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Laplace积分变换反演的自适应方法(PDF)

《哈尔滨工程大学学报》[ISSN:1006-6977/CN:61-1281/TN]

期数:
2010年06期
页码:
0
栏目:
出版日期:
2010-06-25

文章信息/Info

Title:
Adaptive inversion method for the Laplace integral transform
作者:
程靳; 郭宝科;  张莉
（哈尔滨工业大学航天科学与力学系，黑龙江哈尔滨150001）
Author(s):
CHENG Jin; GUO Baoke; ZHANG Li
(Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin 150001, China)
关键词:
自适应方法; Laplace变换; 积分反演; 截断误差; 计算误差
分类号:
O241.4
DOI:
-
文献标识码:
A
摘要:
为了进一步提高Laplace积分变换数值反演结果的准确性和在实际计算中误差的易控性，一种更加准确的自适应数值积分方法被应用于Laplace的积分反演.首先，通过复变函数中的Euler恒等式把复数域中沿虚轴的Laplace复变量反演积分化简为实空间无限域中的广义积分.然后，引入一个合适的截断误差，将得到的广义积分化为一个有限区间的正常实积分.最后，指定一个相应的计算误差，再采用自适应梯形积分公式计算Laplace反演积分.反演实例表明：这种自适应方法除了个别特殊点外，如原函数的无穷大点、跳跃点等，在其他连续点处的计算结果都非常准确.这种方法的计算原理更加简单，且反演结果的总体误差容易控制.

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备注/Memo

备注/Memo:
国家级自然科学基金资助项目（10502018）
更新日期/Last Update: 2010-07-06