Algebraic approximations for Laplace's equation in the neighborhood of interfaces

Author:
J. W. Sheldon

Journal:
Math. Comp. **12** (1958), 174-186

MSC:
Primary 65.00

DOI:
https://doi.org/10.1090/S0025-5718-1958-0105821-4

MathSciNet review:
0105821

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**[1]**J. H. Jeans,*The Mathematical Theory of Electricity and Magnesism*, Cambridge University Press, London, 1948.**[2]**W. R. Smythe,*Static and Dynamic Electricity*, McGraw-Hill Book Co., New York, 1939.**[3]**Ray E. Kidder,*Motion of the interface between two immiscible liquids of unequal density in a porous solid*, J. Appl. Phys.**27**(1956), 1546–1548. MR**0088270****[4]**G. H. Shortley & R. Weller, ``The numerical solution of Laplace's equation,''*Jn. Appl. Phys.*, v. 9, 1938, p. 334-348.**[5]**R. V. Viswanathan,*Solution of Poisson’s equation by relaxation method—normal gradient specified on curved boundaries*, Math. Tables Aids Comput.**11**(1957), 67–78. MR**0086396**, https://doi.org/10.1090/S0025-5718-1957-0086396-4**[6]**R. S. Varga, ``Numerical solution of the two-group diffusion equations in geometry,'' WAPD-159 AEC Research and Development Report, 1956, p. 8-12.**[7]**E. L. Wachspress, ``CURE: A generalized two-space-dimension multigroup coding for the IBM 704,'' KAPL-1724 AEC Research and Development Report, 1957, p. 20-28.**[8]**O. D. Kellogg,*Foundations of Potential Theory*, Frederick Unger, New York, 1929, p. 286-315.**[9]**L. Bieberbach,*Conformal mapping*, Chelsea Publishing Co., New York, 1953. Translated by F. Steinhardt. MR**0051321****[10]**J. Douglas, Jr., A. O. Gardner, & D. W. Peaceman, ``Numerical solution of a two-dimensional moving boundary problem,'' Paper presented at Association for Computing Machinery Meeting, University of Houston, June 19-21, 1957. (Unpublished.)**[11]**O. D. Kellogg, Op. Cit., p. 261.**[12]**R. J. Arms, L. D. Gates, and B. Zondek,*A method of block iteration*, J. Soc. Indust. Appl. Math.**4**(1956), 220–229. MR**0119405**

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DOI:
https://doi.org/10.1090/S0025-5718-1958-0105821-4

Article copyright:
© Copyright 1958
American Mathematical Society