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