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Volumn 38, Issue 1, 2001, Pages 292-328

A nonstiff Euler discretization of the complex Ginzburg-Landau equation in one space dimension

Author keywords

Complex Ginzburg Landau equation; Finite Fourier series approximation; Temporal Euler discretization

Indexed keywords


EID: 0034455222     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142998332852     Document Type: Article
Times cited : (9)

References (37)
  • 1
    • 0000922548 scopus 로고
    • On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation
    • M. BARTUCCELLI, P. CONSTANTIN, C. R. DOERING, J. D. GIBBON, AND M. GISSELFALT, On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation, Phys. D, 44 (1990), pp. 421-444.
    • (1990) Phys. D , vol.44 , pp. 421-444
    • Bartuccelli, M.1    Constantin, P.2    Doering, C.R.3    Gibbon, J.D.4    Gisselfalt, M.5
  • 4
    • 84968484137 scopus 로고
    • On the rate of convergence of the nonlinear Galerkin methods
    • CH. DEVULDER, M. MARION, AND E. S. TITI, On the rate of convergence of the nonlinear Galerkin methods, Math. Comp., 60 (1993), pp. 495-514.
    • (1993) Math. Comp. , vol.60 , pp. 495-514
    • Devulder, Ch.1    Marion, M.2    Titi, E.S.3
  • 5
    • 0000719102 scopus 로고
    • Finite-dimensional models, of the Ginzburg-Landau equation
    • A. DOELMAN, Finite-dimensional models, of the Ginzburg-Landau equation, Nonlinearity, 4 (1991), pp. 231-250.
    • (1991) Nonlinearity , vol.4 , pp. 231-250
    • Doelman, A.1
  • 6
    • 0000287007 scopus 로고
    • Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation
    • A. DOELMAN AND E. S. TITI, Regularity of solutions and the convergence of the Galerkin method in the Ginzburg-Landau equation, Numer. Funct. Anal. Optim., 14 (1993), pp. 299-321.
    • (1993) Numer. Funct. Anal. Optim. , vol.14 , pp. 299-321
    • Doelman, A.1    Titi, E.S.2
  • 7
    • 0000153785 scopus 로고
    • Low-dimensional behaviour in the complex Ginzburg-Landau equation
    • C. A. DOERING, J. D. GIBBON, D. D. HOLM, AND B. NICOLAENKO, Low-dimensional behaviour in the complex Ginzburg-Landau equation, Nonlinearity, 1 (1988), pp. 279-309.
    • (1988) Nonlinearity , vol.1 , pp. 279-309
    • Doering, C.A.1    Gibbon, J.D.2    Holm, D.D.3    Nicolaenko, B.4
  • 8
    • 0000967970 scopus 로고
    • Weak and strong solutions of the complex Ginzburg-Landau equation
    • C. A. DOERING, J. D. GIBBON, AND C. D. LEVERMORE, Weak and strong solutions of the complex Ginzburg-Landau equation, Phys. D, 71 (1994), pp. 285-318.
    • (1994) Phys. D , vol.71 , pp. 285-318
    • Doering, C.A.1    Gibbon, J.D.2    Levermore, C.D.3
  • 9
    • 0001024873 scopus 로고
    • Global existence theory for a generalized Ginzburg-Landau equation
    • J. DUAN, P. HOLMES, AND E. S. TITI, Global existence theory for a generalized Ginzburg-Landau equation, Nonlinearity, 5 (1992), pp. 1303-1314.
    • (1992) Nonlinearity , vol.5 , pp. 1303-1314
    • Duan, J.1    Holmes, P.2    Titi, E.S.3
  • 10
    • 0000815546 scopus 로고
    • Regularity, approximation and asymptotic for a generalized Ginzburg-Landau equation
    • J. DUAN, E. S. TITI, AND P. HOLMES, Regularity, approximation and asymptotic for a generalized Ginzburg-Landau equation, Nonlinearity, 6 (1993), pp. 915-933.
    • (1993) Nonlinearity , vol.6 , pp. 915-933
    • Duan, J.1    Titi, E.S.2    Holmes, P.3
  • 11
  • 12
    • 0042467707 scopus 로고
    • Gevrey class regularity for the solutions of the Navier-Stokes equations
    • C. FOIAS AND R. TEMAM, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal., 89 (1989), pp. 259-269.
    • (1989) J. Funct. Anal. , vol.89 , pp. 259-269
    • Foias, C.1    Temam, R.2
  • 13
    • 0000322045 scopus 로고
    • Dimension of the attractors associated to the Ginzburg- Landau partial differential equation
