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A numerical study of variable coefficient elliptic Cauchy problem via projection method

Gupta, Hari Shanker (2012) A numerical study of variable coefficient elliptic Cauchy problem via projection method. In: International Journal of Computer Mathematics, 89 (6). pp. 795-809.

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0020716...


In this paper, we investigate a numerical method for the solution of an inverse problem of recovering lacking data on some part of the boundary of a domain from the Cauchy data on other part for a variable coefficient elliptic Cauchy problem. In the process, the Cauchy problem is transformed into the problem of solving a compact linear operator equation. As a remedy to the ill-posedness of the problem, we use a projection method which allows regularization solely by discretization. The discretization level plays the role of regularization parameter in the case of projection method. The balancing principle is used for the choice of an appropriate discretization level. Several numerical examples show that the method produces a stable good approximate solution.

Item Type: Journal Article
Publication: International Journal of Computer Mathematics
Publisher: Taylor and Francis Group
Additional Information: Copyright of this article belongs to Taylor and Francis Group.
Keywords: elliptic Cauchy problem;regularization method;inverse problem;balancing principle;ill-posed problems;elliptic partial differential equations
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 13 Apr 2012 09:07
Last Modified: 13 Apr 2012 09:07
URI: http://eprints.iisc.ac.in/id/eprint/44272

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