Investigating the Laplace transform method's efficiency to a simple engineering problem

In this study, it is aimed to solve the differential equation that forms a simple engineering system and transform it into the Laplace domain, and then to investigate the effectiveness of the method used to compare the solutions with the exact solutions. For this purpose, first, the solutions of a given test function with analytical and numerical Laplace inverse transform methods (Durbin, Stehfest and Talbot) are given comparatively. Although the values obtained from these three methods overlap with each other but it is observed that the Talbot inverse transform method is more suitable than the other two methods due to its lower calculation time requirement. In addition, Talbot’s method and analytical solutions to engineering problems related to the vibratory mechanical system, heat conduction problem and a single matrix block in a fractured reservoir non-isothermal gravity drainage are numerically compared. It is understood that the Talbot inverse transform method is quite effective, and this is evident from the consistency of the numerical results and analytical results of the study. The findings show that the proposed method is very suitable and the method is easy to implement without much difficulty for solving a simple engineering problem.