A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations

In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O ( h 4 + τ 5 ) . It is shown through analysis that the scheme is unconditionally stable. Numerical exp...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2009-08, Vol.230 (2), p.600-606
Main Authors: Ding, Hengfei, Zhang, Yuxin
Format: Article
Language:English
Subjects:
Approximations and expansions
Convection–diffusion equation
Difference scheme
Exact sciences and technology
High accuracy
Krylov subspace method
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Toeplitz matrix
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Summary:In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O ( h 4 + τ 5 ) . It is shown through analysis that the scheme is unconditionally stable. Numerical experiments are conducted to test its high accuracy and to compare it with Crank–Nicolson method.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2008.12.015