| STABILITY ANALYSIS OF NONLINEAR GALERKIN ＆ GALERKIN METHODS FOR NONLINEAR EVOLUTION EQUATIONS |
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| 作者姓名： | lIEYINNIAN LIKAITAI |
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| 摘 要： | Abstract. Ogr object in this artlcle is to describe tbe Galerkln scheme and nonlin-eax Galerkin scheme for the approximation of nonlinear evolution equations, and tostudy the stability of these schemes. Spatial discretizatlon can be pedormed by eitherGalerkln spectral method or nonlinear Galerldn spectral method; time discretizatlort isdone hy Euler sin.heine wklch is explicit or implicit in the nonlinear terms. According tothe stability analysis of the above schemes, the stability of nonllneex Galerkln methodis better than that of Galexkln method.
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| 关 键 词： | 非线性发展方程 非线性Galerkin方法 稳定性分析 偏微分方程 耗散型方程 |
| 收稿时间： | 2 July 1994 |
Stability analysis of nonlinear galerkin & galerkin methods for nonlinear evolution equations |
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| lIEYINNIAN LIKAITAI.Stability analysis of nonlinear galerkin & galerkin methods for nonlinear evolution equations[J].Applied Mathematics A Journal of Chinese Universities,1996,11(2):137-152. |
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| Authors: | Yinnian He Kaitai Li |
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| Institution: | (1) Research Center for Applied Mathematics, Xi’an Jiaotong University, 710049 Xi’an |
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| Abstract: | Our object in this article is to describe the Galerkin scheme and nonlinear Galerkin scheme for the approximation of nonlinear
evolution equations, and to study the stability of these schemes. Spatial discretization can be performed by either Galerkin
spectral method or nonlinear Galerkin spectral method; time discretization is done by Euler scheme which is explicit or implicit
in the nonlinear terms. According to the stability analysis of the above schemes, the stability of nonlinear Galerkin method
is better than that of Galerkin method.
A State Key Basic Research Project Project supported by NSFC. |
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| Keywords: | 35A40 65M60 35Q10 |
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