Unconditional stability of alternating difference schemes with intrinsic parallelism for two-dimensional parabolic systems

Numerical Methods for Partial Differential Equations

Volumn 15, Issue 6, 1999, Pages 625-636

  Yuan, Guang Wei ^a   Shen, Long Jun ^a   Zhou, Yu Lin ^a  

^a INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS   (China)

Author keywords

Alternating difference schemes; Intrinsic parallelism; Parabolic systems; Stability

Indexed keywords

EID: 0038064237     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199911)15:6<625::AID-NUM2>3.0.CO;2-O     Document Type: Article

References (15)

1. D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J SIAM 3 (1955), 28-41.
2. Y. L. Zhou, General finite difference method with intrinsic parallelism for multi-dimensional semilinear parabolic systems, Beijing Math 2 (1996), 1-32.
3. Y. L. Zhou, L. J. Shen, G. W. Yuan, Some practical difference schemes with intrinsic parallelism for nonlinear parabolic systems, Chinese J Numer Math Appl 19 (1997), 46-57.
4. 2, Intern J Comp Math 14 (1983), 325-353.
5. G. W. Yuan, L. J. Shen, and S. Zhu, Unconditional stability of parallel difference schemes with variable time steplengthes for heat equations, preprint.
6. B. L. Zhang and X. Su, Alternating block explicit-implicit method for two-dimensional diffusion equation, Intern J Comp Math 38 (1991), 241-255.
7. J. Chen and B. L. Zhang, A class of alternating block Crank-Nicolson method, Intern J Comp Math 45 (1992), 89-112.
8. 2, Appl Math J Chinese Univ 8 (1993), 150-162.
9. X. Y. Liu and B. L. Zhang, Local one-dimensional ASE-I scheme for 2D diffusion equation, Acta Sci Nat Univ Wuhan (English series), 1 (1996), 515-521.
10. B. L. Zhang, Parallelization of the ADI method for the two-dimensional diffusion equation, China-Italy Workshop on High Performance Computing, Beijing, October 28-29, 1996.
11. B. L. Zhang, T. Xu, and Y. Yang, Block ADI method and parallel computing for two-dimensional diffusion equation, Proc of 5th Chinese Conf Parallel Comp (1997), 45-52 (in Chinese).
12. B. L. Zhang and J. Chen, Finite difference parallel algorithms for parabolic equation, J Numer Meth Comp Appl 16 (1995), 187-195 (in Chinese).
13. J. F. Lu and B. L. Zhang, Alternating group explicit (AGE) method for solving the two-dimensional convection diffusion equation, Ann Report LCP, IAPCM Beijing, 1995, pp. 105-119.
14. J. F. Lu, B. L. Zhang, and T. Xu, AGE method and parallel computing for two-dimensional Burgers equation, Chinese J Comp Phys, to appear.
15. B. L. Zhang, J. F. Lu, and T. Xu, Block ADI method for two-dimensional convection diffusion equation, Chinese J Comp Phys, to appear.