An ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation

被引：49

作者：

Fairweather, Graeme ^{[1
]}

Yang, Xuehua ^{[2
]}

Xu, Da ^{[3
]}

Zhang, Haixiang ^{[2
]}

机构：

[1] Amer Math Soc, Math Reviews, Ann Arbor, MI 48103 USA

[2] Hunan Univ Technol, Sch Sci, Zhuzhou 412008, Hunan, Peoples R China

[3] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2015年 / 65卷 / 03期

关键词：

Two-dimensional fractional diffusion-wave equation; Caputo derivative; Alternating direction implicit method; Orthogonal spline collocation method; Optimal global convergence estimates; Superconvergence; CONVERGENCE ANALYSIS; SCHEME;

D O I：

10.1007/s10915-015-0003-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new method is formulated and analyzed for the approximate solution of a two-dimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit method based on the Crank-Nicolson method combined with the -approximation of the time Caputo derivative of order . It is proved that this scheme is stable, and of optimal accuracy in various norms. Numerical experiments demonstrate the predicted global convergence rates and also superconvergence.

引用

页码：1217 / 1239

页数：23

共 28 条

[1]

[Anonymous], 1974, MATH SCI ENG

[2]

[Anonymous], 2008, FRACT CALC APPL ANAL

[3]

Baleanum D., 2012, SERIES COMPLEXITY NO, V3

[4] Convergence analysis of orthogonal spline collocation for elliptic boundary value problems [J].

Bialecki, B .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (02) :617-631

[5] Orthogonal spline collocation methods for partial differential equations [J].

Bialecki, B ;

Fairweather, G .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 128 (1-2) :55-82

[6] An alternating-direction implicit orthogonal spline collocation scheme for nonlinear parabolic problems on rectangular polygons [J].

Bialecki, Bernard ;

Fernandes, Ryan I. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2006, 28 (03) :1054-1077

[7] ADI-Euler and extrapolation methods for the two-dimensional fractional advection-dispersion equation [J].

Chen S. ;

Liu F. .

J. Appl. Math. Comp., 2008, 1-2 (295-311) :295-311

[8] Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation [J].

Cui, Mingrong .

NUMERICAL ALGORITHMS, 2013, 62 (03) :383-409

[9] Compact alternating direction implicit method for two-dimensional time fractional diffusion equation [J].

Cui, Mingrong .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (06) :2621-2633

[10] Algorithms for almost block diagonal linear systems [J].

Fairweather, G ;

Gladwell, A .

SIAM REVIEW, 2004, 46 (01) :49-58

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