On two-dimensional numerical inverse laplace transforms with transmission line applications

Continuous space-time systems, such as transmission lines (TL) with distributed parameters, are normally described by linear 2D partial differential equations, and hence in these cases it is very difficult or even impossible to obtain the space-time response analytically, which brings out the importance of utilizing numerical techniques [1, 2]. In this paper three 2D numerical inverse Laplace transform (NILT) methods are presented, which have the capability of retrieving the space-time response in one single calculation step. Initially the selected 2D-NILT methods, which are devised based on either Fourier series or Padè approximation, are implemented and verified in the Matlab environment. The numerical methods are examined by the use of relevant test functions in the Laplace domain with pre-known originals. Furthermore, the 2D-NILT methods results are analysed from an electrical engineering point of view to observe their performance as for their accuracy, universality and stability. Following, there will be an application of these 2D-NILTs independently on a transmission line described by a Laplace model.