## ReLaTIve. An Ansi C90 software package for the Real Laplace Transform Inversion.(English)Zbl 1267.65202

Summary: A software package for numerical inversion of Laplace transforms computable everywhere on the real axis is described. Besides the function to invert the user has only to provide the numerical value (even if it is an approximate value) of the abscissa of convergence and the accuracy required for the inverse function. The software provides a controlled accuracy, i.e., it dynamically computes the so-called maximum attainable accuracy such that numerical results are provided within the greatest value between the user’s required accuracy and the maximum attainable accuracy. This is done because the intrinsic ill-posedness of the real inversion problem sometimes may prevent to reach the desired accuracy. The method implemented is based on a Laguerre polynomial series expansion of the inverse function and belongs to the class of polynomial-type methods of inversion of the Laplace transform, formally characterized as collocation methods (C-methods).

### MSC:

 65R10 Numerical methods for integral transforms 44A10 Laplace transform 65R30 Numerical methods for ill-posed problems for integral equations 65Y15 Packaged methods for numerical algorithms
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### References:

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