Paper Info
Title
Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations.
Abstract
The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations.
Year
DOI
Venue
2013
10.1016/j.cpc.2012.07.015
Computer Physics Communications
Keywords
Field
DocType
Adomian decomposition method (ADM),Nonlinear fractional differential equations,Analytic approximate solutions,Initial value problems,Boundary value problems,Adomian polynomials,Non-smooth initial value problems
Differential equation,Boundary value problem,Mathematical optimization,Robin boundary condition,Nonlinear system,Symbolic computation,Test data,Adomian decomposition method,Initial value problem,Mathematics
Journal
Volume
Issue
ISSN
184
1
0010-4655
Citations 
PageRank 
References 
3
0.51
12
Authors
3
Name
Order
Citations
PageRank
Yezhi Lin182.69
Yinping Liu2249.15
Zhibin Li311523.77