Performance Analysis of Zhao and Durbin Numerical Inversion Methods of Laplace Transform

Abstract

The Laplace transform is essential to satisfy the independence of time for the analysis of the transient response of the composite or functionally-graded materials. The time independent boundary value problem may be solved then either by numerically or analytically. The solutions should be inverted to the physical plane using inverse Laplace transform. Therefore, the selected numerical inversion method may be crucial to obtain the high accuracy throughout the whole analysis steps. In the present study, Zhao’s Method I, Zhao’s Method II, Durbin’s Method and Modified Durbin’s Method are applied to dynamic loading conditions. The analysis results show that the accurate and stable solutions even for long time inversion have been obtained by Modified Durbin’s Method and Zhao’s Methods. However, compared with the methods of Zhao’s, the computational and programing load of Durbin’s Methods are minimum.