Computability of series representations for Green's functions in a rectangle

Y.A. Melnikov; M.Y. Melnikov

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Computability of series representations for Green's functions in a rectangle

机译：矩形中格林函数的级数表示的可计算性

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Different series forms of Green's functions are analyzed for various boundary value problems stated for Laplace and Klein-Gordon equation in a rectangular region. The classical double-series representation for the Dirichlet problem for Laplace equation is converted into a single-series form, and a computational experiment is conducted to compare practical convergence of the two forms. By a partial summation of the single-series representation, the singular component of the Green's function is expressed in analytic form radically accelerating convergence of the remaining series for the regular component. Readily computable series forms are obtained for Green's functions of some mixed boundary value problems.

机译：针对在矩形区域中为Laplace和Klein-Gordon方程陈述的各种边值问题，分析了Green函数的不同级数形式。将Laplace方程Dirichlet问题的经典双级表示形式转换为单级形式，并进行了计算实验，比较了这两种形式的实际收敛性。通过单序列表示的部分求和，格林函数的奇异成分以解析形式表示，从而从根本上加速了常规成分的其余序列的收敛。对于某些混合边值问题的格林函数，可以获得易于计算的级数形式。

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来源
《Engineering analysis with boundary elements》 |2006年第9期|p.774-780|共7页
作者
Y.A. Melnikov; M.Y. Melnikov;
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作者单位

Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类工程数学;
关键词
laplace and klein-gordon equation; rectangular region; series forms of green's functions; acceleration of convergence;

机译：拉普拉斯和klein-gordon方程;矩形区域;格林函数的级数形式;收敛速度;

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Computability of series representations for Green's functions in a rectangle

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