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A mollification regularization method with the Dirichlet kernel for two Cauchy problems of three-dimensional Helmholtz equation
International Journal of Computer Mathematics ( IF 1.600 ) Pub Date : 2019-12-09 , DOI: 10.1080/00207160.2019.1697807
Shangqin He; Xiufang Feng

In this paper, two Cauchy problems of Helmholtz equation in a three-dimensional case are considered. To address these problems, a mollification method with bivariate Dirichlet kernel is proposed. Stable errors estimates are obtained based on appropriate a priori choices of mollification parameters. Convergence estimates show that the regularization solution depends continuously on the data and wavenumber. Numerical examples of our interest show that Dirichlet kernel is more effective than the Gaussian kernel under the same parameter selection rule, and our procedure is stable with respect to perturbations noise in the data.
更新日期:2019-12-09

 

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