메뉴 건너뛰기




Volumn 36, Issue 4, 2008, Pages 874-882

A unified lattice Boltzmann model for some nonlinear partial differential equations

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; NUMERICAL ANALYSIS;

EID: 38349099347     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.07.023     Document Type: Article
Times cited : (32)

References (28)
  • 3
    • 0037408898 scopus 로고    scopus 로고
    • Uniformly constructing a series of explict exact solutions to nonlinear equations in mathematical physics
    • Fan E.G. Uniformly constructing a series of explict exact solutions to nonlinear equations in mathematical physics. Chaos, Solitons & Fractals 16 (2003) 819-839
    • (2003) Chaos, Solitons & Fractals , vol.16 , pp. 819-839
    • Fan, E.G.1
  • 4
    • 0034606149 scopus 로고    scopus 로고
    • Extended tanh-function method and its applications to nonlinear equations
    • Fan E.G. Extended tanh-function method and its applications to nonlinear equations. Phys Lett A 277 (2000) 212-219
    • (2000) Phys Lett A , vol.277 , pp. 212-219
    • Fan, E.G.1
  • 5
    • 14144251108 scopus 로고    scopus 로고
    • The extended Fan's sub-equation method and its application to KDV-MKDV, BKK and variant Boussinesq equations
    • Yomba E. The extended Fan's sub-equation method and its application to KDV-MKDV, BKK and variant Boussinesq equations. Phys Lett A 336 (2005) 463-476
    • (2005) Phys Lett A , vol.336 , pp. 463-476
    • Yomba, E.1
  • 6
    • 27144554011 scopus 로고    scopus 로고
    • A comparison between two different methods for solving KdV-Burgers equation
    • Helal M.A., and Mehanna M.S. A comparison between two different methods for solving KdV-Burgers equation. Chaos, Solitons & Fractals 28 (2006) 320-326
    • (2006) Chaos, Solitons & Fractals , vol.28 , pp. 320-326
    • Helal, M.A.1    Mehanna, M.S.2
  • 7
    • 16344382587 scopus 로고    scopus 로고
    • An analytical-numerical method for solving the Korteweg-de Vries equation
    • Özer S., and Kutluay S. An analytical-numerical method for solving the Korteweg-de Vries equation. Appl Math Comput 164 (2005) 789-797
    • (2005) Appl Math Comput , vol.164 , pp. 789-797
    • Özer, S.1    Kutluay, S.2
  • 8
    • 25844433115 scopus 로고    scopus 로고
    • An application for a modified KdV equation by the decomposition method and finite element method
    • Geyikli T., and Kaya D. An application for a modified KdV equation by the decomposition method and finite element method. Appl Math Comput 169 (2005) 971-981
    • (2005) Appl Math Comput , vol.169 , pp. 971-981
    • Geyikli, T.1    Kaya, D.2
  • 9
    • 0035123550 scopus 로고    scopus 로고
    • A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application
    • Helal M.A. A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application. Chaos, Solitons & Fractals 12 (2001) 943-950
    • (2001) Chaos, Solitons & Fractals , vol.12 , pp. 943-950
    • Helal, M.A.1
  • 10
    • 0036645762 scopus 로고    scopus 로고
    • An application for a generalized KdV equation by the decomposition method
    • Kaya D., and Aassila M. An application for a generalized KdV equation by the decomposition method. Phys Lett A 299 (2002) 201-206
    • (2002) Phys Lett A , vol.299 , pp. 201-206
    • Kaya, D.1    Aassila, M.2
  • 11
    • 26044453236 scopus 로고    scopus 로고
    • A numerical application of the decomposition method for the combined KdV-MKdV equation
    • Kaya D., and Inan I.E. A numerical application of the decomposition method for the combined KdV-MKdV equation. Appl Math Comput 168 (2005) 915-926
    • (2005) Appl Math Comput , vol.168 , pp. 915-926
    • Kaya, D.1    Inan, I.E.2
  • 12
    • 0345849866 scopus 로고    scopus 로고
    • A small time solutions for the Korteweg-de Vries equation
    • Kutluay S., Bahadir A.R., and Özeş A. A small time solutions for the Korteweg-de Vries equation. Appl Math Comput 107 (2000) 203-210
    • (2000) Appl Math Comput , vol.107 , pp. 203-210
    • Kutluay, S.1    Bahadir, A.R.2    Özeş, A.3
  • 13
    • 31444443560 scopus 로고    scopus 로고
    • A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations
    • Soliman A.A. A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations. Chaos, Solitons & Fractals 29 (2006) 294-302
    • (2006) Chaos, Solitons & Fractals , vol.29 , pp. 294-302
    • Soliman, A.A.1
  • 14
