Open AccessNumerical evaluation of inverse integral transforms: Dynamic response of elastic materials
Author(s) -
M. D. Sharma,
S. Nain
Publication year - 2020
Publication title -
international journal of engineering, science and technology andb. lagos
Language(s) - English
Resource type - Journals
ISSN - 2141-2839
DOI - 10.4314/ijest.v12i2.4
Subject(s) - laplace transform , inverse laplace transform , inverse , integral transform , fourier transform , mathematics , gravitational singularity , mellin transform , volume integral , two sided laplace transform , laplace–stieltjes transform , numerical integration , integral equation , mathematical analysis , methods of contour integration , calculus (dental) , fractional fourier transform , fourier analysis , geometry , medicine , dentistry
This study discusses the use of numerical integration in evaluating the improper integrals appearing as inverse integral transforms of non-analytic functions. These transforms appear while studying the response of various sources in an elastic medium through integral transform method. In these studies, the inverse Fourier transforms are solved numerically without bothering about the singularities and branch points in the corresponding integrands. References on numerical integration cited in relevant papers do not support such an evaluation but suggest contrary. Approximation of inverse Laplace transform integral into a series is used without following the essential restrictions and assumptions. Volume of the published papers using these dubious procedures has reached to an alarming level. The discussion presented aims to draw the attention of researchers as well as journals so as to stop this menace at the earliest possible.Keywords: Inverse Fourier transforms, inverse Laplace transforms, Romberg integration, improper integral, elastic waves