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Inverse Laplace transform
About: Inverse Laplace transform is a research topic. Over the lifetime, 3758 publications have been published within this topic receiving 69201 citations.
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2,605 citations
TL;DR: A numerical inversion method for Laplace transforms, based on a Fourier series expansion developed by Durbin [5], is presented in this article, where the disadvantage of the inversion methods of that type, the encountered dependence of discretization and truncation error on the free parameters, is removed by the simultaneous application of a procedure for the reduction of the Discretization error, a method for accelerating the convergence of the Fourier Series and a procedure that computes approximately the "best" choice of the free parameter.
1,044 citations
TL;DR: An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method, and the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t.
Abstract: An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method. (Dubner and Abate, 1968). The advantages of this modified procedure are twofold: first, the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t; second, and consequently, the trigonometric series obtained for fit) in terms of F(s) is valid on the whole period 2T of the series. As it is proved, this error bound can be set arbitrarily small, and it is always possible to get good results, even in rather difficult cases. Particular implementations and numerical examples are presented.
953 citations
TL;DR: In this article, an improved procedure for numerical inversion of Laplace transforms is proposed based on accelerating the convergence of the Fourier series obtained from the inversion integral using the trapezoidal rule.
Abstract: An improved procedure for numerical inversion of Laplace transforms is proposed based on accelerating the convergence of the Fourier series obtained from the inversion integral using the trapezoidal rule. When the full complex series is used, at each time-value the epsilon-algorithm computes a .(trigonometric) Pade approximation which gives better results than existing acceleration methods. The quotient-difference algorithm is used to compute the coefficients of the corresponding continued fraction, which is evaluated at each time-value, greatly improving efficiency. The convergence of the continued fraction can in turn be accelerated, leading to a further improvement in accuracy.
844 citations