Numerical inversion of Laplace transform using Haar wavelet operational matrices

In this paper, a unified derivation of the operational matrices of various orthogonal functions including the Haar wavelet is first given. Based on the derived operational matrix, this paper presents a new method for performing numerical inversion of the Laplace transform. Only matrix multiplications and ordinary algebraic operations are involved in the method. The proposed method is much simpler as compared with the dictionary-type method and the contour-integration method.