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    A Novel Method for Solving the Cauchy Problem of Laplace Equation Using the Fictitious Time Integration Method

    Chih-Chang Chi1, Weichung Yeih1,2, Chein-Shan Liu3

    CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 167-190, 2009, DOI:10.3970/cmes.2009.047.167

    Abstract In this study, a novel method for solving the Cauchy problem of Laplace equation is developed. Through the fictitious time integration method (FTIM), the finding of the root of the resulting linear equations can be transformed into for finding the fixed point of a system of first order ordinary differential equations, in which a fictitious time variable is introduced. In such a sense, the inverse of ill-posed leading matrix is not necessary for the FTIM. This method uses the residual of each equation to control the evolution of unknowns in the fictitious time, and it More >

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