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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References | Similar Articles | Additional Information

**[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]**R. E. Kidder, ``Motion of an interface between two immiscible liquids of unequal density in a porous solid,''*Jn.*of*Appl. Phys.*, v. 27, 1956, p. 1546-1548. MR**0088270 (19:493b)****[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,''*MTAC*, v. XI, 1957, p. 67-78. MR**0086396 (19:178e)****[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, p. 149-151. MR**0051321 (14:462c)****[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 (Unpublished.)**[11]**O. D. Kellogg, Op.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]**L. J. Arms, L. D. Gates, & B. Zondek, ``A method of block iteration,'' Soc. for Industrial and Applied Math.,*Jn.*, v. 4, 1956, p. 220-229. MR**0119405 (22:10167)**

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

Article copyright:
© Copyright 1958
American Mathematical Society