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Accelerations of Zhao's methods for the numerical inversion of Laplace transform
Author(s) -
Chen Kui Fu,
Mei Shu Li
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1306
Subject(s) - laplace transform , inversion (geology) , computation , laplace transform applied to differential equations , algorithm , inverse laplace transform , fourier transform , two sided laplace transform , mellin transform , mathematics , sampling interval , range (aeronautics) , computer science , mathematical optimization , mathematical analysis , fractional fourier transform , geology , engineering , fourier analysis , statistics , paleontology , structural basin , aerospace engineering
Zhao recently presented two accurate and universal approaches to the numerical inversion of the Laplace transform. Both approaches are based on irregularly spaced intervals. Compared with the conventional approach by Durbin, the computational burden of Zhao's approaches is significantly heavier. In this report, the author proposed refinements by which the efficiency of Zhao's approaches can be improved significantly. This is achieved by subdividing the entire integrating range into several sub‐bands, but the sampling interval in each sub‐band is constant. In this way, the computation is accelerated by either applying Clenshaw's recurrence or the Chirp‐Z transform. The efficiency of both accelerating approaches is verified numerically by three examples, which makes Zhao's two approaches practicable. In addition, the history of applying the fast Fourier transform to the Laplace transform is reviewed briefly. Copyright © 2009 John Wiley & Sons, Ltd.