Name
Title | ||
|---|---|---|
Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions. |
Abstract | ||
|---|---|---|
The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.cpc.2011.08.001 | Computer Physics Communications |
Keywords | Field | DocType |
Adomian decomposition method (ADM),Initial value problem,Analytic approximate solution,Two-step Adomian decomposition method,Brusselator model,Adomian polynomials | Byte,Mathematical optimization,Identifier,Polynomial,Padé approximant,Mathematical analysis,Symbolic computation,Initial value problem,Adomian decomposition method,Test data,Mathematics | Journal |
Volume | Issue | ISSN |
183 | 1 | 0010-4655 |
Citations | PageRank | References |
3 | 0.43 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yezhi Lin | 1 | 8 | 2.69 |
| Yinping Liu | 2 | 24 | 9.15 |
| Zhibin Li | 3 | 115 | 23.77 |