For numerically solving a partial differential equation (PDE) what advantage does operational calculus (OC) has over common methods like finite difference (FD), and finite element (FE)?


I mean OC in the sense of Heaviside, as developped by Mikusinski. 


I know that the choice between FE and FD, is a matter of taste, except if the PDE is of high order.  

I couldn't find anyone sharing his impression on the usage of OC to solve PDEs.



What are the advantage of using operational calculus for numerically solving pde compared to FE or FD?
In my humble opinion, the use of HOC (Heaviside Operationnal Calculus) is limited to equations with constant coefficients witch is a drastic restriction if one wants to analyse a physical phenomenon with great precison. In Oprationnal methods by Maslov a description of a special OC witch could be used to tract PDE with variable coefficients is presented and this approach is close to the use of Pseudodifferential Operators (in Hormander's sense). Note that in using this calculus the goal is to perform a qualitative analysis of the phenomenon described by the PDE rather that getting numeric values witch can be obtained by Finite Elements Methods or Finire Difference Methods. I agree with Igor Khavine to cite spectral methods. there is also wavelets methods and their families (chirplets, etc) witch seam to be useful. 


