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Volumn 189, Issue 1, 2007, Pages 949-962

Numerical methods and error analysis for the nonlinear Sivashinsky equation

Author keywords

Completely discrete; Convergence; Finite difference scheme; Finite element; Semidiscrete; Sivashinsky equation

Indexed keywords

ERROR ANALYSIS; EULER EQUATIONS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 34248347107     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.11.169     Document Type: Article
Times cited : (15)

References (23)
  • 1
    • 33845207137 scopus 로고    scopus 로고
    • On the convergence of difference schemes for the Benjamin-Bona-Mahanoy (BBM) equation
    • Achouri T., Khiari N., and Omrani K. On the convergence of difference schemes for the Benjamin-Bona-Mahanoy (BBM) equation. Appl. Math. Comput. 182 (2006) 999-1005
    • (2006) Appl. Math. Comput. , vol.182 , pp. 999-1005
    • Achouri, T.1    Khiari, N.2    Omrani, K.3
  • 2
    • 0041198722 scopus 로고
    • A practical finite element approximation of a semi-definite Neumann problem on a curved domain
    • Barett J.W., and Elliot C.M. A practical finite element approximation of a semi-definite Neumann problem on a curved domain. Numer. Math. 51 (1987) 23-36
    • (1987) Numer. Math. , vol.51 , pp. 23-36
    • Barett, J.W.1    Elliot, C.M.2
  • 3
    • 0000661816 scopus 로고
    • The lumped mass finite element method for a parabolic problem
    • Chen C.-M., and Thomée V. The lumped mass finite element method for a parabolic problem. J. Austral. Math. Soc. Ser. B 26 (1985) 329-354
    • (1985) J. Austral. Math. Soc. Ser. B , vol.26 , pp. 329-354
    • Chen, C.-M.1    Thomée, V.2
  • 4
    • 34248340006 scopus 로고    scopus 로고
    • A second order splitting lumped mass finite element method for the Roseneau equation
    • Chung S.K., and Pani A.K. A second order splitting lumped mass finite element method for the Roseneau equation. Diff. Equat. Dyn. Syst. 12 (1997) 331-351
    • (1997) Diff. Equat. Dyn. Syst. , vol.12 , pp. 331-351
    • Chung, S.K.1    Pani, A.K.2
  • 5
    • 0001475208 scopus 로고
    • A second order splitting method for the Cahn-Hilliard equation
    • Elliot C.M., French D.A., and Milner F.A. A second order splitting method for the Cahn-Hilliard equation. Numer. Math. 54 (1989) 575-590
    • (1989) Numer. Math. , vol.54 , pp. 575-590
    • Elliot, C.M.1    French, D.A.2    Milner, F.A.3
  • 6
    • 0001583367 scopus 로고
    • Large cells in nonlinear Rayleigh-Bénard convection
    • Gertsberg V.G., and Sivashinsky G.I. Large cells in nonlinear Rayleigh-Bénard convection. Prog. Theor. Phys. 66 (1981) 1219
    • (1981) Prog. Theor. Phys. , vol.66 , pp. 1219
    • Gertsberg, V.G.1    Sivashinsky, G.I.2
  • 7
    • 34248400375 scopus 로고    scopus 로고
    • N. Khiari, T. Achouri, M.L. Ben Mohamed, K.Omrani, Finite difference approximate solutions for the Cahn-Hilliard equation, Numer. Meth. Partial Diff. Equat., in press.
  • 8
    • 0006037477 scopus 로고
    • A lumped mass finite element method with quadrature for a nonlinear parabolic problem
    • Nie Y.-Y., and Thomée V. A lumped mass finite element method with quadrature for a nonlinear parabolic problem. IMA J. Numer. Anal. 5 (1985) 371-396
    • (1985) IMA J. Numer. Anal. , vol.5 , pp. 371-396
    • Nie, Y.-Y.1    Thomée, V.2
  • 9
    • 34248338728 scopus 로고    scopus 로고
    • K. Omrani, Approximation des équations de Sivashinsky et application des ondelettes; Thèse de Doctorat, Faculté des Sciences de Tunis, 2002.
  • 10
    • 0035633446 scopus 로고    scopus 로고
    • A finite element method for the Sivashinsky equation
    • Omrani K. A finite element method for the Sivashinsky equation. Indian J. Pure Appl. Math. 32 3 (2001)
    • (2001) Indian J. Pure Appl. Math. , vol.32 , Issue.3
    • Omrani, K.1
  • 11
    • 84867960112 scopus 로고    scopus 로고
    • A second order splitting method for a finite difference scheme for the Sivashinsky equation
    • Omrani K. A second order splitting method for a finite difference scheme for the Sivashinsky equation. Appl. Math. Lett. 16 (2003) 441-445
