Applications of Fourier Series Technique to Inverse Laplace Transform

Abstract

This paper describes a method of determining the inverse Laplace transform numerically by applying the Fourier series technique to the matric operational functions. The basis of the method is that by choosing the contour of integration, the inverse Laplace transform is converted into the Fourier transform and it is approximated by a certain Fourier series. In this way numerical Laplace inversion is given and the error introduced can be made as small as desired. Furthermore, Fast Fourier Transform method is applied to the method to reduce the computational time. The method has the advantage of needing little programming effort in digital computations and is useful in numerical analysis of systems. Computational algorithms and some numerical examples are given to show usefulness of the method.