Numerical Inversion of the Laplace Transform : a Survey and Comparison of Methods

A large number of different methods for numerically inverting the Laplace transform are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability to various types of functions, numerical accuracy, computational efficiency, and ease of programming and implementation. The methods are presented briefly and classified theoretically into methods which compute a sample, methods which expand f(t) in exponential functions, methods based on Gaussian quadrature, methods based on a bilinear transformation, and methods based on Fourier series. Extensive results are presented, especially on the numerical accuracy of the methods on a set of 16 test functions. The main conclusion is that for attaining high accuracy on a wide range of test functions, the use of Laguerre polynomials is most successful, while methods based on Chebyshev polynomials and on accelerated convergence of a Fourier series are both quite good. However, no single method gives optimum results for all purposes and all occasions; the results obtained in this comparison give some idea of which methods are likely to be suitable for special problems and circumstances.