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| Linearly Compact Difference Scheme forthe Two-Dimensional Kuramoto-TsuzukiEquation with the Neumann BoundaryCondition |
| Qifeng Zhang,Lu Zhang |
| (Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou,
Zhejiang 310018, China;School of Mathematics and Statistics, Xuzhou University of Technology,
Xuzhou, Jiangsu 221018, China) |
| DOI： |
| Abstract: |
| In this paper, we analyze and test a high-order compact difference
scheme numerically for solving a two-dimensional nonlinear Kuramoto-Tsuzuki
equation under the Neumann boundary condition. A three-level average technique is utilized, thereby leading to a linearized difference scheme. The main
work lies in the pointwise error estimate in H2
-norm. The optimal fourth-order
convergence order is proved in combination of induction, the energy method
and the embedded inequality. Moreover, we establish the stability of the difference scheme with respect to the initial value under very mild condition, however, does not require any step ratio restriction. Extensive numerical examples
with/without exact solutions under diverse cases are implemented to validate
the theoretical results. |
| Key words: Kuramoto-Tsuzuki equation, compact difference scheme, pointwise error
estimate, stability, numerical simulation |