    • J.-M. GHIDAGLIA AND B. HÉRON, Dimension of the attractors associated to the Ginzburg- Landau partial differential equation, Phys. D, 28 (1987), pp. 282-304.
    • (1987) Phys. D , vol.28 , pp. 282-304
    • Ghidaglia, J.-M.1    Héron, B.2
  • 14
    • 0000098780 scopus 로고
    • On the theory of superconductivity
    • V. L. GINZBURG AND L. D. LANDAU, On the theory of superconductivity, Zh. Eksp. Teoret. Fiz. (USSR) 20 (1950), p. 1064. English translation in Men of Physics: L. D. Landau, Vol. I, D. Ter Haar ed., Pergamon Press, New York, 1965, pp. 546-568.
    • (1950) Zh. Eksp. Teoret. Fiz. (USSR) , vol.20 , pp. 1064
    • Ginzburg, V.L.1    Landau, L.D.2
  • 15
    • 0002585056 scopus 로고
    • English translation D. Ter Haar ed., Pergamon Press, New York
    • V. L. GINZBURG AND L. D. LANDAU, On the theory of superconductivity, Zh. Eksp. Teoret. Fiz. (USSR) 20 (1950), p. 1064. English translation in Men of Physics: L. D. Landau, Vol. I, D. Ter Haar ed., Pergamon Press, New York, 1965, pp. 546-568.
    • (1965) Men of Physics: L. D. Landau , vol.1 , pp. 546-568
  • 16
    • 0022134240 scopus 로고
    • Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation
    • L. R. KEEFE, Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation, Stud. Appl. Math., 73 (1985), pp. 91-153.
    • (1985) Stud. Appl. Math. , vol.73 , pp. 91-153
    • Keefe, L.R.1
  • 17
    • 0009228949 scopus 로고    scopus 로고
    • Attractors and inertial manifolds for finite-difference approximations of the complex Ginzburg-Landau equation
    • G. J. LORD Attractors and inertial manifolds for finite-difference approximations of the complex Ginzburg-Landau equation, SIAM J. Numer. Anal., 34 (1997), pp. 1483-1512.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1483-1512
    • Lord, G.J.1
  • 18
    • 0041465981 scopus 로고
    • Discrete Gevrey regularity, attractors and upper-semicontinuity for a finite difference approximation to the Ginzburg-Landau equation
    • G. J. LORD AND A. M. STUART, Discrete Gevrey regularity, attractors and upper-semicontinuity for a finite difference approximation to the Ginzburg-Landau equation, Numer. Funct. Anal. Optim., 16 (1995), pp. 1003-1047.
    • (1995) Numer. Funct. Anal. Optim. , vol.16 , pp. 1003-1047
    • Lord, G.J.1    Stuart, A.M.2
  • 19
    • 84968504982 scopus 로고
    • Runge-Kutta methods for parabolic equations and convolution quadrature
    • CH. LUBICH AND A. OSTERMANN, Runge-Kutta methods for parabolic equations and convolution quadrature, Math. Comp., 60 (1993), pp. 105-131.
    • (1993) Math. Comp. , vol.60 , pp. 105-131
    • Lubich, C.H.1    Ostermann, A.2
  • 20
    • 84968497603 scopus 로고
    • Runge-Kutta approximation of quasi-linear parabolic equations
    • CH. LUBICH AND A. OSTERMANN, Runge-Kutta approximation of quasi-linear parabolic equations, Math. Comp., 64 (1995), pp. 601-627.
    • (1995) Math. Comp. , vol.64 , pp. 601-627
    • Lubich, Ch.1    Ostermann, A.2
  • 21
    • 0001637513 scopus 로고
    • Transitions to chaos in the Ginzburg-Landau equation
    • H. T. MOON, P. HUERRE, AND L. G. REDEKOPP, Transitions to chaos in the Ginzburg-Landau equation, Phys. D, 7 (1993), pp. 135-150.
    • (1993) Phys. D , vol.7 , pp. 135-150
    • Moon, H.T.1    Huerre, P.2    Redekopp, L.G.3
  • 22
    • 0014662728 scopus 로고
    • Finite bandwidth, finite amplitude convection
    • A. C. NEWELL AND J. A. WHITEHEAD, Finite bandwidth, finite amplitude convection, J. Fluid Mech., 38 (1969), pp. 279-303.
    • (1969) J. Fluid Mech. , vol.38 , pp. 279-303
    • Newell, A.C.1    Whitehead, J.A.2
  • 23
    • 84968502295 scopus 로고
    • Runge-Kutta methods for partial differential equations and fractional orders of convergence
    • A. OSTERMANN AND M. ROCHE, Runge-Kutta methods for partial differential equations and fractional orders of convergence, Math. Comp., 59 (1993) pp. 403-420.
    • (1993) Math. Comp. , vol.59 , pp. 403-420
