The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations

Authors:
Jun-Sheng Duan;Temuer Chaolu;Randolph Rach;Lei Lu
Affiliations:
School of Sciences, Shanghai Institute of Technology, Shanghai 201418, PR China;College of Sciences and Arts, Shanghai Maritime University, Shanghai 200135, PR China;316 South Maple Street, Hartford, MI 49057-1225, USA;School of Sciences, Shanghai Institute of Technology, Shanghai 201418, PR China
Venue:
Computers & Mathematics with Applications
Year:
2013

Citing 5
Cited 0

Analytical approximate solutions for nonlinear fractional differential equations

Applied Mathematics and Computation
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Numerical algorithm based on Adomian decomposition for fractional differential equations

Computers & Mathematics with Applications
Application of Legendre wavelets for solving fractional differential equations

Computers & Mathematics with Applications
A new approach for solving a system of fractional partial differential equations

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, we present the Adomian decomposition method and its modifications combined with convergence acceleration techniques, such as the diagonal Pade approximants and the iterated Shanks transforms, to solve nonlinear fractional ordinary differential equations. Two nonlinear numeric examples demonstrate that either the diagonal Pade approximants or the iterated Shanks transforms can efficiently extend the effective convergence region of the decomposition series solution.