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A Unifled Framework for Numerically Inverting Laplace ...

A Unified Framework for Numerically Inverting LaplaceTransformsJoseph Abate900 Hammond Road, Ridgewood, New Jersey 07450-2908, USA,Ward WhittDepartment of Industrial Engineering and Operations Research, Columbia University, New York, NewYork 10027-6699, USA, introduce and investigate a Framework for constructing algorithms to Numerically invertLaplace transforms. Given a Laplace transform fof a complex-valued function of a nonneg-ative real-variable,f, the functionfis approximated by a finite linear combination of thetransform values; , we use the inversion formulaf(t) fn(t) 1tn k=0 k f( kt),0< t < ,where the weights kand nodes kare complex numbers, which depend onn, but do notdepend on the transform for the time argumentt. Many different algorithms can be put intothis Framework , because it remains to specify the weights and nodes.

Given a Laplace transform f^of a complex-valued function of a nonneg- ative real-variable, f , the function f is approximated by a flnite linear combination of the transform values; i.e., we use the inversion formula

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  Framework, Inverting, Transform, Laplace transforms, Laplace, Numerically, Framework for numerically inverting laplace

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