A modification of the weeks method for numerical inversion of the Laplace transform
Mathematics of Computation
Error analysis of the bjo¨rck-pereyra algorithms for solving vandermonde systems
Numerische Mathematik
More on the Weeks method for the numerical inversion of the Laplace transform
Numerische Mathematik
Algorithm 682: Talbot's method of the Laplace inversion problems
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
An analysis of bilinear transform polynomial methods of inversion of Laplace transforms
Numerische Mathematik
ACM Transactions on Mathematical Software (TOMS)
Algorithm 619: automatic numerical inversion of the Laplace transform [D5]
ACM Transactions on Mathematical Software (TOMS)
Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
An implementation of a Fourier series method for the numerical inversion of the Laplace transform
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Algorithm 368: Numerical inversion of Laplace transforms [D5]
Communications of the ACM
Journal of Computational and Applied Mathematics
Numerical Methods for Laplace Transform Inversion
Numerical Methods for Laplace Transform Inversion
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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 sometime 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).