Review of numerical inversion of Laplace transforms using Fourier analysis, fast Fourier transform and orthogonal polynomials

  • Vinod Mishra


In real situations, sometimes it is difficult or rather impossible to find Laplace transform inversion in classical way. Such situations are tackled by numerical evaluation of inverse Laplace transform. The numerical techniques for finding inverse of Laplace transforms were introduced in the sixties by Bellman et al. Since then enormous progress has taken place. This paper mainly discusses series methods for numerically inverting Laplace transforms such as by (1) Euler, Post-Widder and Crump, (2) Fast Fourier transform and (3) Laguerre Legendre and Chebyshev polynomials. Historical development and instances of certain engineering applications have been taken into consideration.