Numerical Laplace inversion in problems of elastodynamics: Comparison of four algorithms. (November 2017) - Adamek, Vitezslav; Vales, Frantisek; Cerv, Jan
Highlights: Four numerical algorithms tested for Laplace transform inversion in elastodynamics. Some methods can reach nearly arbitrary precision using multi-precision computations. The combination of FFT and Wynns algorithm seems to be the most powerful. Results of numerical inversion need to be always verified by another method. Presented Maple codes can be directly applied to particular problems. Abstract: The objective of this work is to find a suitable algorithm for numerical Laplace inversion which could be used for effective and precise solution of elastodynamic problems. For this purpose, the capabilities of four algorithms are studied using three transforms resulted from analytical solutions of longitudinal waves in a thin rod, flexural waves in a thin beam and plane waves in a strip. In particular, the Gaver–Stehfest algorithm, the Gaver–Wynn's rho algorithm, the Fixed-Talbot algorithm and the FFT algorithm combined with Wynn's epsilon accelerator are tested. The codes written in Maple 16 employing multi-precision computations are presented for each method. Given the results obtained, the last mentioned algorithm proves to be the best. It is most efficient and it gives results of reasonable accuracy nearly for all tested times ranging from 3 × 10 − 7 s to 3 × 10 3  s.