ABSTRACT
The inversion of the Laplace transform on the real line is well known to be an illposed problem, since it basically deals with solving a Fredholm integral equation of the first kind (see Chapter 9). In view of this ill-posedness, there are different Laplace inversion methods, some of which, as expected, give better results for certain classes of transforms and not for all transforms. In this chapter we present various approximation formulas for the indicial function f(t) and indicate where a particular method converges and where it fails numerically.
