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Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case. (English) Zbl 1398.65361

Summary: We are concerned with Gaver’s formula, which is at the heart of a numerical algorithm, widely used in scientific and engineering applications, for computing approximations of inverse Laplace transform in multi-precision arithmetic systems. We demonstrate that, once parameters \(n\) (i.e. the number of terms of Gaver’s formula) and \(\delta\) (i.e. an upper bound on noise on data) are given, then the number of correct significant digits of computed values of the inverse function is bounded above by \(-\lceil\log_{10}(\delta)\rceil+1\). In case of noise free data this number is arbitrarily large, as it is bounded below by \(n\). We establish the requirement of the multi-precision system ensuring that the quality of numerical results is fulfilled. Experiments and comparisons validate the effectiveness of such approach.

MSC:

65R32 Numerical methods for inverse problems for integral equations
44A10 Laplace transform
65Y04 Numerical algorithms for computer arithmetic, etc.
68W40 Analysis of algorithms
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