The Global Solution and Numerical Computation of the Generalized Nonlinear SinGordon Equation
The Global Solution and Numerical Computation of the Generalized Nonlinear SinGordon Equation
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发表时间：
2003
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通讯作者：
Liang Zhongqi
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作者：
Liang Zhongqi
本文考虑了广义非线性SinGordon方程的周期初值问题，利用非线性Galerkin方法证明了整体解的存在唯一性，并给出了边界吸引子集的存在性，建立了Fourier拟谱显式格式，证明了其收敛性，用界延拓法证明了该方法的稳定性和误差估计，最后用数值算例验证了理论的可行性，为进一步研究该方法提供了理论依据。为方程的数值分析提供了理论基础和有效的计算方法。
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.