Laplace积分变换反演的自适应方法  

Adaptive inversion method for the Laplace integral transform

作　　者：程靳[1] 郭宝科[1] 张莉[1] 

机构地区：[1]哈尔滨工业大学航天科学与力学系,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2010年第6期731-735,共5页Journal of Harbin Engineering University

基　　金：国家级自然科学基金资助项目(10502018)

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.To expand its area of application as well as improve the accuracy of the results of numerical inversion using the Laplace integral transform inversion,a more exact adaptive method for the numerical integral was employed.First,by means of the Euler identity,from complex function theory,the inversion integral in complex domain was simplified into a general integral with real variables and an infinite interval.Then,a truncation error was introduced and the inversion integral was calculated in a special finite interval numerically using an adaptive trapezium integral method with a set calculation error.The inversion results indicated that this adaptive method is very accurate at all continuous points except for some special points,for example infinite and jump points.The theory of this method is simple,and errors can be controlled more easily.

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[理学—计算数学]