On a functional approximation for inversion of Laplace transforms via shifted Chebyshev series

A functional representation for inversion of the Laplace transform of a function is considered. The function is given as a shifted Chebyshev series expansion. Using special operational properties, each Laplace transform is converted into a set of simultaneous linear algebraic equations that are then easily solved to give the coefficients of the Chebyshev series. The method is simple and very suitable for computer programming. Applications to rational and irrational Laplace transforms are presented to demonstrate the satisfactory results that the method provides.