|
[1]
|
Perring, J.K. and Skyrme, T.H.R. (1962) A model unified field equation. Nuclear Physics, 31, 550-555.
http://dx.doi.org/10.1016/0029-5582(62)90774-5 [Google Scholar] [CrossRef]
|
|
[2]
|
Whitham, G.B. (1999) Linear and nonlinear waves. Wi-ley-Interscience, New York.
http://dx.doi.org/10.1002/9781118032954 [Google Scholar] [CrossRef]
|
|
[3]
|
Guo, B.Y., Pascual, P.J., Rodriguez, M.J. and Vazquez, L. (1986) Numerical solution of the sine-Gordon equation. Applied Mathematics and Computation, 18, 1-14. http://dx.doi.org/10.1016/0096-3003(86)90025-1 [Google Scholar] [CrossRef]
|
|
[4]
|
Strauss, W.A. and Vázquez, L. (1978) Numerical solution of a nonlinear Klein-Gordon equation. Journal of Computational Physics, 28, 271-278. http://dx.doi.org/10.1016/0021-9991(78)90038-4 [Google Scholar] [CrossRef]
|
|
[5]
|
Dehghan, M. (2006) Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Mathematics and Computers in Simulation, 71, 16-30.
http://dx.doi.org/10.1016/j.matcom.2005.10.001 [Google Scholar] [CrossRef]
|
|
[6]
|
Dehghan, M. (2005) On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Numerical Methods for Partial Differential Equations, 21, 24-40.
http://dx.doi.org/10.1002/num.20019 [Google Scholar] [CrossRef]
|
|
[7]
|
Dehghan, M. and Shokri, A. (2008) A numerical method for one-dimensional nonlinear sine-Gordon equation using collocation and radial basis functions. Numerical Methods for Partial Differential Equations, 24, 687-698.
http://dx.doi.org/10.1002/num.20289 [Google Scholar] [CrossRef]
|
|
[8]
|
Ramos, J.I. (2001) The Sine-Gordon equation in the finite line. Applied Mathematics and Computation, 124, 45-93.
http://dx.doi.org/10.1016/S0096-3003(00)00080-1 [Google Scholar] [CrossRef]
|
|
[9]
|
Lu, X. (2001) Symplectic computation of solitary waves for general sine-Gordon equations. Mathematics and Computers in Simulation, 55, 519-532. http://dx.doi.org/10.1016/S0378-4754(00)00300-1 [Google Scholar] [CrossRef]
|
|
[10]
|
Batiha, B., Noorani, M.S.M. and Hashim, I. (2007) Nu-merical solution of sine-Gordon equation by variational iteration method. Physics Letters A, 370, 437-440. http://dx.doi.org/10.1016/j.physleta.2007.05.087 [Google Scholar] [CrossRef]
|
|
[11]
|
Bratsos, A.G. and Twizell, E.H. (1996) The solution of the Sine-Gordon equation using the method of lines. International Journal of Computer Mathematics, 61, 271-292. http://dx.doi.org/10.1080/00207169608804516 [Google Scholar] [CrossRef]
|
|
[12]
|
Bratsos, A.G. (2008) A fourth order numerical scheme for the one-dimensional sine-Gordon equation. International Journal of Computer Mathematics, 85, 1083-1095. http://dx.doi.org/10.1080/00207160701473939 [Google Scholar] [CrossRef]
|
|
[13]
|
Piller, M. and Stalio, E. (2004) Finite-volume compact schemes on staggered grids. Journal of Computational Physics, 197, 299-340. http://dx.doi.org/10.1016/j.jcp.2003.10.037 [Google Scholar] [CrossRef]
|
|
[14]
|
Li, S. and Vu-Quoc, L. (1995) Finite difference calculus invariant structure of a class of algorithms for the Klein- Gordon equation. SIAM Journal on Numerical Analysis, 32, 1839-1875. http://dx.doi.org/10.1137/0732083 [Google Scholar] [CrossRef]
|
|
[15]
|
李庆扬, 王能超 (2006) 数值分析. 第四版, 华中科技大学出版社, 武汉.
|
|
[16]
|
Gottlieb, S., Shu, C.-W. and Tadmor, E. (2001) Strong stability-preserving high-order time discretization methods. SIAM Review, 43, 89-112. http://dx.doi.org/10.1137/S003614450036757X [Google Scholar] [CrossRef]
|
|
[17]
|
Wei, G.W. (2000) Discrete singular convolution for the Sine-Gordon equation. Physica D, 137, 247-259.
http://dx.doi.org/10.1016/S0167-2789(99)00186-4 [Google Scholar] [CrossRef]
|