Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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$.

References [Enhancements On Off] (What's this?)

  • [1] 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) MR 0043563
  • [2] 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) MR 0186955
  • [3] J. Albrecht, Taylor-Entwicklungen und finite Ausdrücke für $ \Delta u$ u und $ \Delta \Delta u$ 1u. Z. Angew. Math. Mech. 33, 41-48 (1953) MR 0054343

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DOI: https://doi.org/10.1090/qam/218035
Article copyright: © Copyright 1967 American Mathematical Society

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