The Fourier-Bessel method for solving the Cauchy problem connected with the Helmholtz equation

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• 作者：Minghui Liu^a ; ^{lmh09@mails.jlu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{liuminghuime@163.com" class="auth_mail" title="E-mail the corresponding author} ; Deyue Zhang^b ; Xu Zhou^c ; Feng Liu^a
• 关键词：Cauchy problem ; Helmholtz equation ; Fourier&ndash ; Bessel expansion ; Truncated SVD ; No meshing
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：183-193
• 全文大小：528 K

文摘

This paper is concerned with the Cauchy problem connected with the Helmholtz equation. We investigate the denseness of Fourier–Bessel functions and propose a numerical method for approximating the solution to the problem. The convergence and stability are analyzed with truncated singular value decomposition method. Numerical experiments are also presented to show the effectiveness of our method.