Stable second-order scheme for integrating the Kuramoto-Sivanshinsky equation in polar coordinates using distributed approximating functionals

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 3, 2005, Pages

  Blomgren, Peter ^a   Gasner, Scott ^a   Palacios, Antonio ^a  

^a SAN DIEGO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRANK-NICOLSON SCHEME; KURAMOTO-SIVANSHINSKY EQUATION; NEWTON SOLVER;

ALGORITHMS; APPROXIMATION THEORY; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 28844446306     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.036701     Document Type: Article

References (24)

1. Q. Ouyang and H. L. Swinney, Nature (London) NATUAS 0028-0836 10.1038/352610a0 352, 610 (1991).
2. M. S. Heutmaker and J. P. Gollub, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.242 35, 242 (1987).
3. M. Gorman, M. el Hamdi, and K. Robbins, Combust. Sci. Technol. CBSTB9 0010-2202 98, 47 (1994).
4. M. Gorman, M. el Hamdi, and K. Robbins, Combust. Sci. Technol. CBSTB9 0010-2202 98, 79 (1994).
5. M. Gorman, M. el Hamdi, and K. Robbins, Combust. Sci. Technol. CBSTB9 0010-2202 98, 71 (1994).
6. M. Gorman, M. el Hamdi, and K. Robbins, Combust. Sci. Technol. CBSTB9 0010-2202 98, 25 (1994).
7. Y. Kuramoto, Suppl. Prog. Theor. Phys. PTPSAL 0375-9687 64, 346 (1978).
8. G. I. Sivashinsky, Combust. Sci. Technol. CBSTB9 0010-2202 15, 137 (1977).
9. G. I. Sivashinsky, Acta Astronaut. AASTCF 0094-5765 10.1016/0094-5765(77)90096-0 4, 1177 (1977).
10. M. Gorman, M. el-Hamdi, B. Pearson, and K. A. Robbins, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.228 76, 228 (1996).
11. D. S. Zhang, G. W. Wei, D. J. Kouri, D. K. Hoffman, M. Gorman, A. Palacios, and G. H. Gunaratne, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.3353 60, 3353 (1999).
12. J. Crank and P. Nicolson, Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 43, 50 (1947);
13. J. Crank and P. Nicolson, republished in Adv. Comput. Math. ACMHEX 1019-7168 6, 207 (1997), John Crank 80th birthday special issue.
14. D. K. Hoffman, T. L. Marchioro II, M. Arnold, Y. Huang, W. Zhu, and D. J. Kouri, J. Math. Chem. JMCHEG 0259-9791 10.1007/BF01165159 20, 117 (1996).
15. D. K. Hoffman, M. Arnold, and D. J. Kouri, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100195a007 96, 6539 (1992).
16. D. K. Hoffman and D. J. Kouri, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100182a030 96, 1179 (1992).
17. D. K. Hoffman, G. W. Wei, D. S. Zhang, and D. J. Kouri, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.57.6152 57, 6152 (1998).
18. A. M. Frishman, D. K. Hoffman, R. J. Rakauskas, and D. J. Kouri, Chem. Phys. Lett. CHPLBC 0009-2614 151, 62 (1996).
19. S. S. Iyengar, G. A. Parker, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.478962 110, 10283 (1999).
20. D. J. Kouri, W. Zhu, X. Ma, B. M. Pettitt, and D. K. Hoffman, J. Phys. Chem. JPCHAX 0022-3654 10.1021/j100203a013 96, 9622 (1992).
21. D. S. Zhang, G. W. Wei, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.473520 106, 5216 (1997).
22. J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd ed. (SIAM, Philadelphia, PA, 2004).
23. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd ed. (SIAM, Philadelphia, PA, 1994).
24. P. Blomgren, S. Gasner, and A. Palacios, Chaos CHAOEH 1054-1500 15, 013706 (2005).