A Legendre pseudospectral method for solving nonlinear Klein-Gordon equation

Journal of Computational Mathematics

Volumn 15, Issue 2, 1997, Pages 105-126

  Li, X ^a   Guo, B Y ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008480071     PISSN: 02549409     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. J.L. Lions, Quèlques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969.
2. B.Y. Guo and L. Vázquez, A numerical scheme for nonlinear Klein-Gordon equations, J. Appl. Sci., 1(1983), 25-32.
3. B.Y. Guo, Numerical solution of nonlinear wave equation, Numerical Mathematics, 4 (1982), 46-56.
4. W. Strauss and L. Vázquez, Numerical solution of nonlinear Klein-Gordon equation, J. Comp. Phys., 28(1978), 271-278.
5. B.Y. Guo, W.M. Cao and N.B. Tahira, A Fourier spectral scheme for solving nonlinear Klein-Gordon equation, Numerical Mathematics, 2(1993), 38-56.
6. W.M. Cao and B.Y. Guo, Fourier collocation method for solving nonlinear Klein-Gordon equation, J. Comp. Phys., 108(1993), 296-305.
7. B.Y. Guo, X. Li and L. Vázquez, A Legendre spectral method for solving nonlinear Klein-Gordon equation, J. Comp. Phys. Appl. Math., 15(1996), 19-36.
8. C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev space, Math. Comp., 38(1982), 67-86.
9. C. Bernardi and Y. Maday, Polynomial interpolation results in Sobolev spaces, J. Comp. Appl. Math., 43(1992), 53-80.
10. P. Nevai, Orthogonal Polynomials, Men. Amer. Math. Soc., 213, Amer. Mathematical Soc., Providence. RI, 1979.
11. J. Szabados and P. Vértesi, A survey on mean convergence of interpolatory processes, J. Comp. Appl. Math., 43(1992), 3-18.
12. G.H. Hardy, J.E. Littlewood and G. Polya, Inequalites, 2'nd edition, Cambridge Univ. Press, Cambridge, 1952.
13. B.Y. Guo, Difference Methods for Partial Differential Equations, Science Press, Beijing, 1988.
14. R.D. Richtmyer and K.W. Morton, Finite Difference Methods for Initial Value Problems, 2'nd edition, Interscience, New York, 1967.
15. B.Y. Guo, On stability of discretization, Scientia Sinica, 25A(1982), 702-715.
16. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin, 1988.
17. H.P. Ma, Spectral methods for the generalized Korteweg-de Vries-Burgers system and their error estimates, J. Comput. Math., 4(1987), 337-355.