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Inversion of Laplace Transforms [PDF]
, 2002 The problem of the inversion of Laplace transforms is a special case of integral equations of the first kind on the infinite interval (0, ∞). In these equations the free term F(s) is the Laplace transform of an unknown function f(t), 0 < t < ∞, where s is the variable of the transform.
Prem K. Kythe, Pratap Puri
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Inversion of the Laplace transform [PDF]
Inverse Problems, 1986 Let integral 0b exp(-pt)f(t) dt=F(p) p>0 where b>0 is a given number. The author gives a formula for f(t) in terms of F(p), p>0.
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2002
General formulae 0. \(\mathcal{L}_\gamma ^{ - 1}\left( {F\left( \gamma \right)} \right) = :f(y), where F\left( \gamma \right) = \mathop \smallint \limits_0^\infty {e^{ - \gamma y}}f(y)dy, Re \gamma \geqslant 0 \)
Paavo Salminen, Andrei N. Borodin
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General formulae 0. \(\mathcal{L}_\gamma ^{ - 1}\left( {F\left( \gamma \right)} \right) = :f(y), where F\left( \gamma \right) = \mathop \smallint \limits_0^\infty {e^{ - \gamma y}}f(y)dy, Re \gamma \geqslant 0 \)
Paavo Salminen, Andrei N. Borodin
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MACSYMS's inverse Laplace transform
ACM SIGSAM Bulletin, 1989The inverse Laplace transform capability of MACSYMA has been improved and extended. It has been extended to evaluate certain limits, sums, derivatives and integrals of Laplace transforms. It also takes advantage of the inverse Laplace transform convolution theorem, and can deal with a wider range of symbolic parameters.
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Methods for laplace transform inversion
Vestnik St. Petersburg University: Mathematics, 2011In solving problems by operational methods, the most difficult stage is inversion, i.e., the reconstruction of an original from its image. There is no universal inversion method which gives satisfactory results for any image F(p). Any particular inversion method must take into account the specific behavior of the image (or of the original function ...
V. M. Ryabov, N. I. Poroshina
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Numerical Inversion of Laplace Transforms
1978There are many problems whose solution may be found in terms of a Laplace or Fourier transform, which is then too complicated for inversion using the techniques of complex analysis. In this section we discuss some of the methods which have been developed — and in some cases are still being developed — for the numerical evaluation of the Laplace ...
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Rational inversion of the Laplace transform
Journal of Evolution Equations, 2012This paper studies new inversion methods for the Laplace transform of vector-valued functions arising from a combination of A-stable rational approximation schemes to the exponential and the shift operator semigroup. Each inversion method is provided in the form of a (finite) linear combination of the Laplace transform of the function and a finite ...
Jara, Patricio +2 more
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On the numerical inversion of the Laplace transform
Bulletin of the Seismological Society of America, 1964abstract Methods are demonstrated for the numerical calculation of the inverse Laplace transform g(t) of a function g(p) given on the positive real axis of the p-plane.
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Numerical Inversion of the Laplace Transform
1981We wish to present a practical way to numerically reconstruct G(r) from the experimentally measured correlation function g(x), i.e. deal with polydispersity problems: $$g\left( tau \right) = \int_o^\infty {G\left( T \right)} {e^{ - \Gamma \tau }}dT$$ (1)
Nicole Ostrowsky, Didier Sornette
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The Laplace Transform Inversion by Inspection
The American Mathematical Monthly, 1986Illustration d'une methode d'inversion de la transformation de Laplace par inspection sur l'exemple d'un probleme aux valeurs ...
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