Solution of the Balance Equation by Fourier Transform and Gauss Elimination

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  • 1 Department of Meteorology, University of Utah, Salt Lake City, Utah 84112
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Abstract

Efficient algorithms for the solution of the nonlinear balance equation in a spherical coordinate system are presented. These methods based upon expansion of the longitudinal dependence of the dependent variables in a Fourier series whose coefficients are obtained by means of Gauss elimination. Two different iterative approaches are used on the nonlinear term of the equation. One of these is a generalization of methods originally suggested by Miyakoda (1956) and Shuman (1957a); the other a generalization of a method discussed by Arnason (1958). Thirteen data tests indicate that the former method is slightly more efficient than the latter, and both methods are significantly more efficient than methods based on relaxation.

Abstract

Efficient algorithms for the solution of the nonlinear balance equation in a spherical coordinate system are presented. These methods based upon expansion of the longitudinal dependence of the dependent variables in a Fourier series whose coefficients are obtained by means of Gauss elimination. Two different iterative approaches are used on the nonlinear term of the equation. One of these is a generalization of methods originally suggested by Miyakoda (1956) and Shuman (1957a); the other a generalization of a method discussed by Arnason (1958). Thirteen data tests indicate that the former method is slightly more efficient than the latter, and both methods are significantly more efficient than methods based on relaxation.

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