Adomian分解法在时间分数阶磁流体方程中的应用  

Application of Adomian Decomposition Method in Time Fractional MHD Equation

作　　者：冷春勇[1] 李宁 苏文火 LENG Chun-yong;LI Ning;SU Wen-huo(College of Mathematics and Computer Science,Yichun University,Yichun 336000,China)

机构地区：[1]宜春学院数学与计算机科学学院,江西宜春336000

出　　处：《宜春学院学报》2021年第12期35-40,80,共7页Journal of Yichun University

基　　金：江西省教育厅科学技术研究项目(编号:GJJ201629)。

摘　　要：Adomian分解法在分数阶微分方程中不仅有重要的理论成果,而且具有很好的应用价值,Adomian分解法常应用于线性与非线性微分方程的求解,它的基本思想是:将待求解的方程分解成线性部分和非线性部分,把方程的解分解成级数形式,再将方程中的非线性部分参数化,得到等价的非线性多项式,然后利用逆算子运算法将低阶解的分量推导到高阶解的分量,于是得到方程的高阶逼近解,甚至是精确解。而分数阶磁流体方程由于其求导数阶数的特殊性,在实际应用当中,解析解往往不能求解出来,根据Adomian分解法的运算特点,可以求解出逼近解,本文主要利用Adomian分解法的思想给出分数阶磁流体方程在特殊初值条件下的一组精确解。Adomiand ecomposition method not only has important theoretical results in fractional differential equations,but also has significant application.It is often used to solve linear and nonlinear differential equations.Its basic idea is firstly decomposing the equation into linear and nonlinear parts,and decomposing the solution of the equation into series form.Then parameterize the nonlinear part of the equation to obtain the equivalent nonlinear polynomials.And then the components of the lower order solution are derived to the components of the higher order solution by using the inverse operator algorithm.Finally,the higher order approximation solution or even the exact solution of the equation is obtained.Because of the particularity of the derivative order of the fractional order MHD equation,the analytical solution is hard to be solved in practical applications.In this paper,the idea of Adomian decomposition method is used to give a group of exact solutions of the fractional order MHD equation under special initial conditions.

关 键 词：ADOMIAN分解法 分数阶磁流体方程 精确解 逼近解 

分 类 号：O175[理学—数学]