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J.H. Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B 20 (2006) 1141-1199
    • (2006) Int J Mod Phys B , vol.20 , pp. 1141-1199
    • He, J.H.1
  • 15
    • 13844320326 scopus 로고
    • The lattice Boltzmann equation: theory and applications
    • Benzi R., Succi S., and Vergassola M. The lattice Boltzmann equation: theory and applications. Phys Rep 222 (1992) 147-197
    • (1992) Phys Rep , vol.222 , pp. 147-197
    • Benzi, R.1    Succi, S.2    Vergassola, M.3
  • 16
    • 1542471855 scopus 로고    scopus 로고
    • Lattice Boltzmann method for fluid flows, Annu
    • Chen S., and Doolen G.D. Lattice Boltzmann method for fluid flows, Annu. Rev Fluid Mech 30 (1998) 329-364
    • (1998) Rev Fluid Mech , vol.30 , pp. 329-364
    • Chen, S.1    Doolen, G.D.2
  • 18
    • 0036011823 scopus 로고    scopus 로고
    • Lattice Bhatnagar-Gross-Krook simulation of turbulent natural convection in a cavity
    • Shi B.C., Guo Z.L., and Wang N.C. Lattice Bhatnagar-Gross-Krook simulation of turbulent natural convection in a cavity. Chin Phys Lett 19 (2002) 515-517
    • (2002) Chin Phys Lett , vol.19 , pp. 515-517
    • Shi, B.C.1    Guo, Z.L.2    Wang, N.C.3
  • 19
    • 24144467365 scopus 로고    scopus 로고
    • A new lattice Bhatnagar-Gross-Krook model for convection-diffusion equation with a source term
    • Deng B., Shi B.C., and Wang G.C. A new lattice Bhatnagar-Gross-Krook model for convection-diffusion equation with a source term. Chin Phys Lett 22 (2005) 267-270
    • (2005) Chin Phys Lett , vol.22 , pp. 267-270
    • Deng, B.1    Shi, B.C.2    Wang, G.C.3
  • 21
    • 24644453492 scopus 로고    scopus 로고
    • Lattice Boltzmann method for Burgers equation
    • Shen Z., Yuan G., and Shen L. Lattice Boltzmann method for Burgers equation. Chin J Comput Phys 17 (2000) 166-172
    • (2000) Chin J Comput Phys , vol.17 , pp. 166-172
    • Shen, Z.1    Yuan, G.2    Shen, L.3
  • 22
    • 0346453190 scopus 로고    scopus 로고
    • Simulation of the MKdV equation with lattice Boltzmann method
    • [in chinese]
    • Li H.B., Huang P.H., Liu M.R., and Kong L.J. Simulation of the MKdV equation with lattice Boltzmann method. Acta Phys Sini 50 (2001) 837-840 [in chinese]
    • (2001) Acta Phys Sini , vol.50 , pp. 837-840
    • Li, H.B.1    Huang, P.H.2    Liu, M.R.3    Kong, L.J.4
  • 23
    • 4444377230 scopus 로고    scopus 로고
    • A lattice Boltzmann model and simulation of KdV-Burgers equation
    • Zhang C.Y., Tan H.L., Liu M.R., and Kong L.J. A lattice Boltzmann model and simulation of KdV-Burgers equation. Commun Theor Phys 42 (2004) 281-284
    • (2004) Commun Theor Phys , vol.42 , pp. 281-284
    • Zhang, C.Y.1    Tan, H.L.2    Liu, M.R.3    Kong, L.J.4
  • 24
    • 24644479765 scopus 로고    scopus 로고
    • A new lattice Boltzmann model for KdV-Burgers equation
    • Ma C.F. A new lattice Boltzmann model for KdV-Burgers equation. Chin Phys Lett 22 (2005) 2313-2315
    • (2005) Chin Phys Lett , vol.22 , pp. 2313-2315
    • Ma, C.F.1
  • 25
    • 33751580668 scopus 로고    scopus 로고
    • Discrete lattice effects on the forcing term in the lattice Boltzmann method
    • Guo Z., Zheng C., and Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys Rev E 65 (2002) 046308
    • (2002) Phys Rev E , vol.65 , pp. 046308
    • Guo, Z.1    Zheng, C.2    Shi, B.3
  • 26
    • 0036643088 scopus 로고    scopus 로고
    • Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics
    • Helal M.A. Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics. Chaos, Solitons & Fractals 13 (2002) 1917-1929
    • (2002) Chaos, Solitons & Fractals , vol.13 , pp. 1917-1929
    • Helal, M.A.1
  • 27
    • 0036334507 scopus 로고    scopus 로고
    • Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method
    • Guo Z.L., Zheng C.G., and Shi B.C. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin Phys 11 (2002) 366-374
    • (2002) Chin Phys , vol.11 , pp. 366-374
    • Guo, Z.L.1    Zheng, C.G.2    Shi, B.C.3
  • 28
    • 0001051950 scopus 로고
    • Galerkin methods for some model equations for nonlinear dispersive waves
    • Alexander M.E., and Morris J.L.L. Galerkin methods for some model equations for nonlinear dispersive waves. J Comput Phys 30 (1979) 428-451
    • (1979) J Comput Phys , vol.30 , pp. 428-451
    • Alexander, M.E.1    Morris, J.L.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.