A quasi-reversibility regularization method for a Cauchy problem of the modified Helmholtz-type equation View Full Text


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Article Info

DATE

2019-12

AUTHORS

Hong Yang, Yanqi Yang

ABSTRACT

The Cauchy problem of the modified Helmholtz-type equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Thus the regularization methods are required to recover the numerical stability. In this paper, we propose a quasi-reversibility regularization method to deal with this ill-posed problem. Convergence estimates are obtained under a-priori bound assumptions for the exact solution and the selection of regularization parameter. Some numerical results are given to show that this method is stable and feasible. More... »

PAGES

29

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URI

http://scigraph.springernature.com/pub.10.1186/s13661-019-1142-z

DOI

http://dx.doi.org/10.1186/s13661-019-1142-z

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https://app.dimensions.ai/details/publication/pub.1111919319


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