    • Ostermann, A.1    Roche, M.2
  • 25
    • 0025725569 scopus 로고
    • Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differential equations
    • K. PROMISLOW, Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differential equations, Nonlinear Anal., 16 (1991), pp. 959-980.
    • (1991) Nonlinear Anal. , vol.16 , pp. 959-980
    • Promislow, K.1
  • 26
    • 0039175969 scopus 로고
    • Localization and approximation of attractors for the Ginzburg- Landau equation
    • K. PROMISLOW AND R. TEMAM, Localization and approximation of attractors for the Ginzburg- Landau equation, J. Dynam. Differential Equations, 3 (1991), pp. 491-514.
    • (1991) J. Dynam. Differential Equations , vol.3 , pp. 491-514
    • Promislow, K.1    Temam, R.2
  • 27
    • 0002367721 scopus 로고
    • Low-dimensional dynamics for the complex Ginzburg- Landau equation
    • J. D. RODRIGUEZ AND L. SIROVICH, Low-dimensional dynamics for the complex Ginzburg- Landau equation, Phys. D, 43 (1990), pp. 77-86.
    • (1990) Phys. D , vol.43 , pp. 77-86
    • Rodriguez, J.D.1    Sirovich, L.2
  • 28
    • 84959644006 scopus 로고
    • A non-linear instability theory for a wave system in a plane Poiseville flow
    • K. STEWARTSON AND J. T. STUART, A non-linear instability theory for a wave system in a plane Poiseville flow, J. Fluid Mech., 48 (1971), pp. 529-545.
    • (1971) J. Fluid Mech. , vol.48 , pp. 529-545
    • Stewartson, K.1    Stuart, J.T.2
  • 29
    • 0001267451 scopus 로고
    • Taylor-vortex flow: A dynamical system
    • J. T. STUART, Taylor-vortex flow: A dynamical system, SIAM Rev., 28 (1986), pp. 315-342.
    • (1986) SIAM Rev. , vol.28 , pp. 315-342
    • Stuart, J.T.1
  • 30
    • 0017983543 scopus 로고
    • The Eckhaus and Benjamin-Feir resonance mechanisms
    • J. T. STUART AND R. C. DI PRIMA, The Eckhaus and Benjamin-Feir resonance mechanisms, Proc. Roy. Soc. London Ser. A, 362 (1978), pp. 27-41.
    • (1978) Proc. Roy. Soc. London Ser. A , vol.362 , pp. 27-41
    • Stuart, J.T.1    Di Prima, R.C.2
  • 31
    • 0007642894 scopus 로고
    • Invariant 2-tori in the time-dependent Ginzburg-Landau equation
    • P. TAKÁČ, Invariant 2-tori in the time-dependent Ginzburg-Landau equation, Nonlinearity, 5 (1992), pp. 289-321.
    • (1992) Nonlinearity , vol.5 , pp. 289-321
    • Takáč, P.1
  • 32
    • 0042968947 scopus 로고
    • Dynamics on the attractor for the complex Ginzburg-Landau equation
    • P. TAKÁČ, Dynamics on the attractor for the complex Ginzburg-Landau equation, Rostock. Math. Kolloq., 49 (1995), pp. 163-184.
    • (1995) Rostock. Math. Kolloq. , vol.49 , pp. 163-184
    • Takáč, P.1
  • 33
    • 0041967192 scopus 로고    scopus 로고
    • Bifurcations to Invariant 2-Tori for the Complex Ginzburg-Landau equation
    • P. TAKÁČ, Bifurcations to Invariant 2-Tori for the Complex Ginzburg-Landau equation, Appl. Math. Comput., 89 (1998), pp. 241-258.
    • (1998) Appl. Math. Comput. , vol.89 , pp. 241-258
    • Takáč, P.1
  • 34
    • 0030530210 scopus 로고    scopus 로고
    • Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg- Landau equation
    • P. TAKÁČ, P. BOLLERMAN, A. DOELMAN, A. VAN HARTEN, AND E. S. TITI, Analyticity of essentially bounded solutions to semilinear parabolic systems and validity of the Ginzburg- Landau equation, SIAM J. Math. Anal., 27 (1996), pp. 424-448.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 424-448
    • Takáč, P.1    Bollerman, P.2    Doelman, A.3    Van Harten, A.4    Titi, E.S.5
  • 36
    • 0030283593 scopus 로고    scopus 로고
    • Explicit Runge-Kutta methods for parabolic partial differential equations
    • J. G. VERWER, Explicit Runge-Kutta methods for parabolic partial differential equations, Appl. Numer. Math., 22 (1996), pp. 359-380.
    • (1996) Appl. Numer. Math. , vol.22 , pp. 359-380
    • Verwer, J.G.1


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