利用Adomian分解方法求非线性反常次扩散方程近似解

Abstract

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.

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.