Error analysis for solving the Korteweg-de Vries equation by a Legendre pseudo-spectral method

Numerical Methods for Partial Differential Equations

Volumn 16, Issue 6, 2000, Pages 513-534

  Li, Jian ^a   Ma, Heping ^b   Sun, Weiwei ^c  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

^b SHANGHAI UNIVERSITY   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Korteweg de Vries equation; Legendre pseudo spectral method

Indexed keywords

EID: 0043028813     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1098-2426(200011)16:6<513::aid-num2>3.0.co;2-%23     Document Type: Article

References (19)

1. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zan, Spectral methods in fluid dynamics, Springer-Verlag, Berlin, 1988.
2. C. Bernardi and Y. Maday, Spectral methods, Handbook of numerical analysis, Vol. V, Techniques of scientific computing (Part 2), P. G. Ciarlet and J. L. Lions (Editors), Elsevier, Amsterdam, 1997, pp. 209-486.
3. Ben-Yu Guo, Spectral methods and their applications, World Scientific, Singapore, 1998.
4. He-Ping Ma and Ben-Yu Guo, The Fourier pseudo-spectral method with a restrain operator for the Korteweg-de Vries equation, J Comp Phys 65 (1986), 120-137.
5. 2AN, 22 (1988), 499-529.
6. D. Pavoni, Single and multidomain Chebyshev collocation methods for the Korteweg-de Vries equation, Calcolo 25 (1988), 311-346.
7. N. Bressan and D. Pavoni, Truncation versus mapping in the spectral approximation to the Korteweg-de Vries equation, Comp Meth Appl Mech Eng 80 (1990), 443-450.
8. G. F. Carey and Y. Shen, Approximations of the KdV equation by least squares finite elements, Comp Meth Appl Mech Eng 93 (1991), 1-11.
9. K. Djidjeli, W. G. Price, E. H. Twizell, and Y. Wang, Numerical methods for the solution of the third- and fifth-order dispersive Korteweg-de Vries equations, J Comp Appl Math 58 (1995), 307-336.
10. W. J. Merryfield and B. