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Volumn 71, Issue 241, 2003, Pages 247-262

A holistic finite difference approach models linear dynamics consistently

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EID: 0037232578     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (30)

References (21)
  • 1
    • 0003289290 scopus 로고
    • Applications of centre manifold theory
    • Springer-Verlag, MR 83g:34039
    • J. Carr. Applications of centre manifold theory, volume 35 of Applied Math. Sci. Springer-Verlag, 1981. MR 83g:34039
    • (1981) Applied Math. Sci. , vol.35
    • Carr, J.1
  • 2
    • 0001226484 scopus 로고
    • The application of centre manifold theory to amplitude expansions. II. Infinite dimensional problems
    • MR 85d:58057b
    • J. Carr and R. G. Muncaster. The application of centre manifold theory to amplitude expansions. II. Infinite dimensional problems. J. Diff. Eqns, 50:280-288, 1983. MR 85d:58057b
    • (1983) J. Diff. Eqns , vol.50 , pp. 280-288
    • Carr, J.1    Muncaster, R.G.2
  • 3
    • 0003241758 scopus 로고
    • Integral manifolds and inertial manifolds for dissipative partial differential equations
    • Springer-Verlag, MR 90a:35026
    • P. Constantin, C. Foias, B. Nicolaenko, and R. Temam. Integral manifolds and inertial manifolds for dissipative partial differential equations, volume 70 of Applied Math. Sci. Springer-Verlag, 1989. MR 90a:35026
    • (1989) Applied Math. Sci. , vol.70
    • Constantin, P.1    Foias, C.2    Nicolaenko, B.3    Temam, R.4
  • 4
    • 0000317970 scopus 로고
    • Initial conditions for models of dynamical systems
    • MR 96e:34072
    • S. M. Cox and A. J. Roberts. Initial conditions for models of dynamical systems. Physica D, 85:126-141, 1995. MR 96e:34072
    • (1995) Physica D , vol.85 , pp. 126-141
    • Cox, S.M.1    Roberts, A.J.2
  • 7
    • 0001686992 scopus 로고
    • Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
    • MR 90k:35031
    • C. Foias, G. R. Sell, and E. S. Titi. Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations. J. Dyn. & Diff. Eqns, 1:199-244, 1989. MR 90k:35031
    • (1989) J. Dyn. & Diff. Eqns , vol.1 , pp. 199-244
    • Foias, C.1    Sell, G.R.2    Titi, E.S.3
  • 8
    • 0000166593 scopus 로고
    • Determining nodes, finite difference schemes and inertial manifolds
    • MR 92a:65241
    • C. Foias and E. S. Titi. Determining nodes, finite difference schemes and inertial manifolds. Nonlinearity, 4:135-153, 1991. MR 92a:65241
    • (1991) Nonlinearity , vol.4 , pp. 135-153
    • Foias, C.1    Titi, E.S.2
  • 9
    • 0000051734 scopus 로고    scopus 로고
    • Postprocessing the Galerkin method: The finite element case
    • MR 2001h:65112
    • B. García-Archilla and E. S. Titi. Postprocessing the Galerkin method: the finite element case. SIAM J. Num. Anal., 37:470-499, 2000. MR 2001h:65112
    • (2000) SIAM J. Num. Anal. , vol.37 , pp. 470-499
    • García-Archilla, B.1    Titi, E.S.2
  • 10
    • 34047228827 scopus 로고
    • Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
    • MR 91f:35217
    • 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 91f:35217
    • (1990) Physica D , vol.44 , pp. 38-60
    • Jolly, M.S.1    Kevrekidis, I.G.2    Titi, E.S.3
  • 11
    • 4243628856 scopus 로고    scopus 로고
    • Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation
    • [Online]
    • T. Mackenzie and A. J. Roberts. Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation. ANZIAM J., 42(E):C918-C935, 2000. [Online] http://anziamj.austms.org.au/V42/CTAC99/Mack.
