Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 326-340.
Published online: 2009-02
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This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain $0 <x\le 1$, $y\in R$. The Cauchy data at $x=0$ is given and the solution is then sought for the interval $0< x\le 1$. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m88032}, url = {http://global-sci.org/intro/article_detail/nmtma/6027.html} }This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain $0 <x\le 1$, $y\in R$. The Cauchy data at $x=0$ is given and the solution is then sought for the interval $0< x\le 1$. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable.