REAL INVERSION OF A LAPLACE TRANSFORM FUNCTION

In this paper we describe some recent developments related to the nume rical inversion of a Laplace Transform function when the data function is known on the real axis only. This work is a part of a larger resea rch project that the authors are developing together with others resea rchers within the activities of the Research Center of Parallel Comput ing and Supercomputers. This project is devoted to build a mathematica l software package for the numerical inversion of a Laplace Transform function that should be used in real applications and that should allo w the user to get the more appropriate algorithm according to the spec ific user problem. If we can state that the complex inversion problem has been mainly solved, this is not true for the real case. In this la st case it is much more difficult to develop stable algorithms due to the strong amplification of the errors during the solution procedure. Briefly, this is due to an intrinsic ill-posedness of the real inversi on problem. Therefore, our attention has been devoted to the analysis of some discretization schemes which we consider the most promising on es in order to point out some computational issues related to the real inversion problem and to provide useful guidelines in the development of efficient and stable algorithms.