Complex variable and regularization methods of inversion of the Laplace transform (original) (raw)

1989, Math. Comp

Laplace transform g on (0, oo), ie, J f(t) exp(-st) dt = g(s). Assuming that ge L2(0, oo), the first method is based on a Sine-like rational approximation of g, the second on a Sine solution of the integral equation J f(t) exp(-st) dt = g(s) via standard regu-larization, and the third ...

On the numerical inversion of Laplace transforms

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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