| 钟万勰,高强.WKBJ近似保辛吗?[J].计算力学学报,2005,22(1):1~7 |
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| WKBJ近似保辛吗? |
| Is the WKBJ approximation symplectic conservative? |
| 修订日期：2004-12-01 |
| DOI：10.7511/jslx20051002 |
| 中文关键词: WKBJ近似 保守系统 保辛 正则变换 |
| 英文关键词:WKBJ approximation,conservative system,symplectic conservation,canonical (transforma-)tion |
| 基金项目:国家自然科学基金(10372019)资助项目，科学院自动化所复杂系统与智能科学重点实验室开放课题. |
| 钟万勰 高强 |
| [1]中科院院士 [2]大连理工大学工业装备结构分析国家重点实验室,大连116023 |
| 摘要点击次数: 1603 |
| 全文下载次数: 12 |
| 中文摘要: |
| WKBJ短波近似是最常用的有效求解方法之一。保守体系的微分方程可用Hamilton体系的方法描述，其特点是保辛。保辛给出保守体系结构最重要的特性。但WKBJ短波近似却未曾考虑保辛的问题。本文给出验证近似解保辛的条件，并指出WKBJ近似难于保辛。然后给出正则变换的摄动保辛方法。数值例题展示了提出的保辛算法的有效性。 |
| 英文摘要: |
| The well-known WKBJ short wave length approximation is one of the popularly applied approaches for the solution of differential equations. The differential equation of a conservative system can be described by means of the Hamilton system theory, for which the key characteristic is symplectic conservation, one of the most important features of a conservative system. However, the WKBJ approximation has not taken the symplectic conservation into consideration. The present paper presents the symplectic conservative condition for an approximate solution and then describes that the WKBJ approximate solution cannot ensure symplectic conservation. The canonical transformation method is proposed for symplectic conservative perturbation approximation. Numerical examples demonstrate the effectiveness of the proposed symplectic conservative algorithms. |
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