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In this paper, we consider a three dimensional Ginzburg–Landau type equation with a periodic initial value condition. A fully
discrete Galerkin–Fourier spectral approximation scheme is constructed, and then the dynamical properties of the discrete
system are analyzed. First, the existence and convergence of global attractors of the discrete system are proved by a priori
estimates and error estimates of the discrete solution, and the numerical stability and convergence of the discrete scheme
are proved. Furthermore, the long-time convergence and stability of the discrete scheme are proved.
*This work was supported by the National Natural Science Foundation of China (No.: 10432010 and 10571010) 相似文献
2.
This paper deals with the asymptotic stability of exact and discrete solutions of neutral multidelay-integro-differential
equations. Sufficient conditions are derived that guarantee the asymptotic stability of the exact solutions. Adaptations of
classical Runge–Kutta and linear multistep methods are suggested for solving such systems with commensurate delays. Stability
criteria are constructed for the asymptotic stability of these numerical methods and compared to the stability criteria derived
for the continuous problem. It is found that, under suitable conditions, these two classes of numerical methods retain the
stability of the continuous systems. Some numerical examples are given that illustrate the theoretical results.
This research is supported by Fellowship F/02/019 of the Research Council of the K.U.Leuven, NSFC (No.10571066) and SRF for
ROCS, SEM. 相似文献
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Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998 相似文献
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Fbio M. Amorin Natali Ademir Pastor Ferreira 《Journal of Mathematical Analysis and Applications》2008,347(2):428-441
In the present paper we show some results concerning the orbital stability of dnoidal standing wave solutions and orbital instability of cnoidal standing wave solutions to the following Klein–Gordon equation:
utt−uxx+u−|u|2u=0.