A note on the inverse Laplace transform
Cadernos do IME - Série Matemática, 2018 In this note we show that the method for finding inverse Laplace transform without using integration on the complex plane can be used to find integral representations on the positive real axis for some functions. Furthermore, this inversion method allows us to study the inverse Laplace transform of non-tabulated functions.
Eliana Contharteze Grigoletto +1 more
semanticscholar +4 more sources
About Inverse Laplace Transform of a Dynamic Viscosity Function. [PDF]
Materials (Basel), 2022 A dynamic viscosity function plays an important role in water hammer modeling. It is responsible for dispersion and decay of pressure and velocity histories.
Urbanowicz K +3 more
europepmc +2 more sources
Complete analytic solutions for convection-diffusion-reaction-source equations without using an inverse Laplace transform. [PDF]
Sci Rep, 2020 Transient mass-transfer phenomena occurring in natural and engineered systems consist of convection, diffusion, and reaction processes. The coupled phenomena can be described by using the unsteady convection-diffusion-reaction (CDR) equation, which is ...
Kim AS.
europepmc +2 more sources
Inverse Laplace transform and multiexponential fitting analysis of T2 relaxometry data: a phantom study with aqueous and fat containing samples. [PDF]
Eur Radiol Exp, 2020 Background The inverse Laplace transform (ILT) is the most widely used method for T2 relaxometry data analysis. This study examines the qualitative agreement of ILT and a proposed multiexponential (Mexp method) regarding the number of T2 components.
Ioannidis GS +5 more
europepmc +2 more sources
A Semi-Analytical Solution of Inverse Laplace Transform [PDF]
Journal of Mathematics, 2022 We propose a general method for constructing the semi-analytical solution of the inverse Laplace transform, realized through the powerful exponential approximation invented by Wang et al. in 1993.
Shuang Luo, Fu-yao Zhao
doaj +2 more sources
Applications of Laplace Transforms and their Inverses [PDF]
Proceedings of the American Mathematical Society, 1972 By means of Laplace transforms and their inverses we first solve the Varma transform, considered as an integral equation for an unknown function in the integrand. We then express two operators of fractional integration in terms of Laplace and inverse Laplace transforms.
Charles W. Fox
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Inverse Laplace transform based on Widder's method for Tsallis exponential [PDF]
arXiv, 2022 A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex integration method.
S. S. Naina Mohammed +4 more
arxiv +3 more sources
Stabilization of the inverse Laplace transform of multiexponential decay through introduction of a second dimension. [PDF]
J Magn Reson, 2013 Celik H +4 more
europepmc +4 more sources
Pressure-Dependent Rate Constant Predictions Utilizing the Inverse Laplace Transform: A Victim of Deficient Input Data. [PDF]
ACS Omega, 2018 k(E) can be calculated either from the Rice–Ramsperger–Kassel–Marcus theory or by inverting macroscopic rate constants k(T). Here, we elaborate the inverse Laplace transform approach for k(E) reconstruction by examining the impact of k(T) data fitting ...
Firaha DS +3 more
europepmc +2 more sources
Regularization of the inverse Laplace transform by mollification
Inverse Problems, 2023 Abstract In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace transform using the concept of mollification.
Pierre Maréchal +2 more
openaire +4 more sources