4.4 Article

Conservative compact difference scheme for the generalized Korteweg-de Vries equation

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 100, Issue 1, Pages 133-152

Publisher

TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2022.2085035

Keywords

GKdV equation; multi-solitary waves; stability; finite difference scheme; conservation

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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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