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Convergence of a nonlinear finite difference scheme for the Kuramoto–Tsuzuki equation

✍ Scribed by Shanshan Wang; Tingchun Wang; Luming Zhang; Boling Guo

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
255 KB
Volume
16
Category
Article
ISSN
1007-5704

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✦ Synopsis

A nonlinear finite difference scheme is studied for solving the Kuramoto-Tsuzuki equation. Because the maximum estimate of the numerical solution can not be obtained directly, it is difficult to prove the stability and convergence of the scheme. In this paper, we introduce the Brouwer-type fixed point theorem and induction argument to prove the unique existence and convergence of the nonlinear scheme. An iterative algorithm is proposed for solving the nonlinear scheme, and its convergence is proved. Based on the iterative algorithm, some linearized schemes are presented. Numerical examples are carried out to verify the correction of the theory analysis. The extrapolation technique is applied to improve the accuracy of the schemes, and some interesting results are obtained.

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