Two Alternating Direction Implicit Difference Schemes for Solving the Two-Dimensional Time Distributed-Order Wave Equations

被引：26

作者：

Gao, Guang-hua ^{[1
]}

Sun, Zhi-zhong ^{[2
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2016年 / 69卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Distributed order; Fractional wave equations; Difference scheme; ADI; Stability; Convergence; FRACTIONAL DIFFUSION-EQUATIONS; BOUNDARY-VALUE-PROBLEMS; NUMERICAL APPROXIMATION; EXTRAPOLATION METHOD;

D O I：

10.1007/s10915-016-0208-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two alternating direction implicit difference schemes are established for solving a class of two-dimensional time distributed-order wave equations. The schemes are proved to be unconditionally stable and convergent in the maximum norm with the convergence orders and respectively, where and are the step sizes in time, space and distributed order. Also, several numerical experiments are carried out to validate the theoretical results.

引用

页码：506 / 531

页数：26

共 26 条

[1] Numerical methods of solutions of boundary value problems for the multi-term variable-distributed order diffusion equation [J].

Alikhanov, Anatoly A. .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 268 :12-22

[2]

[Anonymous], 2006, THEORY APPL FRACTION

[3] Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations [J].

Atanackovic, Teodor M. ;

Pilipovic, Stevan ;

Zorica, Dusan .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2009, 465 (2106) :1893-1917

[4] Fractional Langevin equations of distributed order [J].

Eab, C. H. ;

Lim, S. C. .

PHYSICAL REVIEW E, 2011, 83 (03)

[5]

Ford NJ, 2015, ELECTRON T NUMER ANA, V44, P289

[6] 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

[7] Two unconditionally stable and convergent difference schemes with the extrapolation method for the one-dimensional distributed-order differential equations [J].

Gao, Guang-hua ;

Sun, Zhi-zhong .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2016, 32 (02) :591-615

[8] Some high-order difference schemes for the distributed-order differential equations [J].

Gao, Guang-hua ;

Sun, Hai-wei ;

Sun, Zhi-zhong .

JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 298 :337-359

[9] Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations [J].

Gao, Guang-hua ;

Sun, Zhi-zhong .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 69 (09) :926-948

[10] Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density [J].

Gorenflo, Rudolf ;

Luchko, Yuri ;

Stojanovic, Mirjana .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (02) :297-316

← 1 2 3 →