    • (2000) ANZIAM J. , vol.42 , Issue.E
    • Mackenzie, T.1    Roberts, A.J.2
  • 12
    • 0000547750 scopus 로고
    • Nonlinear Galerkin methods
    • MR 91a:65220
    • M. Marion and R. Temam. Nonlinear Galerkin methods. SIAM J. Numer. Anal., 26(5):1139-1157, 1989. MR 91a:65220
    • (1989) SIAM J. Numer. Anal. , vol.26 , Issue.5 , pp. 1139-1157
    • Marion, M.1    Temam, R.2
  • 13
    • 14344275251 scopus 로고
    • Modern computing methods, 2nd ed.
    • Her Majesty's Stationary Office, MR 22:8637
    • National Physical Laboratory. Modern Computing Methods, 2nd ed., volume 16 of Notes on Applied Science. Her Majesty's Stationary Office, 1961. MR 22:8637
    • (1961) Notes on Applied Science , vol.16
  • 14
    • 0002563770 scopus 로고
    • Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems
    • MR 90h:58075
    • A. J. Roberts. Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems. J. Austral. Math. Soc. B, 31:48-75, 1989. MR 90h:58075
    • (1989) J. Austral. Math. Soc. B , vol.31 , pp. 48-75
    • Roberts, A.J.1
  • 15
    • 0000144318 scopus 로고
    • The utility of an invariant manifold description of the evolution of a dynamical system
    • MR 91f:58088
    • A. J. Roberts. The utility of an invariant manifold description of the evolution of a dynamical system. SIAM J. Math. Anal., 20:1447-1458, 1989. MR 91f:58088
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 1447-1458
    • Roberts, A.J.1
  • 16
    • 0042515579 scopus 로고    scopus 로고
    • Low-dimensional models of thin film fluid dynamics
    • MR 97b:76041
    • A. J. Roberts. Low-dimensional models of thin film fluid dynamics.Phys. Letts. A, 212:63-72, 1996. MR 97b:76041
    • (1996) Phys. Letts. A , vol.212 , pp. 63-72
    • Roberts, A.J.1
  • 17
    • 0034635946 scopus 로고    scopus 로고
    • Computer algebra derives correct initial conditions for low-dimensional dynamical models
    • A. J. Roberts. Computer algebra derives correct initial conditions for low-dimensional dynamical models. Comput. Phys. Comm., 126(3):187-206, 2000.
    • (2000) Comput. Phys. Comm. , vol.126 , Issue.3 , pp. 187-206
    • Roberts, A.J.1
  • 18
    • 0035341644 scopus 로고    scopus 로고
    • Holistic discretisation ensures fidelity to Burgers' equation
    • A. J. Roberts. Holistic discretisation ensures fidelity to Burgers' equation. Applied Numerical Math., 37:371-396, 2001.
    • (2001) Applied Numerical Math. , vol.37 , pp. 371-396
    • Roberts, A.J.1
  • 19
    • 0000242930 scopus 로고    scopus 로고
    • The asymptotic completeness of inertial manifolds
    • MR 98m:34124
    • J. C. Robinson. The asymptotic completeness of inertial manifolds. Nonlinearity, 9:1325-1340, 1996. MR 98m:34124
    • (1996) Nonlinearity , vol.9 , pp. 1325-1340
    • Robinson, J.C.1
  • 20
    • 0002425680 scopus 로고
    • Inertial manifolds
    • MR 91i:58087
    • R. Temam. Inertial manifolds. Mathematical Intelligencer, 12:68-74, 1990. MR 91i:58087
    • (1990) Mathematical Intelligencer , vol.12 , pp. 68-74
    • Temam, R.1
  • 21
    • 0002876557 scopus 로고
    • Centre manifolds, normal forms and elementary bifurcations
    • MR 90g:58092
    • A. Vanderbauwhede. Centre manifolds, normal forms and elementary bifurcations. Dynamics Reported, pages 89-169, 1989. MR 90g:58092
    • (1989) Dynamics Reported , pp. 89-169
    • Vanderbauwhede, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.