Laplace’s Equation in Spherical Coordinates

Mapping Intimacies ◽

10.1017/9781009024822.015 ◽

2021 ◽

pp. 195-202

Keyword(s):

Laplace’S Equation ◽

Spherical Coordinates ◽

Laplace's Equation

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Solution of Laplace’s equation in spherical coordinates

Near-Surface Applied Geophysics ◽

10.1017/cbo9781139088435.016 ◽

2013 ◽

pp. 363-366

Author(s):

Mark E. Everett

Keyword(s):

Laplace’S Equation ◽

Spherical Coordinates ◽

Laplace's Equation

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Laplace’s Equation: Spherical Coordinates

Mathematical Methods ◽

10.1007/978-0-387-09504-2_26 ◽

2008 ◽

pp. 607-637

Author(s):

Sadri Hassani

Keyword(s):

Laplace’S Equation ◽

Spherical Coordinates ◽

Laplace's Equation

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Numerical Solution to Laplace's Equation in Spherical Coordinates with Axial Symmetry

Journal of Applied Physics ◽

10.1063/1.1659137 ◽

1970 ◽

Vol 41 (5) ◽

pp. 1879-1882 ◽

Author(s):

P. S. Hoeper ◽

Robert S. Wenstrup

Keyword(s):

Numerical Solution ◽

Axial Symmetry ◽

Laplace’S Equation ◽

Spherical Coordinates ◽

Laplace's Equation

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Numerical Solution of Laplace's Equation in Spherical Coordinates.

Journal of geomagnetism and geoelectricity ◽

10.5636/jgg.48.1515 ◽

1996 ◽

Vol 48 (12) ◽

pp. 1515-1521 ◽

Author(s):

Tsuneji Rikitake

Keyword(s):

Numerical Solution ◽

Laplace’S Equation ◽

Spherical Coordinates ◽

Laplace's Equation

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Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries

Numerical Algorithms ◽

10.1007/s11075-021-01150-5 ◽

2021 ◽

Author(s):

Li-Ping Zhang ◽

Zi-Cai Li ◽

Ming-Gong Lee ◽

Hung-Tsai Huang

Keyword(s):

Stability Analysis ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation

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Central difference regularization method for the Cauchy problem of the Laplace’s equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.01.056 ◽

2006 ◽

Vol 181 (1) ◽

pp. 675-684 ◽

Author(s):

Xiang-Tuan Xiong ◽

Chu-Li Fu

Keyword(s):

Cauchy Problem ◽

Regularization Method ◽

Laplace’S Equation ◽

Central Difference ◽

Laplace's Equation ◽

The Cauchy Problem

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Approximate analytic solution of the Dirichlet problems for Laplace’s equation in planar domains by a perturbation method

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2011.10.072 ◽

2012 ◽

Vol 63 (1) ◽

pp. 60-67 ◽

Author(s):

E. Di Costanzo ◽

A. Marasco

Keyword(s):

Perturbation Method ◽

Analytic Solution ◽

Approximate Analytic Solution ◽

Laplace’S Equation ◽

Dirichlet Problems ◽

Laplace's Equation ◽

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An efficient finite element method for treating singularities in Laplace's equation

Journal of Computational Physics ◽

10.1016/0021-9991(91)90242-d ◽

1991 ◽

Vol 96 (2) ◽

pp. 391-410 ◽

Author(s):

Lorraine G Olson ◽

Georgios C Georgiou ◽

William W Schultz

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Laplace’S Equation ◽

Laplace's Equation ◽

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A note on the estimation of the optimum successive overrelaxation parameter for Laplace's equation

The Computer Journal ◽

10.1093/comjnl/10.4.400 ◽

1968 ◽

Vol 10 (4) ◽

pp. 400-401 ◽

Author(s):

T. J. Randall

Keyword(s):

Laplace’S Equation ◽

Successive Overrelaxation ◽

Laplace's Equation

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Note on the electric capacity coefficients of spheres

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1912.0101 ◽

1912 ◽

Vol 87 (598) ◽

pp. 485-487

Keyword(s):

General Solution ◽

Laplace’S Equation ◽

Laplace's Equation ◽

Electric Capacity ◽

Physical Problems

In the 'Proceedings' of the Society, vol. 87, p. 109, Mr. Jeffery obtains a general solution of Laplace’s equation in a form suitable for physical problems in connection with two spheres. As an illustration he applies his solution to the problem of finding the capacity coefficients of two equal spheres, obtaining a result which he shows to be equivalent to one of Maxwell’s series formulæ. He then computes a table of the numerical values of these coefficients.

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