    • (2003) Appl. Math. Lett. , vol.16 , pp. 441-445
    • Omrani, K.1
  • 12
    • 33845200395 scopus 로고    scopus 로고
    • A linearized difference scheme for the Sivashinsky equation
    • Omrani K., and Ben Mohamed M.L. A linearized difference scheme for the Sivashinsky equation. Far East J. Appl. Math. 20 (2005) 179-188
    • (2005) Far East J. Appl. Math. , vol.20 , pp. 179-188
    • Omrani, K.1    Ben Mohamed, M.L.2
  • 13
    • 33845189660 scopus 로고    scopus 로고
    • A second-order accurate difference scheme on nonuniform meshes for nonlinear heat-conduction equation
    • Omrani K. A second-order accurate difference scheme on nonuniform meshes for nonlinear heat-conduction equation. Far East. J. Appl. Math. 20 2 (2005) 355-365
    • (2005) Far East. J. Appl. Math. , vol.20 , Issue.2 , pp. 355-365
    • Omrani, K.1
  • 14
    • 2942737438 scopus 로고    scopus 로고
    • On the numerical approach of the enthalpy method for the Stefan problem
    • Omrani K. On the numerical approach of the enthalpy method for the Stefan problem. Numer. Meth. Partial Diff. Equat. 20 4 (2004) 527-551
    • (2004) Numer. Meth. Partial Diff. Equat. , vol.20 , Issue.4 , pp. 527-551
    • Omrani, K.1
  • 15
    • 26444462611 scopus 로고    scopus 로고
    • Convergence of Galerkin approximations for the Kuramoto-Tsuzuki equation
    • Omrani K. Convergence of Galerkin approximations for the Kuramoto-Tsuzuki equation. Numer. Meth. Partial Diff. Equat. 21 5 (2005) 961-975
    • (2005) Numer. Meth. Partial Diff. Equat. , vol.21 , Issue.5 , pp. 961-975
    • Omrani, K.1
  • 16
    • 33748977285 scopus 로고    scopus 로고
    • The convergence of fully discrete Galerkin approximations for the Benjamin-Bona-Mahony (BBM) equation
    • Omrani K. The convergence of fully discrete Galerkin approximations for the Benjamin-Bona-Mahony (BBM) equation. Appl. Math. Comput. 180 2 (2006) 614-621
    • (2006) Appl. Math. Comput. , vol.180 , Issue.2 , pp. 614-621
    • Omrani, K.1
  • 17
    • 34248368476 scopus 로고    scopus 로고
    • ∞ error estimates for finite element Galerkin methods for nonlinear evolution equations, J. Appl. Math. Comput., in press.
  • 18
    • 0020778244 scopus 로고
    • On cellular instability in the solidification of a dilute binary alloy
    • North-Holland Publishing Company
    • Sivashinsky G.I. On cellular instability in the solidification of a dilute binary alloy. Physica 8 D (1983), North-Holland Publishing Company 243-248
    • (1983) Physica 8 D , pp. 243-248
    • Sivashinsky, G.I.1
  • 19
    • 0042210193 scopus 로고
    • A new class of difference schemes for linear parabolic differential equations
    • (in Chinese)
    • Sun Z.-z. A new class of difference schemes for linear parabolic differential equations. Math. Numer. Sinica 16 (1994) 115-130 (in Chinese)
    • (1994) Math. Numer. Sinica , vol.16 , pp. 115-130
    • Sun, Z.-z.1
  • 20
    • 2442534887 scopus 로고
    • A new class of difference schemes for linear parabolic differential equations
    • Sun Z.-z. A new class of difference schemes for linear parabolic differential equations. Chin. J. Numer. Math. Appl. Appl. 16 3 (1994) 1-20
    • (1994) Chin. J. Numer. Math. Appl. Appl. , vol.16 , Issue.3 , pp. 1-20
    • Sun, Z.-z.1
  • 21
    • 0043212476 scopus 로고
    • The method of the reduction of order for numerical solution to elliptic differential equations
    • (in Chinese)
    • Zhi-zhong S. The method of the reduction of order for numerical solution to elliptic differential equations. J. Southeast Univ. 23 6 (1993) 8-16 (in Chinese)
    • (1993) J. Southeast Univ. , vol.23 , Issue.6 , pp. 8-16
    • Zhi-zhong, S.1
  • 22
    • 21844485652 scopus 로고
    • A second-order accurate linearized difference scheme for two dimensional Cahn-Hilliard equation
    • Sun Z.-z. A second-order accurate linearized difference scheme for two dimensional Cahn-Hilliard equation. Math. Comput. 64 (1995) 1463-1471
    • (1995) Math. Comput. , vol.64 , pp. 1463-1471
    • Sun, Z.-z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.