Delta \Delta u$ u. Z. Angew. Math. Mech. 33, 41-48 (1953)
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Article copyright:
© Copyright 1967
American Mathematical Society
