基于Gegenbauer多项式求解分数阶对流扩散方程  

SOLVING FRACTIONAL CONVECTION-DIFFUSION EQUATION BASED ON GEGENBAUER POLYNOMIAL

作　　者：潘超 陈豫眉 张嘉杰 Pan Chao;Chen Yumei;Zhang Jiajie(College of Mathematics and Information,China West Normal University,Nanchong 637009;College of Mathematics Education,China West Normal University,Nanchong 637009)

机构地区：[1]西华师范大学数学与信息学院,南充637009 [2]西华师范大学公共数学学院,南充637009

出　　处：《高等学校计算数学学报》2023年第2期111-129,共19页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金面上项目(11971094);四川省科技厅项目(2017JY0186)资助。

摘　　要：1引言对流扩散方程是一种重要的运动方程,包括对流项和扩散项,用于描述质量、热量、能量等流动系统的质量传递规律.许多自然过程都可用对流扩散方程来模拟,如烟雾或灰尘对大气污染物的输送、地下水的污染、有机溶剂中化学溶质的扩散、河流系统的热污染等.但异常扩散现象在自然界中无处不在,从某种意义上说正常扩散和异常扩散的根本区别在于速度.对于异常扩散,情况变得复杂.In this paper,a numerical method is proposed for solving the fractional convection-diffusion equation.The derivative is Atangana-Baleanu-Caputo(ABC)fractional derivative in the sense of Caputo.Firstly,the fractional integral operation matrix of the AB derivative based on the shifted Gegenbauer polynomial is obtained by the Mittag-Leffler function of the nonsingular and nonlocal kernel.The fractional convection-diffusion equation is transformed into equations by using the operation matrix and the integral expression of ABC fractional derivative,and the expression of the numerical solution is proposed.The coefficient matrix is derived by computing the equations.Finally,the numerical solution is obtained by putting the matrix into the expression of the numerical solution.Numerical results show that the algorithm is feasible and effective.

关 键 词：对流扩散方程 流动系统 传递规律 大气污染物 有机溶剂 热污染 根本区别 扩散项 

分 类 号：O241.8[理学—计算数学]