%0 Journal Article %1 abate2004multiprecision %A Abate, J. %A Valkó, P. P. %D 2004 %I John Wiley & Sons, Ltd. %J International Journal for Numerical Methods in Engineering %K Laplace_inversion %N 5 %P 979--993 %R 10.1002/nme.995 %T Multi-precision Laplace transform inversion %U http://dx.doi.org/10.1002/nme.995 %V 60 %X Abstract For the numerical inversion of Laplace transforms we suggest to use multi-precision computing with the level of precision determined by the algorithm. We present two such procedures. The Gaver–Wynn–Rho (GWR) algorithm is based on a special sequence acceleration of the Gaver functionals and requires the evaluation of the transform only on the real line. The fixed Talbot (FT) method is based on the deformation of the contour of the Bromwich inversion integral and requires complex arithmetic. Both GWR and FT have only one free parameter: M, which is the number of terms in the summation. Both algorithms provide increasing accuracy as M increases and can be realized in a few lines using current Computer Algebra Systems. Copyright © 2004 John Wiley & Sons, Ltd.

@article{abate2004multiprecision, abstract = {Abstract For the numerical inversion of Laplace transforms we suggest to use multi-precision computing with the level of precision determined by the algorithm. We present two such procedures. The Gaver–Wynn–Rho (GWR) algorithm is based on a special sequence acceleration of the Gaver functionals and requires the evaluation of the transform only on the real line. The fixed Talbot (FT) method is based on the deformation of the contour of the Bromwich inversion integral and requires complex arithmetic. Both GWR and FT have only one free parameter: M, which is the number of terms in the summation. Both algorithms provide increasing accuracy as M increases and can be realized in a few lines using current Computer Algebra Systems. Copyright © 2004 John Wiley & Sons, Ltd.}, added-at = {2011-08-15T04:42:33.000+0200}, author = {Abate, J. and Valkó, P. P.}, biburl = {https://www.bibsonomy.org/bibtex/222a33004d91c2cac12d4c28511c159f8/peter.ralph}, description = {Multi-precision Laplace transform inversion - Abate - 2004 - International Journal for Numerical Methods in Engineering - Wiley Online Library}, doi = {10.1002/nme.995}, interhash = {79135ef427e0b3d8cdbf03751a2c06c6}, intrahash = {22a33004d91c2cac12d4c28511c159f8}, issn = {1097-0207}, journal = {International Journal for Numerical Methods in Engineering}, keywords = {Laplace_inversion}, number = 5, pages = {979--993}, publisher = {John Wiley & Sons, Ltd.}, timestamp = {2012-03-23T20:17:13.000+0100}, title = {Multi-precision Laplace transform inversion}, url = {http://dx.doi.org/10.1002/nme.995}, volume = 60, year = 2004 }