TY - JOUR T1 - Linearly Compact Difference Scheme for the Two-Dimensional Kuramoto-Tsuzuki Equation with the Neumann Boundary Condition AU - Zhang , Qifeng AU - Zhang , Lu JO - Annals of Applied Mathematics VL - 1 SP - 49 EP - 78 PY - 2023 DA - 2023/04 SN - 39 DO - http://doi.org/10.4208/aam.OA-2022-0015 UR - https://global-sci.org/intro/article_detail/aam/21633.html KW - Kuramoto-Tsuzuki equation, compact difference scheme, pointwise error estimate, stability, numerical simulation. AB -

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 $H^2$-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.