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Boundary Contraction Solution of Laplace's Differential Equation II

Authors:

Tse-Sun Chow,

Harold Willis MilnesAuthors Info & Claims

Journal of the ACM (JACM), Volume 7, Issue 1

Pages 37 - 45

https://doi.org/10.1145/321008.321013

Published: 01 January 1960 Publication History

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Abstract

In this paper the numerical solution of Laplace's equation for the circle is discussed and consideration is given to the convergence of the solution obtained by the boundary contraction method to the analytic solution. It is proved that in order to achieve this a relation between the mesh sizes in the circumferential and radial direction must exist. It is also demonstrated that the error due to the contraction of boundaries can be made insignificant.

References

[1]

H. W. MILNES AND R. B. POTTS, Boundary contraction solution of Laplace's differential equation, J. Assoc. Comp. Mach. 6 (1959), 226-235.

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[2]

H. W. MILN~S AND R. B. POTTS, Stability criteria for the numerical solution of partial differential equations by boundary contraction, Quart. A ppl. Math. (to appear).

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Chow TMilnes H(1962)Numerical Solution of a Class of Hyperbolic-Parabolic Partial Differential Equations by Boundary ContractionJournal of the Society for Industrial and Applied Mathematics10.1137/011001210:1(124-148)Online publication date: Mar-1962
https://doi.org/10.1137/0110012
Chow TMilnes H(1962)Boundary contraction method for numerical solution of partial differential equations: convergence and boundary conditionsQuarterly of Applied Mathematics10.1090/qam/14220020:3(209-230)Online publication date: 1962
https://doi.org/10.1090/qam/142200
Chow TMilnes H(1962)Solution of Laplace's equation by boundary contraction over regions of irregular shapeNumerische Mathematik10.1007/BF013863144:1(209-225)Online publication date: 1-Dec-1962
https://dl.acm.org/doi/10.1007/BF01386314
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Index Terms

Boundary Contraction Solution of Laplace's Differential Equation II
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations

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Published In

Journal of the ACM Volume 7, Issue 1

Jan. 1960

79 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321008

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1960

Published in JACM Volume 7, Issue 1

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Chow TMilnes H(1962)Numerical Solution of a Class of Hyperbolic-Parabolic Partial Differential Equations by Boundary ContractionJournal of the Society for Industrial and Applied Mathematics10.1137/011001210:1(124-148)Online publication date: Mar-1962
https://doi.org/10.1137/0110012
Chow TMilnes H(1962)Boundary contraction method for numerical solution of partial differential equations: convergence and boundary conditionsQuarterly of Applied Mathematics10.1090/qam/14220020:3(209-230)Online publication date: 1962
https://doi.org/10.1090/qam/142200
Chow TMilnes H(1962)Solution of Laplace's equation by boundary contraction over regions of irregular shapeNumerische Mathematik10.1007/BF013863144:1(209-225)Online publication date: 1-Dec-1962
https://dl.acm.org/doi/10.1007/BF01386314
Chow TMilnes H(1961)Numerical Solution of the Neumann and Mixed Boundary Value Problems by Boundary ContractionJournal of the ACM10.1145/321075.3210788:3(336-358)Online publication date: 1-Jul-1961
https://dl.acm.org/doi/10.1145/321075.321078

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Recommendations

Boundary conditions of the second-order differential equation and the Riccati equation

Numerical Solution of Boundary Value Problems in Differential-Algebraic Systems

Numerical solution of a parabolic equation with non-local boundary specifications

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