The Limit of the Numerical Method of Inverting the Laplace Transformation and the Uniqueness of Relaxation Distribution Function Obtained by the Method

Mitsuhiro Matsumoto,Hiroshi Watanabe

doi:10.1007/978-1-4684-3497-2_3

The Limit of the Numerical Method of Inverting the Laplace Transformation and the Uniqueness of Relaxation Distribution Function Obtained by the Method

Mitsuhiro Matsumoto, Hiroshi Watanabe

https://doi.org/10.1007/978-1-4684-3497-2_3

Copy DOI

Publication Date: Jan 1, 1979

Citations: 1

Affiliation: Tokushima University, The University of Tokyo

#Relaxation Distribution Function #Set Of Rectangles + Show 8 more

Abstract
Full-Text PDF
Similar Papers

Abstract

It is shown that the high frequency components of the relaxation distribution function (RDF) lose their significance in the process of numerical inversion of the Laplace transformation. Five different methods of approximating the RDF are compared. The methods of approximating the RDF by a polynomial, that is by a continuous function, reproduce all features of the original function, whereas the method of approximating the RDF by line spectra shows a great deal of arbitrariness in the result. This can be understood in terms of the loss of high frequency components in the process of transformation. The effect of approximating the RDF by a set of rectangles or trapezia on the inverting procedure is also discussed.

Full Text