Abstract: In numerical calculations of fracture problems in space shuttle, vre often have to find the numerical inversion of Laplace transformations. In this paper, 1, a fast numerical inversion method for Laplace transform using a Fourier series expansion is given. 2,A fast numerical inversion method for Laplace transform using delta function expansion is given.3,A numerical inversion method for Laplace transform using the shifted Legendre polynomial expansion is given.

Key words: Laplace transform, Legendre Polynomial, Fourer series, Astronautics.