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
DOI: https://doi.org/10.1090/S0025-5718-1958-0105821-4
MathSciNet review: 0105821
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

    J. H. Jeans, The Mathematical Theory of Electricity and Magnesism, Cambridge University Press, London, 1948. W. R. Smythe, Static and Dynamic Electricity, McGraw-Hill Book Co., New York, 1939.
  • 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 88270
  • G. H. Shortley & R. Weller, “The numerical solution of Laplace’s equation,” Jn. Appl. Phys., v. 9, 1938, p. 334-348.
  • 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 86396, DOI https://doi.org/10.1090/S0025-5718-1957-0086396-4
  • 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. 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. O. D. Kellogg, Foundations of Potential Theory, Frederick Unger, New York, 1929, p. 286-315.
  • L. Bieberbach, Conformal mapping, Chelsea Publishing Co., New York, 1953. Translated by F. Steinhardt. MR 0051321
  • 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 (Unpublished.) O. D. Kellogg, Op. Cit., p. 261.
  • R. J. Arms, L. D. Gates, and B. Zondek, A method of block iteration, J. Soc. Indust. Appl. Math. 4 (1956), 220–229. MR 119405

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