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On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation

✍ Scribed by Ai-Lin Qian; Xiang-Tuan Xiong; Yu-Jiang Wu

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
609 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper, we consider the Cauchy problem for the Helmholtz equation in a rectangle, where the Cauchy data is given for y = 0 and boundary data are for x = 0 and x = Ο€. The solution is sought in the interval 0 < y ≀ 1. A quasi-reversibility method is applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates.

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