求解拉普拉斯方程柯西问题的截断赫尔米特展开方法

Abstract

Abstract: We investigate a Cauchy problem for the Laplace equation in this paper. To obtain a stable numerical solution for this ill posed problem, we present a truncation method based on Hermite functions expansion. Error estimate are obtained together with a discrepancy principle for the regularization parameter. Some numerical tests show that the method works effectively.

Key words: Ill-posed problem, Cauchy problem for Laplace equation, Regularization, Discrepancy principle, Truncation method

CLC Number:

O124

Xie Ou, Meng Zehong, Zhao Zhenyu, You Lei. A Truncation Method Based on Hermite Functions Expansion for a Cauchy Problem of the Laplace Equation[J].Acta mathematica scientia,Series A, 2017, 37(3): 457-468.

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A Truncation Method Based on Hermite Functions Expansion for a Cauchy Problem of the Laplace Equation

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