Laplace Transform Inversion Using Two-point Rational Approximants

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Abstract
A new method of Laplace transform inversion is introduced using two-point rational approximants. Using well known theorems of Laplace transform theory expansions of the original function f(t) are derived for small and large values of t without necessarily knowing the transform f(p) explicitly. By constructing a class of continued fractions, called M fractions, which correspond simultaneously to a given, possibly different, number of terms of each series, rational approximants to f(t) can be found. Using two-point rational approximants in this way, the convergence difficulties experienced with the usual Padé, or one-point, approximants can be overcome.

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