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- Title
A second-order convergent and linearized difference scheme for the initial-boundary value problem of the Korteweg-de Vries equation.
- Authors
Wang Xuping; Sun Zhizhong
- Abstract
To numerically solve the initial-boundary value problem of the Korteweg-de Vries equation, an equivalent coupled system of nonlinear equations is obtained by the method of reduction of order. Then, a difference scheme is constructed for the system. The new variable introduced can be separated from the difference scheme to obtain another difference scheme containing only the original variable. The energy method is applied to the theoretical analysis of the difference scheme. Results show that the difference scheme is uniquely solvable and satisfies the energy conservation law corresponding to the original problem. Moreover, the difference scheme converges when the step ratio satisfies a constraint condition, and the temporal and spatial convergence orders are both two. Numerical examples verify the convergence order and the invariant of the difference scheme. Furthermore, the step ratio constraint is unnecessary for the convergence of the difference scheme. Compared with a known two-level nonlinear difference scheme, the proposed difference scheme has more advantages in numerical calculation.
- Subjects
KORTEWEG-de Vries equation; BOUNDARY value problems; NONLINEAR equations; NUMERICAL calculations; ENERGY conservation laws; STOCHASTIC convergence
- Publication
Journal of Southeast University (English Edition), 2022, Vol 38, Issue 2, p203
- ISSN
1003-7985
- Publication type
Article
- DOI
10.3969/j.issn.1003-7985.2022.02.013