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 龙格定理
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 Theorem C. 定理C. 短句来源 Wormald's result. Wormald的定理。 短句来源 THE GAUSS-TYPE RUNGE-KUTTA NUMERICAL INTEGRATOR 高斯型龙格库塔积分器 短句来源 Structure Program Composition Method of Runge-Kutta 龙格—库塔法结构程序设计方法 短句来源 Application of Runge-Kutta Method in Mathematica 龙格-库塔法及其Mathematica实现 短句来源

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 runge ' s theorem
 First results have been published by Bers [3] (Runge's theorem), Ismailov and Taglieva [8].
 In order to calculate the engineering electromagnetic problems,a new semi-analytical method,sub-region expansion method(SEM) is presented,which takes advantages of both the analytical methods and numerical methods.The basic idea is: firstly,the entire solving domain is divided into simple shaped sub-regions,and in each sub-region a semi-analytical expansion is used to approximate the solution;then all these sub-region expansions are jointed together by the continuity conditions;and finally the coefficients of... In order to calculate the engineering electromagnetic problems,a new semi-analytical method,sub-region expansion method(SEM) is presented,which takes advantages of both the analytical methods and numerical methods.The basic idea is: firstly,the entire solving domain is divided into simple shaped sub-regions,and in each sub-region a semi-analytical expansion is used to approximate the solution;then all these sub-region expansions are jointed together by the continuity conditions;and finally the coefficients of all expansions are determined by using point-matching technique(PMT).This scheme can overcome some shortcomings of the conventional semi-analytical methods based on the entire-domain-bases,and has a lot of important advantages: the expansion expression is simple and the calculation is reduced;the system matrix is sparse,with a smaller conditioning number,easily to be solved;and lastly the method is easily for implementation.Numerical examples are given to verify the validity of the method. 针对电磁场分析中有限元法适应能力强,但计算量大,效率低,而解析法计算量小,但适用范围窄的各自优缺点,将有限元方法与解析方法相结合,提出了一种分域展开的半解析方法用以求解工程电磁场问题。依据龙格定理,把复杂的求解场域分割为若干形状简单的子域,在每个子域内利用本征函数构造半解析展开式逼近方程的解,然后通过子域拼接得到整个场域的解。展开式系数用配点法确定。由于采用解析展开式,逼近效率高,减少了未知数个数;同时由于是局域逼近,具有解函数形式简单,计算量小,矩阵是稀疏的,条件数小,易于求解,实施方便等优点。以二维La-place问题为研究对象,数值算例验证了方法的有效性,表明该方法花费时间短,计算精确度高。
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