摘要
本文考察了一类广义非线性Sin Gordon方程的周期初值问题 ,利用非线性Galerkin方法 ,证明了其整体解的存在性和唯一性 ,并给出了其有界吸引集的存在性 .构造了全离散的Fourier拟谱显格式 ,利用有界延拓法证明了其格式的收敛性与稳定性 ,并给出了误差估计、算法分析及计算复杂度 ,最后 ,通过数值例子 ,检验了理论结果的可信性 .为对此模型的数值分析提供了理论基础和一个有效的算法 .
The generalized nonlinear SinGordon equation with p er iodic initial value problems are considered in this paper.The existence and uniq ueness of global solution is proved by nonlinear Galerkin method and the existen ce of boundary attractor set is provided.The Fourier quasispectrum explicit sc heme is established.The convergence,stability and error estimation are proved by the bound extension method.Finally the theoretical feasibility is tested with n umerical computation examples so as to provide a theoretical basis for numerical analysis of the equation and an effective computation method.
出处
《应用数学》
CSCD
北大核心
2003年第4期40-49,共10页
Mathematica Applicata
基金
福建省自然科学基金资助项目 (A9910 0 17)
集美大学科研资助项目
