The Dynamical control step size of difference methods for fuzzy partial differential equations by using the CADNA library

In this study, we investigated heat and wave equations as classical models of fuzzy partial differential equations (FPDEs), and a reliable scheme to their solve. For this purpose, the stochastic arithmetic (SA) and the CESTAC1 method are applied to validate the results. In order to implement the propsed algorithm, the CADNA2 library is used. In this case, the optimal number of nodes and optimal step size are found. The examples illustrate the efficiency and importance of using the SA in place of the floating point arithmetic(FPA).

Keywords:

Difference methods , Stochastic arithmetic , CESTAC method , CADNA Library , Fuzzy partial differential equations(FPDE) , Fuzzy numbers , Fuzzy sets