A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation

被引：67
|
作者：
Zhang, Hui [1 ]
Liu, Fawang [2 ]
Jiang, Xiaoyun [1 ]
Zeng, Fanhai [2 ]
Turner, Ian [2 ,3 ]
机构：
[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[3] Queensland Univ Technol, Australian Res Council Ctr Excellence Math & Stat, Brisbane, Qld, Australia
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 76卷 / 10期
基金：
中国国家自然科学基金; 澳大利亚研究理事会;
关键词：
Two-dimensional Riesz space distributed-order advection-diffusion equation; ADI Galerkin-Legendre spectral method; Gauss quadrature; Stability and convergence analysis; FOKKER-PLANCK EQUATION; IMPLICIT NUMERICAL-METHOD; DIFFERENTIAL-EQUATIONS; WAVE EQUATION; BOUNDED DOMAINS; VARIABLE-ORDER; TERM; APPROXIMATION; CONVERGENCE; MODEL;
D O I：
10.1016/j.camwa.2018.08.042
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper, a Crank-Nicolson alternating direction implicit (ADI) Galerkin-Legendre spectral scheme is presented for the two-dimensional Riesz space distributed-order advection-diffusion equation. The Gauss quadrature has a higher computational accuracy than the mid-point quadrature rule, which is proposed to approximate the distributed order Riesz space derivative so that the considered equation is transformed into a multi-term fractional equation. Moreover, the transformed equation is solved by discretizing in space by the ADI Galerkin-Legendre spectral scheme and in time using the Crank-Nicolson difference method. Stability and convergence analysis are verified for the numerical approximation. A lot of numerical results are demonstrated to justify the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.
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页码：2460 / 2476
页数：17
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