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Volume 37, Issue 4
A Fourth-Order Compact and Conservative Difference Scheme for the Generalized Rosenau-Korteweg de Vries Equation in Two Dimensions

Jue Wang & Qingnan Zeng

DOI: 10.4208/jcm.1810-m2016-0774

J. Comp. Math., 37 (2019), pp. 541-555.

Published online: 2019-06

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  • Abstract

In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries (RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energy and mass. Existence and uniqueness of its difference solution have been shown. The order of $O(τ^2 +h^4)$ in the discrete $L^∞$-norm with time step $τ$ and mesh size $h$ is obtained. Some important lemmas are proposed to prove the high order convergence. We prove that the present scheme is unconditionally stable. Numerical results are also given in order to check the properties of analytical solution.

  • Keywords

RKdV equation, Conservation, Existence, Uniqueness, Stability, Convergence.

  • AMS Subject Headings

65N06, 65M12, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wangjue3721@163.com (Jue Wang)

zengqingnanexo@163.com (Qingnan Zeng)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-541, author = {Wang , Jue and Zeng , Qingnan}, title = {A Fourth-Order Compact and Conservative Difference Scheme for the Generalized Rosenau-Korteweg de Vries Equation in Two Dimensions}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {4}, pages = {541--555}, abstract = {

In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries (RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energy and mass. Existence and uniqueness of its difference solution have been shown. The order of $O(τ^2 +h^4)$ in the discrete $L^∞$-norm with time step $τ$ and mesh size $h$ is obtained. Some important lemmas are proposed to prove the high order convergence. We prove that the present scheme is unconditionally stable. Numerical results are also given in order to check the properties of analytical solution.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1810-m2016-0774}, url = {http://global-sci.org/intro/article_detail/jcm/13211.html} }
TY - JOUR T1 - A Fourth-Order Compact and Conservative Difference Scheme for the Generalized Rosenau-Korteweg de Vries Equation in Two Dimensions AU - Wang , Jue AU - Zeng , Qingnan JO - Journal of Computational Mathematics VL - 4 SP - 541 EP - 555 PY - 2019 DA - 2019/06 SN - 37 DO - http://doi.org/10.4208/jcm.1810-m2016-0774 UR - https://global-sci.org/intro/article_detail/jcm/13211.html KW - RKdV equation, Conservation, Existence, Uniqueness, Stability, Convergence. AB -

In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries (RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energy and mass. Existence and uniqueness of its difference solution have been shown. The order of $O(τ^2 +h^4)$ in the discrete $L^∞$-norm with time step $τ$ and mesh size $h$ is obtained. Some important lemmas are proposed to prove the high order convergence. We prove that the present scheme is unconditionally stable. Numerical results are also given in order to check the properties of analytical solution.

Jue Wang & Qingnan Zeng. (2019). A Fourth-Order Compact and Conservative Difference Scheme for the Generalized Rosenau-Korteweg de Vries Equation in Two Dimensions. Journal of Computational Mathematics. 37 (4). 541-555. doi:10.4208/jcm.1810-m2016-0774
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