The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Numerical inversion of two-dimensional Laplace transforms—Fourier series representation
Applied Numerical Mathematics
Numerical inversion of multidimensional Laplace transforms by the Laguerre method
Performance Evaluation
An implementation of a Fourier series method for the numerical inversion of the Laplace transform
ACM Transactions on Mathematical Software (TOMS)
Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Estimating Time Required to Reach Bid Levels in Online Auctions
Journal of Management Information Systems
Numerical simulations of 2D fractional subdiffusion problems
Journal of Computational Physics
The BEM for numerical solution of partial fractional differential equations
Computers & Mathematics with Applications
Boundary particle method for Laplace transformed time fractional diffusion equations
Journal of Computational Physics
Computers & Mathematics with Applications
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The problem of numerically inverting the double Laplace transform arises, for instance, in solving linear partial differential equations of fractional order on the semi-infinite domain. This work introduces two algorithms for numerical inversion of the double Laplace transform. The algorithms have only one free parameter (the number of terms in the summation) and provide increasing accuracy with increasing value of the parameter. They utilize the public domain one-dimensional routines: FT and GWR. Inherent in the algorithms is multi-precision computing with automatically adjusting the required number of precision digits. By using simple transform pairs and the example of classical diffusion in a force field we show that the procedures can provide extremely high accuracy. Then we derive the operational solution of the fractional diffusion equation subject to reflecting and absorbing boundary conditions at the origin. Finally, we compare the inversion results to the exact solutions given by Metzler and Klafter [Physica A 278 (2000) 107].