参考文献/References:
[1] DANG Q A,LE T S.Iterative method for solving a problem with mixed boundary conditions for biharmonic equation[J].Adv Appl Math Mech,2009,1(5):683-698.
[2] DANG Q A,LUAN V T.Iterative method for solving a nonlinear fourth order boundary value problem[J].Computers and Mathematics with Applications,2010,60(1):112-121.
[3] ZHUANG Qing-qu.A Legendre spectral-element method for the one-dimensional fourth-order equations[J].Applied Mathematics and Computation,2011,218(7):3587-3595.
[4] KARMAN T,BIOT M A.Mathematical methods in engineering[M].New York:McGraw-Hill,1940.
[5] SEMPER B.Finite element methods for suspension bridge models[J].Computers and Mathematics with Applications,1993,26(5):77-91.
[6] SEMPER B.Finite element approximation of a fourth order integro-differential equation[J].Applied Mathematics Letters,1994,7(1):59-62.
[7] BREZZI F,FORTIN M.Mixed and hybrid finite element methods[M].New York:Springer-Verlag,1991.
[8] SHERMAN A H.On newton-iterative methods for the solution of systems of nonlinear equations[J].SIAM Journal on Numerical Analysis,1978,15(4):755-771.
[9] KUSRAEV A G.Discrete maximum principle[J].Mathematical Notes,1983,34(2):617-620.
[10] FEIREISl E.Exponential attractors for non-autonomous systems:Long-time behaviour of vibrating beams[J].Mathematical methods in the applied sciences,1992,15(4):287-297.
[11] LIONS J L,MAGENES E.Problemes aux limites non homogenes et applications[M].Paris:Dunod,1968.
[12] SAMARSKII A A.The theory of difference schemes[M].New York:Marcel Dekker,2001.
相似文献/References:
[1]任全伟,庄清渠.一类四阶微积分方程的紧差分格式[J].华侨大学学报(自然科学版),2014,35(2):232.[doi:10.11830/ISSN.1000-5013.2014.02.0232]
REN Quan-wei,ZHUANG Qing-qu.Compact Difference for a Class of Fourth-Order Integro-Differential Equations[J].Journal of Huaqiao University(Natural Science),2014,35(6):232.[doi:10.11830/ISSN.1000-5013.2014.02.0232]