A Convergence Analysis of a Numerical Method for Solving the Balance Equation

S. J. Bijlsma Royal Netherlands Meteorological Institute, De Bilt, The Netherlands

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R. J. Hoogendoorn Royal Netherlands Meteorological Institute, De Bilt, The Netherlands

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Abstract

In this paper the convergence of an iterative method for solving the nonlinear balance equation is analyzed. It is shown that this iterative method, originally proposed by Miyakoda and Shuman, is convergent if a sufficiently accurate initial approximation is used and if the successive iterates satisfy the ellipticity condition. Otherwise the method may be divergent. Experimental results are presented.

Abstract

In this paper the convergence of an iterative method for solving the nonlinear balance equation is analyzed. It is shown that this iterative method, originally proposed by Miyakoda and Shuman, is convergent if a sufficiently accurate initial approximation is used and if the successive iterates satisfy the ellipticity condition. Otherwise the method may be divergent. Experimental results are presented.

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