Unique solvability of the CCD scheme for convection-diffusion equations with variable convection coefficients

被引：4

作者：

Wang, Qinghe ^{[1
]}

Pan, Kejia ^{[1
]}

Hu, Hongling ^{[2
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China

[2] Hunan Normal Univ, Sch Math & Stat, Key Lab High Performance Comp & Stochast Informat, Changsha, Hunan, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2018年

基金：

中国国家自然科学基金;

关键词：

Combined compact difference scheme; Convection-diffusion equation; Unique solvability; Variable coefficient; Periodic boundary conditions; COMPACT DIFFERENCE SCHEME; CASCADIC MULTIGRID METHOD; NONLINEAR SCHRODINGER-EQUATIONS; SHALLOW-WATER EQUATIONS; ADI METHOD; NUMERICAL ALGORITHM; ELLIPTIC PROBLEMS; FLOW;

D O I：

10.1186/s13662-018-1591-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The combined compact difference (CCD) scheme has better spectral resolution than many other existing compact or noncompact high-order schemes, and is widely used to solve many differential equations. However, due to its implicit nature, very little theoretical results on the CCD method are known. In this paper, we provide a rigorous theoretical proof for the unique solvability of the CCD scheme for solving the convection-diffusion equation with variable convection coefficients subject to periodic boundary conditions.

引用

页数：9

共 42 条

[1]

[Anonymous], 2012, AM MATH SOC

[2] A SPECTRAL LEGENDRE-GAUSS-LOBATTO COLLOCATION METHOD FOR A SPACE-FRACTIONAL ADVECTION DIFFUSION EQUATIONS WITH VARIABLE COEFFICIENTS [J].

Bhrawy, A. H. ;

Baleanu, D. .

REPORTS ON MATHEMATICAL PHYSICS, 2013, 72 (02) :219-233

[3] A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations [J].

Chen, Buyun ;

He, Dongdong ;

Pan, Kejia .

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2018, 11 (02) :299-320

[4] An interpolation based finite difference method on non-uniform grid for solving Navier-Stokes equations [J].

Chen, Weijia ;

Chen, Jim C. ;

Lo, Edmond Y. .

COMPUTERS & FLUIDS, 2014, 101 :273-290

[5] A three-point sixth-order nonuniform combined compact difference scheme [J].

Chu, PC ;

Fan, CW .

JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 148 (02) :663-674

[6] A three-point combined compact difference scheme [J].

Chu, PC ;

Fan, CW .

JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 140 (02) :370-399

[7] A three-point sixth-order staggered combined compact difference scheme [J].

Chu, PC ;

Fan, CW .

MATHEMATICAL AND COMPUTER MODELLING, 2000, 32 (3-4) :323-340

[8] Combined compact difference scheme for the time fractional convection-diffusion equation with variable coefficients [J].

Cui, Mingrong .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 246 :464-473

[9] Three-point combined compact difference schemes for time-fractional advection-diffusion equations with smooth solutions [J].

Gao, Guang-Hua ;

Sun, Hai-Wei .

JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 298 :520-538

[10] Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations [J].

Gao, Guang-Hua ;

Sun, Hai-Wei .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2015, 17 (02) :487-509

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