Inversion of the Laplace transform from the real axis using an adaptive iterative method (original) (raw)
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ACM Transactions on Mathematical Software, 1993
Three frequently used methods for numerically inverting Laplace transforms are tested on complicated transforms taken from the literature. The first method is a straightforward application of the trapezoidal rule to Bromwich's integral. The second method, developed by Weeks [22], integrates Bromwich's integral by using Laguerre polynomials. The third method, devised by Talbot [18], deforms Bromwich's contour so that the integrand of Bromwich's integral is small at the beginning and end of the contour. These methods are also applied to joint Laplace-Fourier transform problems. All three methods give satisfactory results; Talbot's, however, has an accurate method for choosing required parameters.
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This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.
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Mathematics in Engineering, Science and Aerospace, 2014
In real situations, sometimes it is difficult or rather impossible to find Laplace transform inversion in classical way. Such situations are tackled by numerical evaluation of inverse Laplace transform. The numerical techniques for finding inverse of Laplace transforms were introduced in the sixties by Bellman et al. Since then enormous progress has taken place. This paper mainly discusses series methods for numerically inverting Laplace transforms such as by (1) Euler, Post-Widder and Crump, (2) Fast Fourier transform and (3) Laguerre Legendre and Chebyshev polynomials. Historical development and instances of certain engineering applications have been taken into consideration.
Numerical Inversion of the Laplace Transform from the Real Axis
Journal of Mathematical Analysis and Applications, 2000
A numerical method for inversion of the Laplace transform F (p) given for p > 0 only is proposed. Recommendations for the choice of the abscissa of convergence and parameters of numerical integration are given. The results of the numerical tests are discussed.
Validation of Numerical Inversion Method for Laplace Transform
elth.ucv.ro
Currently there are several numerical methods for inverting the Laplace transform (ILT) but not all of them are used in electrical engineering. The main difficulty regarding the electric circuits is, among others, to find the transfer function poles represented by high degree ...
An implementation of a Fourier series method for the numerical inversion of the Laplace transform
ACM Transactions on Mathematical Software, 1999
Our method is based on the numerical evaluation of the integral which occurs in the Riemann Inversion formula. The trapezoidal rule approximation to this integral reduces to a Fourier series. We analyze the corresponding discretization error and demostrate how this expression can be used in the development of an automatic routine, one in which the user needs to specify only the required accuracy.
Numerical inversion of the Laplace transform
2005
We give a short account on the methods for numerical inversion of the Laplace transform and also propose a new method. Our method is inspired and motivated from a problem of the evaluation of the Müntz polynomials (see [1]), as well as the construction of the generalized Gaussian quadrature rules for the Müntz systems (see [2]). As an illustration of our method we consider an example with 100 real poles distributed uniformly on (−1/2, 100). A numerical investigation shows the efficiency of the proposed method.