Abstract
Anomalous Reaction-Sub-diffusion equations play an important role transferred in a lot of our daily applications in our life, especially in applied chemistry. In the presented work, a modified type of these models is considered which is the Reaction-Sub-diffusion equation of variable order, the linear and nonlinear models and we will refer to it by VORSDE. An accurate technique depends on a mix of the finite difference methods (FDM) together with Hermite formula is introduced to study these important types of anomalous equations. Regarding the analysis of the stability for the mentioned, it is done using the variable Von-Neumann technique; also the convergent analysis is introduced. As a result of the previous steps, we derived a stability condition which will be held for many discretization schemes of the variable order derivative and some other parameters and we checked it numerically.