Kolmogorov-Spieqel-Siveshinky方程大时间问题的Fourier拟谱逼近  

The Fourier Pseudo-spectral Approximation of the Large-time Problem of Kolmogorov-Spieqel-Siveshinky Equation

作　　者：梁宗旗[1] 

机构地区：[1]集美大学理学院,厦门361021

出　　处：《数学物理学报（A辑）》2008年第5期886-896,共11页Acta Mathematica Scientia

基　　金：福建省自然科学基金(2008J0198;Z0511043);福建省青年创新基金(2005J037)资助

摘　　要：该文讨论了Kolmogorov-Spieqel-Siveshinky方程的周期初值问题,研究了半离散Fourier拟谱解的长时间行为,证明了半离散系统的收敛性和整体吸引子的存在性.构造了全离散的三层显式Fourier拟谱格式,并证明了该格式的收敛性,最后通过数值计算验证了格式的可信性.数值结果表明:该格式是长时间稳定并可取时间大步长.作者模拟了方程的解在相空间的轨线,得到了一些有意义的结论.The paper is concerned with the Kolmogorov-Spieqel-Siveshinky equation with periodic initial value problems. The long-time behavior of the solutions for semi-discrete Fourier pseudo-spectral scheme is studied.The convergence and the existence of the global attractors for the discrete system is proposed. The full-discrete Fourier pseudo-spectral explicit scheme and its convergence is discussed. Finally, the credibility of the scheme is examined by numerical examples to show that the scheme is stable for a long time and the step-length is long. The orbits in the phase space of the solution are presented.

关 键 词：Kolmogorov-Spieqel-Siveshinky方程 半离散拟谱方法 全离散拟谱方法 收敛性 

分 类 号：O241.82[理学—计算数学]