STABILITY AND CONVERGENCE OF IMPLICIT EULER METHOD FOR FRACTIONAL DIFFUSION EQUATION
AWNI M. ABU-SAMAN *
Department of Mathematics, Al-azhar University-Gaza (AUG), P. O.Box 1277, Gaza, Palestine
ATEF M. ASSAF
Department of Mathematics, Al-Aqsa-University, Gaza, Palestine
*Author to whom correspondence should be addressed.
This paper describes a practical numerical algorithm to solve the one dimensional fractional diffusion equation with variable coefficients. The algorithm, based on Implicit Euler method and Grunwald a approximation to fractional derivatives, will be implemented and simulated as a user-subroutine on MATLAB. The user-subroutine is considering MATLAB features for reducing round-off error. Analytical and computational results show that the algorithm is consistent and unconditionally stable.
Keywords: Fractional order differential equation, diffusion, Implicit Euler method, stability, convergence