ON THE DISCRETIZATION OF A PARTIAL-DIFFERENTIAL EQUATION IN THE NEIGHBORHOOD OF A PERIODIC ORBIT

被引：13

作者：

ALOUGES, F

DEBUSSCHE, A

机构：

[1] ECOLE NORMALE SUPER,CMLA,61 AVE PRESIDENT WILSON,F-94235 CACHAN,FRANCE

[2] UNIV PARIS 11,ANAL NUMER LAB,F-91405 ORSAY,FRANCE

来源：

NUMERISCHE MATHEMATIK | 1993年 / 65卷 / 02期

关键词：

D O I：

10.1007/BF01385746

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with the concerned with the comparison of the dynamic of a partial differential equation and its time discretization. We restrict our attention to the neighborhood of a hyperbolic periodic orbit. We show that the discretization possesses an invariant closed curve near the periodic orbit and that the trajectories of the semigroups defined by the partial differential equation and its approximation are close in a sense to be precised provided that different data are allowed. This answers partly an open problem posed in [4]. Examples of application to dissipative partial equations are provided.

引用

页码：143 / 175

页数：33

共 21 条

[1] ON THE QUALITATIVE BEHAVIOR OF THE ORBITS OF A PARABOLIC PARTIAL-DIFFERENTIAL EQUATION AND ITS DISCRETIZATION IN THE NEIGHBORHOOD OF A HYPERBOLIC FIXED-POINT [J].