STABILITY AND CONVERGENCE OF IMPLICIT EULER METHOD FOR FRACTIONAL DIFFUSION EQUATION

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Published: 2015-07-19

Page: 151-158


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.


Abstract

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


How to Cite

ABU-SAMAN, A. M., & ASSAF, A. M. (2015). STABILITY AND CONVERGENCE OF IMPLICIT EULER METHOD FOR FRACTIONAL DIFFUSION EQUATION. Asian Journal of Mathematics and Computer Research, 6(2), 151–158. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/245

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