Comparison of different numerical Laplace inversion methods for engineering applications

Abstract Laplace transform is a powerful method for enabling solving differential equation in engineering and science. Using the Laplace transform for solving differential equations, however, sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analytical means. Numerical inversion methods are then used to convert the obtained solution from the Laplace domain into the real domain. Four inversion methods are evaluated in this paper. Several test functions, which arise in engineering applications, are used to evaluate the inversion methods. We also show that each of the inversion methods is accurate for a particular case. This study shows that among all these methods, the Fourier transform inversion technique is the most powerful but also the most computationally expensive. Stehfest’s method, which is used in many engineering applications is easy to implement and leads to accurate results for many problems including diffusion-dominated ones and solutions that behave like e − t type functions. However, this method fails to predict e t type functions or those with an oscillatory response, such as sine and wave functions.