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A class of one-parameter alternating direction implicit methods for two-dimensional wave equations with discrete and distributed time-variable delays |
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| Authors: | Changyang Tang Chengjian Zhang Hai-wei Sun |
| Institution: | 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China
Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, China Contribution: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing - original draft;2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, China;3. Department of Mathematics, University of Macau, Macao, China Contribution: Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Writing - review & editing |
| Abstract: | For solving the initial-boundary value problem of two-dimensional wave equations with discrete and distributed time-variable delays, in the present paper, we first construct a class of basic one-parameter methods. In order to raise the computational efficiency of this class methods, we remold the methods as one-parameter alternating direction implicit (ADI) methods. Under the suitable conditions, the remolded methods are proved to be stable and convergent of second order in both of time and space. With several numerical experiments, the computational effectiveness and theoretical exactness of the methods are confirmed. Moreover, it is illustrated that the proposed one-parameter ADI method has the better advantage in computational efficiency than the basic one-parameter methods. |
| Keywords: | discrete and distributed time-variable delays error analysis numerical stability one-parameter ADI methods two-dimensional wave equations |