Comments on the paper ”A conservative linear difference scheme for the 2D regularized long-wave equation”, by Xiaofeng Wang, Weizhong Dai and Shuangbing Guo [Applied Mathematics and Computation, 342 (2019) 55-70]
作者：
Highlights：
• The convergence analysis and the techniques used in Lemma 3.3 by X. Wang et al. in [1] are based essentially on Sobolev’s inequality in one dimension and they cannot be extended to two dimensions.
• All results based on Lemma 3.3 are false, in particular Theorem 3.3, Theorem 4.1, Theorem 5.1 and Theorem 5.2.
• Regarding the conservation of mass and energy, the initial terms Q0 and E0 depends on U0 and on U1 and the authors consider only Eq. (4) without taking into account Eq. (7). Therfore, there is an error in Theorem 3.1 and Theorem 3.2.
• In Theorem 4.1, the authors did not show that u1 is uniquely determined by Eq. (7).
摘要
•The convergence analysis and the techniques used in Lemma 3.3 by X. Wang et al. in [1] are based essentially on Sobolev’s inequality in one dimension and they cannot be extended to two dimensions.•All results based on Lemma 3.3 are false, in particular Theorem 3.3, Theorem 4.1, Theorem 5.1 and Theorem 5.2.•Regarding the conservation of mass and energy, the initial terms Q0 and E0 depends on U0 and on U1 and the authors consider only Eq. (4) without taking into account Eq. (7). Therfore, there is an error in Theorem 3.1 and Theorem 3.2.•In Theorem 4.1, the authors did not show that u1 is uniquely determined by Eq. (7).
论文关键词：Regularized long-wave (RLW) equation,Linearized difference scheme,Discrete Sobolev inequality,Convergence,Stability
论文评审过程：Received 31 May 2020, Revised 9 February 2021, Accepted 10 June 2021, Available online 28 June 2021, Version of Record 28 June 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126455
