参考文献/References:
[1] CAHN J W,HILLEARD J E.Free energy of a nonuniform system(Ⅰ): Interfacial free energy[J].Journal of Chemical Physics,1958,28(2):258-267.DOI:10.1063/1.1744102.
[2] MICHELSON D M,SIVASHINSKY G I.Nonlinear analysis of hydrodynamic instability in laminar flames(Ⅱ): Numerical experiments[J].Acta Astronautica,1977,4(11/12):1207-1221.DOI:10.1016/0094-5765(77)90097-2.
[3] QUANG A D,LUAN V T,LONG Dangquang.Iterative method for solving a fourth order differential equation with nonlinear boundary condition[J].Applied Mathematical Sciences,2010,4(70):3467-3481.
[4] ZHUANG Qingqu.A legendre spectral-element method for the one-dimensional fourth-order equations[J].Applied Mathematics and Computation,2011,218(7):3587-3595.DOI:10.1016/j.amc.2011.08.107.
[5] FUNARO D,HEINRICHS W.Some results about the pseudospectral approximation of one-dimensional fourth-order problems[J].Numerische Mathematik,1990,58(1):399-418.DOI:10.1007/BF01385633.
[6] MALEK A,PHILLIPS T N.Pseudospectral collocation methods for fourth-order differential equations[J].Ima Journal of Numerical Analysis,1994,15(4):523-553.DOI:10.1093/imanum/15.4.523.
[7] NOOR M A,MOHYUD-DIN S T.An efficient method for fourth-order boundary value problems[J].Computers and Mathematics with Applications,2007,54(7/8):1101-1111.DOI:10.1016/j.camwa.2006.12.057.
[8] SUN Tao,YI Lijun.A new Galerkin spectral element method for fourth-order boundary value problems[J].International Journal of Computer Mathematics,2015,93(6):915-928.DOI:10.1080/00207160.2015.1011142.
[9] DANG-VU H,DELCARTE C.An accurate solution of the poisson equation by the chebyshev collocation method[J].Journal of Computational Physics,1993,104(1):211-220.DOI:10.1006/jcph.1993.1021.
[10] ZHU Huajun,TANG Lingyan,SONG Songhe,et al.Symplectic wavelet collocation method for Hamiltonian wave equations[J].Journal of Computational Physics,2010,229(7):2550-2572.DOI:10.1016/j.jcp.2009.11.042.
[11] SHEN Jie,TANG Tao.Spectral and high-order methods with applications[M].Beijing:Science Press of China,2006.
[12] COSTABILE F,NAPOLI A.A method for polynomial approximation of the solution of general second order BVPs[J].Far East Journal of Applied Mathematics,2006,25(3):289-305.DOI:10.1016/j.cam.2006.10.081.
[13] COSTABILE F,NAPOLI A.A class of collocation methods for numerical integration of initial value problems[J].Computers and Mathematics with Applications,2011,62(8):3221-3235.DOI:10.1016/j.camwa.2011.08.036.
[14] COSTABILE F,NAPOLI A.Collocation for high order differential equations with two-points Hermite boundary conditions[J].Applied Numerical Mathematics,2014,87:157-167.DOI:10.1016/j.apnum.2014.09.008.
[15] BOOR C D,SWARTZ B.Collocation at Gaussian points[J].Siam Journal on Numerical Analysis,1973,10(4):582-606.DOI:10.1137/0710052.
[16] COSTABILE F,NAPOLI A.Collocation for high-order differential equations with lidstone boundary conditions[J].Journal of Applied Mathematics,2012,2012(1110-757X):701-708.DOI:10.1155/2012/120792.
[17] COSTABILE F A,LONGO E.A Birkhoff interpolation problem and application[J].Calcolo,2010,47(1):49-63.DOI:10.1007/s10092-009-0014-9.
[18] GUANG Shiying.Theory of Birkhoff interpolation[M].New York:Nova Publishers,2003.
[19] LORENTZ G G,JETTER K,RIEMENSCHNEIDER S D.Birkhoff interpolation[M].Oxford:Cambridge University Press,1984.
[20] WANG Lilian,SAMSON M D,ZHAO Xiaodan.A well-conditioned collocation method using a pseudospectral integration matrix[J].SIAM Journal on Scientific Computing,2014,36(3):A907-A929.DOI:10.1137/130922409.
[21] SHEN Jie,TANG Tao,WANG Lilian.Spectral methods: Algorithms, analysis and applications[M].Berlin: Springer-Verlag,2011.