Bi-parameter incremental unknowns ADI iterative methods for elliptic problems

Authors:
Aili Yang;Yujiang Wu;Yongqing Wu;Dawei Ren
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China 730000;School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China 730000;School of Mathematics and Statistics, Lanzhou University, Lanzhou, People's Republic of China 730000;School of Science, Xi'an University of Technology, Xi'an, People's Republic of China 710048
Venue:
Numerical Algorithms
Year:
2012

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Abstract

Bi-parameter incremental unknowns (IU) alternating directional implicit (ADI) iterative methods are proposed for solving elliptic problems. Condition numbers of the coefficient matrices for these iterative schemes are carefully estimated. Theoretical analysis shows that the condition numbers are reduced significantly by IU method, and the iterative sequences produced by the bi-parameter incremental unknowns ADI methods converge to the unique solution of the linear system if the two parameters belong to a given parameter region. Numerical examples are presented to illustrate the correctness of the theoretical analysis and the effectiveness of the bi-parameter incremental unknowns ADI methods.