Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
MathSciNet review: 0105821
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [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 $ x - y$ 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 (Unpublished.)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)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.00

Retrieve articles in all journals with MSC: 65.00

Additional Information

Article copyright: © Copyright 1958 American Mathematical Society

American Mathematical Society