Lyapunov-Sylvesters operators for (2+1)-Boussinesq equation
This article studies a technique for solving a two-dimensional Boussinesq equation discretized using a finite difference method. It consists of an order reduction method into a coupled system of second-order equations, and to formulate the fully discretized, implicit time-marched system as a Lya...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/268/abstr.html |
| Summary: | This article studies a technique for solving a two-dimensional Boussinesq
equation discretized using a finite difference method. It consists of an
order reduction method into a coupled system of second-order equations,
and to formulate the fully discretized, implicit time-marched system
as a Lyapunov-Sylvester matrix equation. Convergence and stability is
examined using Lyapunov criterion and manipulating generalized
Lyapunov-Sylvester operators. Some numerical implementations are provided
at the end to validate the theoretical results. |
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| ISSN: | 1072-6691 |