改进的微分变换法对不连续冲击波的求解

邹丽; 王振; 宗智; 邹东阳; 张朔

doi:10.3879/j.issn.1000-0887.2012.12.008

改进的微分变换法对不连续冲击波的求解

doi: 10.3879/j.issn.1000-0887.2012.12.008

邹丽^1,2,
王振⁴,
宗智^1,3,
邹东阳^1,2,
张朔^1,2

¹工业装备结构分析国家重点实验室,辽宁大连 116085;²大连理工大学航空航天学院,辽宁大连 116085;³大连理工大学船舶工程学院,辽宁大连116085;⁴大连理工大学数学科学学院,辽宁大连 116085

基金项目: 国家自然科学基金资助项目(50909017;51109031;50921001;11072053;51009022);教育部博士点基金资助项目(20100041120037);中央高校基本科研业务费专项资金资助项目(DUT12LK52;DUT12LK34);973基金资助项目(2010CB832704;2013CB036101)

详细信息

作者简介:
邹丽(1981—),女,辽宁盘锦人,副教授,博士,硕士生导师(联系人.Tel:+86-411-84706521; E-mail: lizou@dlut.edu.cn).

中图分类号: O242.1
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出版历程
- 收稿日期: 2011-10-21
- 修回日期: 2012-06-14
- 刊出日期: 2012-12-15

Solving shock wave with discontinuity by enhanced differential transform method (EDTM)

ZOU Li^1,2,
WANG Zhen⁴,
ZONG Zhi^1,3,
ZOU Dong-yang^1,2,
ZHANG Shuo^1,2

¹ State Key Laboratory of Structure Analysis for Industrial Equipment, Dalian 116085, Liaoning Province, P. R. China;² School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116085, Liaoning Province, Liaoning Province, P. R. China;³ School of Mathematics, Dalian University of Technology, Dalian 116085, Liaoning Province, P. R. China;⁴ School of Naval Architecture, Dalian University of Technology, Dalian 116085, Liaoning Province, P. R. China

Funds: Project supported by the National Natural Science Foundation of China (Nos. 50909017, 51109031, 50921001, 11072053, and 51009022), the Doctoral Foundation of Ministry of Education of China (No. 20100041120037), the Fundamental Research Funds for the Central Universities (Nos. DUT12LK52 and DUT12LK34), and the Major State Basic Research Development Program of China (973 Program) (Nos. 2010CB832704 and 2013CB036101)

摘要

摘要: 提出了一种改进的微分变换法，将Padé逼近法与标准微分变换法结合，这种改进的微分变换法主要应用于对冲击波的分析处理方面，能够改善级数的收敛性,并且给出收敛的渐进级数解，甚至精确解，从而为求解强非线性间断问题提供了一种有效的解析方法．
- 改进的微分变换法 /
- 冲击波 /
- Padé逼近 /
- Burgers方程
Abstract: An enhanced differential transform method (EDTM), which introduces the Padé technique into the standard differential transform method (DTM), is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact power series solution.
- enhanced differential transform method (EDTM) /
- shock wave /
- Padé tech-nique /
- Burgers equation

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参考文献(30)

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改进的微分变换法对不连续冲击波的求解

doi: 10.3879/j.issn.1000-0887.2012.12.008

作者简介:
邹丽(1981—),女,辽宁盘锦人,副教授,博士,硕士生导师(联系人.Tel:+86-411-84706521; E-mail: lizou@dlut.edu.cn).

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Solving shock wave with discontinuity by enhanced differential transform method (EDTM)

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改进的微分变换法对不连续冲击波的求解

doi: 10.3879/j.issn.1000-0887.2012.12.008

作者简介: 邹丽(1981—),女,辽宁盘锦人,副教授,博士,硕士生导师(联系人.Tel:+86-411-84706521; E-mail: lizou@dlut.edu.cn).

计量

出版历程

Solving shock wave with discontinuity by enhanced differential transform method (EDTM)

计量

出版历程

目录

作者简介:
邹丽(1981—),女,辽宁盘锦人,副教授,博士,硕士生导师(联系人.Tel:+86-411-84706521; E-mail: lizou@dlut.edu.cn).