Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
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Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition
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Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712
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A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data
A Cauchy problem for elliptic equations with nonhomogeneous Neumann data in a cylindrical domain is investigated in this paper. For the theoretical aspect the a-priori and a-posteriori parameter choice rules are suggested and the corresponding error estimates are obtained. About the numerical aspect, for a simple case results given by two methods based on the discrete Sine transform and the finite difference method are presented; an idea of left-preconditioned GMRES (Generalized Minimum Residual) method is proposed to deal with the high dimensional case to save the time; a view of dealing with a general domain is suggested. Some ill-posed problems regularized by the quasi-boundary-value method are listed and some rules of this method are suggested.
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