ON THE NUMERICAL INVERSION OF LAPLACE TRANSFORMS - COMPARISON OF 3 NEW METHODS ON CHARACTERISTIC PROBLEMS FROM APPLICATIONS

Three frequently used methods for numerically inverting Laplace transf orms are tested on complicated transforms taken from the literature. T he first method is a straightforward application of the trapezoidal ru le to Bromwich's integral. The second method, developed by Weeks [22], integrates Bromwich's integral by using Laguerre polynomials. The thi rd method, devised by Talbot [18], deforms Bromwich's contour so that the integrand of Bromwich's integral is small at the beginning and end of the contour. These methods are also applied to joint Laplace-Fouri er transform problems. All three methods give satisfactory results; Ta lbot's, however, has an accurate method for choosing required paramete rs.