| 改进的微分变换法对不连续冲击波的求解 |
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| 引用本文： | 邹丽,王振,宗智,邹东阳,张朔.改进的微分变换法对不连续冲击波的求解[J].应用数学和力学,2012,33(12):1465-1476. |
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| 作者姓名： | 邹丽 王振 宗智 邹东阳 张朔 |
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| 作者单位： | 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 |
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| 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) |
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| 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．
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| 关 键 词： | 改进的微分变换法 冲击波 Padé逼近 Burgers方程 |
| 收稿时间： | 2011-10-21 |
Solving shock wave with discontinuity by enhanced differential transform method (EDTM) |
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| ZOU Li,WANG Zhen,ZONG Zhi,ZOU Dong-yang,ZHANG Shuo.Solving shock wave with discontinuity by enhanced differential transform method (EDTM)[J].Applied Mathematics and Mechanics,2012,33(12):1465-1476. |
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| Authors: | ZOU Li WANG Zhen ZONG Zhi ZOU Dong-yang ZHANG Shuo |
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| Institution: | 1,2(1.State Key Laboratory of Structure Analysis for Industrial Equipment, Dalian,Liaoning 116085,P.R.China; 2.School of Aeronautics and Astronautics,Dalian University of Technology,Dalian,Liaoning 116085,P.R.China; 3.School of Naval Architecture,Dalian University of Technology, Dalian,Liaoning 116085,P.R.China; 4.School of Mathematics,Dalian University of Technology, Dalian,Liaoning 116085,P.R.China) |
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| 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. |
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