Solution of parabolic partial differential equations

In their paper, 1 Curran et al. express some reservation concerning the suggestion 2 that the time dependence in parabolic differential equations be removed by taking the Laplace transform. The caution arises from the necessity for numerical inversion which, they feared, could lead to severe problems. It is true that difficulties can present themselves and some of these are discussed 3 as they occur in transmission-line problems. However, the examples taken to illustrate their basic theory cause no such problem as is shown in reworking their problem 2, which could be expected to present difficulties since it has ‘a discontinuity between the initial and boundary conditions’.