An RBF based meshless method for the distributed order time fractional advection-diffusion equation

被引：14

作者：

Liu, Quanzhen ^{[1
,4
]}

Mu, Shanjun ^{[1
,4
]}

Liu, Qingxia ^{[2
]}

Liu, Baoquan ^{[1
,4
]}

Bi, Xiaolei ^{[1
,4
]}

Zhuang, Pinghui ^{[2
]}

Li, Bochen ^{[3
]}

Gao, Jian ^{[1
,4
]}

机构：

[1] State Key Lab Safety & Control Chem, Qingdao, Shandong, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen, Fujian, Peoples R China

[3] Xiamen Taihang Technol Co Ltd, Xiamen 361000, Fujian, Peoples R China

[4] SINOPEC Res Inst Safety Engn, Qingdao, Shandong, Peoples R China

来源：

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2018年 / 96卷

关键词：

Distributed order; Advection-diffusion equation; Meshless method; RBF; POINT INTERPOLATION METHOD; DIFFERENTIAL-EQUATIONS; 2-DIMENSIONAL SOLIDS; BOUNDED DOMAINS; ELEMENT-METHOD; POROUS-MEDIA; SEEPAGE FLOW; DERIVATIVES; CALCULUS; SCHEMES;

D O I：

10.1016/j.enganabound.2018.08.007

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Distributed order operators and differential equations have been applied to model physical phenomena. Then the numerical methods for these problems are required. In this paper, we consider a meshless method for solving a distributed order time fractional advection diffusion equation. After discretizing the outer integral in the distributed order derivative and the first derivative in the interior integral of the Caputo fractional derivative using the trapezoid formula and the first order difference approximation, respectively, a semi-discrete scheme is obtained. Then for every fixed time, approximating the solution using radial basis function (RBF), a fully discrete scheme is obtained. Five numerical examples in bounded domains containing irregularly shaped domains are presented to show the application of the present technique.

引用

页码：55 / 63

页数：9

共 49 条

[11] Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations [J].

Gao, Guang-hua ;

Sun, Zhi-zhong .

JOURNAL OF SCIENTIFIC COMPUTING, 2016, 66 (03) :1281-1312

[12]

Gorenflo R, 2002, P 2 MAPH LEV C, P120

[13] MESHFREE METHODS AND THEIR COMPARISONS [J].

Gu, Y. T. .

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2005, 2 (04) :477-515

[14] AN ADVANCED MESHLESS METHOD FOR TIME FRACTIONAL DIFFUSION EQUATION [J].

Gu, Y. T. ;

Zhuang, P. ;

Liu, Q. .

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2011, 8 (04) :653-665

[15] A local point interpolation method for static and dynamic analysis of thin beams [J].

Gu, YT ;

Liu, GR .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (42) :5515-5528

[16] A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids [J].

Gu, YT ;

Liu, GR .

COMPUTATIONAL MECHANICS, 2001, 27 (03) :188-198

[17] A coupled element free Galerkin/boundary element method for stress analysis of two-dimensional solids [J].

Gu, YT ;

Liu, GR .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2001, 190 (34) :4405-4419

[18] Approximate analytical solution for seepage flow with fractional derivatives in porous media [J].

He, JH .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 167 (1-2) :57-68

[19] WELL-POSEDNESS OF ABSTRACT DISTRIBUTED-ORDER FRACTIONAL DIFFUSION EQUATIONS [J].

Jia, Junxiong ;

Peng, Jigen ;

Li, Kexue .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (02) :605-621

[20]

Jiao Z, 2012, SPRBRIEF ELECT, P1, DOI 10.1007/978-1-4471-2852-6

← 1 2 3 4 5 →