1996•Journal of geomagnetism and geoelectricityOpen access

Numerical Solution of Laplace's Equation in Spherical Coordinates.

Tsuneji Rikitake

Abstract

A method for numerically solving Laplace's equation in three-dimensional spherical space is developed relying on relaxation technique. It is demonstrated that upward continuation of magnetic potential for the 1990 IGRF non-dipole field expressed by spherical harmonics of low degree and order can be successfully made on a personal computer.

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Key concepts: Spherical harmonics, Laplace's equation, Spherical coordinate system, Laplace transform, Mathematical analysis, Spin-weighted spherical harmonics, Green's function for the three-variable Laplace equation, Bipolar coordinates