Numerical inversion of Laplace transform based on Bernstein operational matrix

Abstract

This paper provides a technique to investigate the inverse Laplace transform by using orthonormal Bernstein operational matrix of integration. The proposed method is based on replacing the unknown function through a truncated series of Bernstein basis polynomials and the coefficients of the expansion are obtained using the operational matrix of integration. This is an alternative procedure to find the inversion of Laplace transform with few terms of Bernstein polynomials. Numerical tests on various functions have been performed to check the applicability and efficiency of the technique. The root mean square error between exact and numerical results is computed, which shows that the method produces the satisfactory results. A rough upper bound for errors is also estimated.