A study on a second order finite difference scheme for fractional advection-diffusion equations

被引：4

作者：

Vong, Seakweng ^{[1
]}

Shi, Chenyang ^{[1
]}

Lyu, Pin ^{[1
,2
]}

机构：

[1] Univ Macau, Dept Math, Ave Univ, Macau, Peoples R China

[2] Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu, Sichuan, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 35卷 / 02期

关键词：

finite difference method; fractional advection-diffusion equations; second order scheme; PRECONDITIONED ITERATIVE METHODS; NUMERICAL APPROXIMATION;

D O I：

10.1002/num.22310

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Second order finite difference schemes for fractional advection-diffusion equations are considered in this paper. We note that, when studying these schemes, advection terms with coefficients having the same sign as those of diffusion terms need additional estimates. In this paper, by comparing generating functions of the corresponding discretization matrices, we find that sufficiently strong diffusion can dominate the effects of advection. As a result, convergence and stability of schemes are obtained in this situation.

引用

页码：493 / 508

页数：16

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