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Numerical transform inversion using Gaussian quadrature. (English) Zbl 1095.65116

The author presents a simple Laplace transform inversion algorithm that can be compute the desired function values for a much larger class of Laplace transforms than the ones that can be inverted with the known methods in the literature. The algorithm can invert Laplace transforms of functions with discontinuities and singularities, even if, the location of these discontinuties and singularities are not known to us a priori. The algorithm only needs numerical values of the Laplace transform, is extremly fast, and the results are almost machine precision. The accuracy and robustness of the algorithm, are illustrated with various numerical examples.

MSC:

65R10 Numerical methods for integral transforms
44A10 Laplace transform
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