|
|||||
|
|
| 利用Adomian分解方法求非线性反常次扩散方程近似解 | |
| 引用本文： | 宋吉茜,刘发旺,庄平辉.利用Adomian分解方法求非线性反常次扩散方程近似解[J].厦门大学学报(自然科学版),2007,46(4):469-473. |
| 作者姓名： | 宋吉茜 刘发旺 庄平辉 |
| 作者单位： | 1. 福州大学阳光学院 2. 昆士兰理工大学数学科学学院,布利斯本,昆士兰4001,澳大利亚 3. 厦门大学数学科学学院,福建,厦门361005 |
| 摘 要： | 对于反常次扩散的一个物理-数学逼近是基于一个包含分数阶导数的一般扩散方程．分数阶核方程已经证明在反常慢扩散（次扩散）情况下特别有用．但是，有效的求解非线性反常次扩散方程的方法仍然处于初期阶段．文中对非线性反常次扩散方程进行了研究，利用Adomian分解方法构造一个近似解，并给出一些数值例子来说明这个方法的有效性和简单性． |
| 关 键 词： | 非线性反常次扩散方程 Adomian分解方法 Riemann-Liouville分数阶导数 |
| 文章编号： | 0438-0479（2007）04-0469-05 |
| 修稿时间： | 2006-12-08 |
An Approximate Solution for the Non-linear Anomalous Subdiffusion Equation Using the Adomian Decomposition Method |
|
| SONG Ji-qian,LIU Fa-wang,ZHUANG Ping-hui.An Approximate Solution for the Non-linear Anomalous Subdiffusion Equation Using the Adomian Decomposition Method[J].Journal of Xiamen University(Natural Science),2007,46(4):469-473. | |
| Authors: | SONG Ji-qian LIU Fa-wang ZHUANG Ping-hui |
| Institution: | 1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China ; 2. School of Mathematical Sciences, Queensland University of Technology, GPO BOX 2434, Brisbane, Qld 4001,Australia |
| Abstract: | A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order.Fractional kinetic equations have proved particularly useful in the context of anomalous slow diffusion(subdiffusion).However,effective methods for the non-linear anomalous subdiffusion equation(NA-SubE) are still in their infancy.In this paper,NA-SubE was considered and an approximate solution was constructed by using Adomian decomposition method.Some examples were presented to show the efficiency and simplicity of the method. |
| Keywords: | nonlinear anomalous subdiffusion equation Adomian decomposition method~ Riemann-Liouville fractional derivative |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |