Numerical algorithm based on Adomian decomposition for fractional differential equations

Dedicated to Professor Qishao Lu on the occasion of his 70th birthday
https://doi.org/10.1016/j.camwa.2009.03.079Get rights and content
Under an Elsevier user license
open archive

Abstract

In this paper, a novel algorithm based on Adomian decomposition for fractional differential equations is proposed. Comparing the present method with the fractional Adams method, we use this derived computational method to find a smaller “efficient dimension” such that the fractional Lorenz equation is chaotic. We also apply this new method to the time-fractional Burgers equation with initial and boundary value conditions. Numerical results and computer graphics show that the constructed numerical is efficient.

Keywords

Predictor–Corrector method
Adomian method
Caputo derivative
Fractional Lorenz system
Time-fractional Burgers equation

Cited by (0)

The present work was supported in part by National Natural Science Foundation of China under Grant No. 10872119, Shanghai Leading Academic Discipline Project under Grant No. J50101.