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We propose a numerical inverse Laplace transformation method without overshoot which is derived from matrix exponential (ME) distributions with minimal coefficient of variation. We discuss the properties of the method through an integral based interpretation of numerical inverse Laplace transformation methods belonging to the Abate–Whitt framework. Compared to the previously applied non-overshooting alternative, the “Erlang” method, the error of the proposed method improves from O ( 1 / n ) to O ( 1 / n 2 ) while it maintains the same computational complexity.

An Optimal Inverse Laplace Transform Method Without Positive and Negative Overshoot – An Integral Based Interpretation