A note on convergence of line iterative methods for a nine-point matrix

Applied Mathematics Letters

Volumn 15, Issue 4, 2002, Pages 495-503

  Karaa, S ^a   Zhang, Jun ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Convection diffusion equation; Fourth order compact scheme; Line Jacobi method; Linear systems; Spectral radius

Indexed keywords

EID: 31244436365     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(01)00164-1     Document Type: Article

References (14)

1. M.M. Gupta, R.P. Manohar and J.W. Stephenson, A fourth-order, cost effective and stable finite difference scheme for the convection-diffusion equation, In Numerical Properties and Methodologies in Heat Transfer, pp. 201-209, Hemisphere, Washington, DC, (1983).
2. M. Bhuruth and D.J. Evans, Block iterative methods for the nine-point approximation to the convection-diffusion equation, Int. J. Comput. Math. 61, 321-335, (1996).
3. M.M. Gupta, R.P. Manohar and J.W. Stephenson, A single cell high-order scheme for the convection-diffusion equation with variable coefficients, Int. J. Numer. Methods Fluids 4, 641-651, (1984).
4. M.M. Gupta, J. Kouatchou and J. Zhang, A compact multigrid solver for convection-diffusion equations, J. Comput. Phys. 132, 123-129, (1997).
5. J. Zhang, On convergence and performance of iterative methods with fourth-order compact schemes, Numer. Methods Partial Differential Equations 14, 262-283, (1998).
6. S. Abarbanel and K. Kumar, Compact high-order scheme for the Euler equations, J. Sci. Comput. 3, 275-288, (1988).
7. 4 finite difference approximations to the operators of Navier-Stokes type, J. Comput. Phys. 85, 390-416, (1989).
8. M. Li, T. Tang and B. Fornberg, A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids 20, 1137-1151, (1995).
9. J. Zhang, Numerical simulation of 2D square driven cavity using fourth-order compact finite difference schemes, Computers Math. Applic. (to appear).
10. J. Zhang, Convergence of iterative methods for a fourth-order discretization scheme, Appl. Math. Lett. 10 (2), 49-55, (1997).
11. R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, (1962).
12. L.M. Hageman and D.M. Young, Applied Iterative Methods, Academic, New York, (1981).
13. H.C. Elman and G.H. Golub, Iterative methods for cyclically reduced non-self-adjoint linear systems I, Math. Comp. 54, 671-700, (1990).
14. R.C.Y. Chin and T.A. Manteuffel, An analysis of block successive overrelaxation for a class of matrices with complex spectra, SIAM J. Numer. Anal 25, 564-585, (1988).