THE NUMERICAL METHODS FOR SOLVING OF THE ONE-DIMENSIONAL ANOMALOUS REACTION-DIFFUSION EQUATION.

This paper presents numerical methods for solving the one-dimensional fractional reaction-diffusion equation with the fractional Caputo derivative. The proposed methods are based on transformation of the fractional differential equation to an equivalent form of a integro-differential equation. The paper proposes an improvement of the existing implicit method, and a new explicit method. Stability and convergence tests of the methods were also conducted. [ABSTRACT FROM AUTHOR]