Free Access
Volume 32, Number 6, 1998
Page(s) 715 - 728
Published online 27 January 2017
  1. N. AUBRY, W. LIAN and E. S. TITI, Preserving symmetries in the proper orthogonal decomposition, SIAM J. Sci. Comp., 14, 483-505, 1993. [MR: 1204243] [Zbl: 0774.65084]
  2. R. BRONSTERING, Some computational aspects on approximate inertial manifolds and finite differences. Discrete and Continuous Dynamical Systems, 2, 417-454, 1996. [MR: 1414079] [Zbl: 0949.65135]
  3. M. CHEN, H. CHOI, T. DUBOIS, J. SHEN and R. TEMAM, The incremental unknowns-multilevel scheme for the simulation of turbulent channel flows. Proceedings of 1996 Summer Program, Center for Turbulence Research, NASA Ames/Stanford Univ., pages 291-308, 1996.
  4. M. CHEN and R. TEMAM. Incremental unknowns for solving partial differential equations. Numerische Mathematik, 59, 255-271, 1991. [EuDML: 133548] [MR: 1106383] [Zbl: 0712.65103]
  5. M. CHEN and R. TEMAM, Nonlinear Galerkin method in the finite difference case and wavelet-like incremental-unknowns. Numerische Mathematik, 64(3), 271-294, 1993. [EuDML: 133706] [MR: 1206665] [Zbl: 0798.65093]
  6. M. CHEN and R. TEMAM, Nonlinear Galerkin method with multilevel incremental-unknowns. In E.P. Agarwal, editor, Contributions in Numerical Mathematics, pages 151-164. WSSIAA, 1993. [MR: 1299757] [Zbl: 0834.65094]
  7. E. J. DOEDEL, X. J. WANG and T. F. FAIRGRIEVE. Software for continuation and bifurcation problems in ordinary differential equations. CRPC-95-2, Center for Research on Parallel Computing, California Institute of Technology, 1995.
  8. C. FOIAS, JOLLY, KEVREKIDIS and E. S. TITI. Dissipativity of numerical schemes. Nonlinearity, pages 591-613, 1991. [MR: 1124326] [Zbl: 0734.65080]
  9. C. FOIAS, O. MANLEY and R. TEMAM. Modeling of the interaction of small and large eddies in two dimensional turbulent flows. Math. Model. and Num. Anal., 22(1), 1988. [EuDML: 193526] [MR: 934703] [Zbl: 0663.76054]
  10. C. FOIAS and E. S. TITI Determining nodes, finite difference schemes and inertial manifolds. Nonlinearity, 4, 135-153, 1991. [MR: 1092888] [Zbl: 0714.34078]
  11. G. GOLUB and C. VAN LOAN. Matrix Computations. The John Hopkins University Press, second edition, 1989. [MR: 1002570] [Zbl: 0733.65016]
  12. J. HALE. Asymptotic Behavior of Dissipative Systems. AMS, 1988. [MR: 941371] [Zbl: 0642.58013]
  13. J. M. HYMAN, B. NICOLAENKO and S. ZALESKI Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces. Physica D, 23, 265-292, 1986. [MR: 876914] [Zbl: 0621.76065]
  14. M. JOLLY Explicit construction of an inertial manifold for a reaction diffusion equation. J. Diff. Eq., 78, 220-261, 1989. [MR: 992147] [Zbl: 0691.35049]
  15. M. S. JOLLY, I. G. KEVREKIDIS and E. S. TITI. Approximate inertial manifolds for the Kuramoto-Sivashinsky equation : Analysis and computations. Physica D, 44, 38-60, 1990. [MR: 1069671] [Zbl: 0704.58030]
  16. M. S. JOLLY, I. G. KEVREKIDIS and E. S. TITI. Preserving dissipation in approximate inertial forms for the Kuramoto-Sivashinsky equation. J. Dyn. Diff. Eq., 3, 179-197, 1991. [MR: 1109435] [Zbl: 0738.35024]
  17. D. A. JONES, L. G. MARGOLIN and E. S. TITI. On the effectiveness of the approximate inertial manifold-a computational study, to appear in Theoretical and Computational Fluid Dynamics, 1995. [Zbl: 0838.76066]
  18. D. A. JONES, L. G. MARGOLIN and A. C. POJE. Enslaved finite difference schemes for nonlinear dissipative pdes. Num. Meth. for PDEs, page to appear. [MR: 1363860] [Zbl: 0879.65063]
  19. KEVREKIDIS, NICOLAENKO and SCOVEL. Back in the saddle again : A computer assisted study of the Kuramoto-Sivashinsky equation. Siam J. Apl. Math., 50, 760-790, 1990. [MR: 1050912] [Zbl: 0722.35011]
  20. E. KORONTINIS and M. R. TRUMMER. A finite difference scheme for Computing inertial manifolds. Z angew Math. Phys., 46, 419-444, 1995. [MR: 1335911] [Zbl: 0824.65125]
  21. L. G. MARGOLIN and D. A. JONES. An approximate inertial manifold for computing Burger's equation. Physica D, 60, 175-184, 1992. [MR: 1195598] [Zbl: 0789.65069]
  22. M. MARION, Approximate inertial manifolds for reaction-diffusion equations in high space dimension. J. Dyn. Diff. Eq., 1, 245-267, 1989. [MR: 1010967] [Zbl: 0702.35127]
  23. M. MARION and R. TEMAM. Nonlinear Galerkin methods. SIAM J. Num. An., 26, 1139-1157, 1989. [MR: 1014878] [Zbl: 0683.65083]
  24. B. NICOLAENKO, B. SCHEURER and R. TEMAM. Some global dynamical properties of the Kuramoto-Sivashinsky equation : Nonlinear stability and attractors. Physica D, 16, 155-183, 1985. [MR: 796268] [Zbl: 0592.35013]
  25. R. TEMAM. Infinite-Dimensional Dynamical Systems in Mechanics and Physics. Springer Verlag, 1988. [MR: 953967] [Zbl: 0662.35001]
  26. R. WALLACE and D. M. SLOAN. Numerical solution of a nonlinear dissipative System using a pseudospectral method and inertial manifolds. Siam J. Sci. Comput., 16, 1049-1070, 1994. [MR: 1346292] [Zbl: 0833.65087]

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