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四次B样条Galerkin有限元方法数值求解Kuramoto-Sivashinsky方程 被引量：2

Numerical Solutions of Kuramoto-Sivashinsky Equations by Quartic B-spline Galerkin Finite Element Method
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摘要 采用四次B样条Galerkin有限元近似和对时间离散的方法,构造了求解(1+1)维Kuramoto-Sivashinsky方程的数值格式.通过4个算例和相关文献的对比,表明了该格式精度高,适应性强. A numerical scheme using quartic B-spline Galerkin finite element method is proposed to solve（1＋1）-dimensional Kuramoto-Sivashinsky.We compare the results obtained with those in the literature and find that the present scheme is highly accurate and adaptable.
作者 张涛锋 孙建安 陶娜 陈继宇 石玉仁
机构地区 西北师范大学物理与电子工程学院
出处 《兰州交通大学学报》 CAS 2010年第6期172-177,共6页 Journal of Lanzhou Jiaotong University
基金 教育部科学研究重点项目(209128) 西北师范大学科技创新工程重点项目(nwnu-kjcxgc-03-53)
关键词 KURAMOTO-SIVASHINSKY方程 四次B样条 GALERKIN方法 有限元方法 数值解. Kuramoto-Sivashinsky equation quartic B-spline Galerkin＇s method finite element method numerical solution
分类号 O242.21 [理学—计算数学]
  • 相关文献

参考文献16

  • 1Kuramoto Y,Tsuzuki T.On the formation of dissipative structures in reaction-diffusion systems[J].Prog.Theor.Phy.,1975,54(3):687-699.
  • 2Sivashinsky G.I,Nonlinear analysis of hydrodynamic instability in laminar flames-I:derivation of basic equations[J].Acta.Astrorsautica,1977(4):1177-1206.
  • 3Hooper A.P.,Grimshaw R..Travelling wave solutions of the Kuramoto-Sivashinsky equation[J].Wave Motion,1988(10):405-420.
  • 4Manickam A.V.,Moudgalya K.M.,Pani A K.Second -order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-sivashinsky equation[J].Comput.Math.AppL,,1998,35:5-25.
  • 5Fan Engui.Extended tanh-function method and its applications to nonlinear equations[J].Phys.Lett.A,2000,277:212-218.
  • 6Xu Yan,Shu Chiwang.Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coplued KdV equations[J].Comput.Meth.Appl.Mech Eng.,2006,195:3430-3447.
  • 7Lopez-Marcos M.A.Numerical analysis of pseudospectral method for the Kuramoto-Sivashinsky equation[J].Numer.Anal.,1994,14:223-242.
  • 8Khater A.H,Temsah R.S.Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods[J],Comput.Math.Appl.,2008,56:1465-1472.
  • 9Akrivis G.,Smyrlis Y.S.Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation[J].Appl.Numer.Math,2004,51:151-169.
  • 10Uddin M.,Hap S,Siraj-ul-Islam.A mesh-free numerical method for solution of the family of KuramotoSivashinsky equations[J].Appl.Math And Comput.,2009,212:458-469.

二级参考文献9

共引文献4

同被引文献16

  • 1Kuramoto Y,Tsuzuki T.On the formation of dissipa-tive structures in reaction-diffusion system[J].Pro-gress of Theoretical Physics,1975,54(3):687-699.
  • 2Sivashinsky G I.Nonlinear analysis of hydrodynamicinstability in laminar flames,Part 1.Derivation of basicequations[J].Acta Astronaut,1977,4(3):1177-1206.
  • 3Conte R.Exact solutions of nonlinear partial differenti-al equations by singularity analysis[M]∥In:Lecturenotes in physics.Berlin:Springer,2003:1-83.
  • 4Sivashinsky G I.Instabilities,pattern-formation,andtrubulence in flames[J].Annual Review of Fluid Me-chanics,1983,15:179-199.
  • 5Manickam A V,Moudgalya K M,Pani A K.Second-or-der splitting combined with orthogonal cubic spline col-location method for the Kuramoto-Sivashinsky equation[J].Computers and Mathematics with Applications,1998,35:5-25.
  • 6Fan Engui.Extended tanh-function method and its ap-plications to nonlinear equations[J].Phys Letters A,2000:212-218.
  • 7Xu Yan,Shu Chi-Wang.Local discontinuous Ganerkinmethods for the Kuramoto-Sivashinsky equations andthe Ito-type coupled KdV equations[J].ComputerMethods in Applied Mechanics and Engineering,2006,195:3430-3447.
  • 8Khater A H,Temsah R S.Numerical solutions of thegeneralized Kuramoto-Sivashinsky equation by Cheby-shev-spectral collocation methods[J].Computers andMathematics with Applications,2008,56:1465-1472.
  • 9Akrivis Georgios,Smyrlis Yiorgos-Sokratis.Implicit-explicit BDF methods for the Kuramoto-Sivashinsky e-quation[J].Applied Numerical Mathematics,2004,51:151-169.
  • 10Mittal R C,Geeta Arora.Quintic B-spline collocationmethod for numerical solution of the Kuramoto-Sivashinsky equation[J].Communications in Nonlin-ear Science and Numerical Simulation,2010,15:2798-2808.

引证文献2

二级引证文献1

兰州交通大学学报
2010年 第6期

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