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 high order evolution equation 高阶演化方程(1)
 高阶演化方程
 Two new classes of three level explicit difference schemes with higher stability are advanced for solving high order evolution equation ut=a 2k+1 ux 2k+1 (where a ≠0 is a constant, k =1,2,3,…)with higher stability. By which the stability condition of similar schemes can be greatly improved. Numerical examples indicate the correctness of the stability analysis given in the present work. 提出解高阶演化方程u／t＝ a（2k＋ 1u）／x2k＋ 1（其中a≠0 为常数，k＝ 1，2，3，…）的两类新的具有高稳定性的三层显式差分格式，较大地改进了同类格式的稳定性条件． 数值例子表明，文中所作的稳定性分析是正确的． 短句来源
 “high order evolution equation”译为未确定词的双语例句
 In allusion to the form solution to high order evolution equation, 4n? 针对高价发展方程的形式解,将二阶发展方程扩展为时滞分布参数系统标准型中的4n? 短句来源
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 On Order 秩序微言 短句来源 On Order 论秩序 短句来源 THEORY OF HIGH ORDER ABERRATIONS 高级象差理论 短句来源 Simplification of High-Order Systems 高阶系统的简化问题 短句来源 2) High-order virial equation. 2)高次维里方程。 短句来源

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 high order evolution equation
 We consider the problem for a high order evolution equation in a cylindrical domain unbounded in the time variable with null boundary conditions.
 Two new classes of three level explicit difference schemes with higher stability are advanced for solving high order evolution equation ut=a 2k+1 ux 2k+1 (where a ≠0 is a constant, k =1,2,3,…)with higher stability.By which the stability condition of similar schemes can be greatly improved.Numerical examples indicate the correctness of the stability analysis given in the present work. 提出解高阶演化方程ｕ／ｔ＝ ａ（２ｋ＋ １ｕ）／ｘ２ｋ＋ １（其中ａ≠０ 为常数，ｋ＝ １，２，３，…）的两类新的具有高稳定性的三层显式差分格式，较大地改进了同类格式的稳定性条件． 数值例子表明，文中所作的稳定性分析是正确的． This paper elucidates the effectiveness of combining the Poincare_Lighthill_Kuo method(PLK method, for short) and symbolic computation. Firstly, the idea and history of the PLK method are briefly introduced. Then, the difficulty of intermediate expression swell, often encountered in symbolic computation, is outlined. For overcoming the difficulty, a semi_inverse algorithm was proposed by the author, with which the lengthy parts of intermediate expressions are first frozen in the form of symbols till the final... This paper elucidates the effectiveness of combining the Poincare_Lighthill_Kuo method(PLK method, for short) and symbolic computation. Firstly, the idea and history of the PLK method are briefly introduced. Then, the difficulty of intermediate expression swell, often encountered in symbolic computation, is outlined. For overcoming the difficulty, a semi_inverse algorithm was proposed by the author, with which the lengthy parts of intermediate expressions are first frozen in the form of symbols till the final stage of seeking perturbation solutions. To discuss the applications of the above algorithm, the related work of the author and his research group on nonlinear oscillations and waves is concisely reviewed. The computer_extended perturbation solution of the Duffing equation shows that the asymptotic solution obtained with the PLK method possesses the convergence radius of 1 and thus the range of validity of the solution is considerably enlarged. The studies on internal solitary waves in stratified fluid and on the head_on collision between two solitary waves in a hyperelastic rod indicate that by means of the presented methods, very complicated manipulation, unconceivable in hand calculation, can be conducted and thus result in higher_order evolution equations and asymptotic solutions. The examples illustrate that the algorithm helps to realize the symbolic computation on micro_commputers. Finally, it is concluded that with the aid of symbolic computation, the vitality of the PLK method is greatly strengthened and at least for the solutions to conservative systems of oscillations and waves, it is a powerful tool. 阐述将PLK方法与符号运算相结合的途径和有效性·　首先简述PLK方法的思路和发展简史 :其次 ,概述运行符号运算时经常遇到的“中间表达式爆炸”困难 ,为克服这一困难 ,作者提出一种半逆序算法 :通过以符号形式“冻结”中间表达式中冗长的部分 ,到最后阶段再予“解冻” ;并且通过综述作者在一系列非线性波动和非线性振动方面的工作 ,讨论PLK_符号运算方法的具体应用 ,其中 ,Duffing方程的摄动解的计算机延伸表明 ,用PLK方法导得的渐近级数解的收敛半径为 1,从而大大拓广了解的适用范围 ;分层流体中内孤立波和超弹性杆中孤立波对撞的研究表明 ,用所提出的方法可以进行手工计算难以进行的复杂运算 ,借此可得出高阶演化方程和高阶渐近解 ,正确地解释实验结果 ;并说明采用半逆序算法后 ,可在微机上实现繁复的符号运算·　最后得出结论 :借助于符号运算 ,可大大增强PLK方法的生命力 ,至少对保守系统的振动和波动问题的求解 ,它是一个非常有效的工具 In allusion to the form solution to high order evolution equation, 4n?2 order evolution equation that is one of the best important standard type about time-delay distributed parameter system expand from two order evolution equation and construct the inner product to become 4n?2 dimension Halberd space at the same time. The generating operator of 4n?2 order evolution equation is obtained and it generates a semigroup when 4n?2 order evolution... In allusion to the form solution to high order evolution equation, 4n?2 order evolution equation that is one of the best important standard type about time-delay distributed parameter system expand from two order evolution equation and construct the inner product to become 4n?2 dimension Halberd space at the same time. The generating operator of 4n?2 order evolution equation is obtained and it generates a semigroup when 4n?2 order evolution equation is changed into one order evolution equation set. The configuration form’s semigroup is constructed and it’s basic character is proved. In particular, the semigroup(n=1) intitules Golstein’s . 针对高价发展方程的形式解,将二阶发展方程扩展为时滞分布参数系统标准型中的4n?2阶发展方程,同时构造内积形成4n?2维Hilbert空间。将4n?2阶发展方程转化为一阶发展方程组,求得4n?2阶发展方程的生成算子和在一定的条件下生成半群。构造出半群的结构式并证明其具有的基本特征。当n=1时为二阶发展方程型的Golstein算子半群。
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