Taylor series approach to functional approximation for inversion of Laplace transforms

The letter is devoted to a functional approximation for inversion of the Laplace transform. The function is approximated by a truncated Taylor series, which is expanded about t0=0. Utilising a special transformation, each Laplace transform is converted into a set of simultaneous linear algebraic equations which are then easily computed to give the coefficients of the basis function. Two examples with satisfactory results are given.