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An accurate numerical method for inversion of Laplace transforms with applications in process dynamics and control
Author(s) -
Fatoorehchi Hooman
Publication year - 2021
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.23926
Subject(s) - laplace transform , inverse laplace transform , laplace transform applied to differential equations , bounded function , post's inversion formula , two sided laplace transform , mathematics , inversion (geology) , mellin transform , algebraic equation , inverse , laplace–stieltjes transform , mathematical analysis , algorithm , mathematical optimization , green's function for the three variable laplace equation , nonlinear system , geometry , fourier transform , physics , fourier analysis , paleontology , structural basin , quantum mechanics , fractional fourier transform , biology
Laplace transforms are frequently used in the design of control structures for chemical engineering processes. In this paper, we have developed a novel numerical method to invert Laplace transforms, which involves a particular system of linear algebraic equations. We have proven that the error of our method is bounded, and the proposed formula asymptotically converges to the exact intended Laplace inverse function. A set of numerical simulations have been carried out to demonstrate the efficiency and reliability of our method. As a salient advantage, in addition to its high accuracy, our method requires the Laplace transform function to be defined only on the real axis.