期刊
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
卷 100, 期 1, 页码 133-152出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2022.2085035
关键词
GKdV equation; multi-solitary waves; stability; finite difference scheme; conservation
In this paper, a linear mass and energy conservative finite difference scheme for the generalized Korteweg-de Vries (GKdV) equation is proposed and analyzed. The scheme has second- and fourth-order accuracy in time and space, respectively, and is proven to be uniquely solvable, stable and convergent. Numerical examples confirm the stability and convergence of the scheme and its effectiveness in handling single and multi-solitary waves.
In this paper, a linear mass and energy conservative finite difference scheme for the generalized Korteweg-de Vries (GKdV) equation is proposed and analyzed. The scheme is three-level and linear implicit and gives second- and fourth-order accuracy in time and space, respectively. It is rigorously proved by using the discrete energy method that the proposed difference scheme is uniquely solvable, stable and convergent. Numerical examples are given to confirm the stability and convergence of the numerical solution with fourth-order accuracy and the effectiveness of the present scheme for handling the single and multi-solitary waves for a long time.
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