Numerical Laplace inversion in problems of elastodynamics: Comparison of four algorithms

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 3×10−7s to 3 × 103 s.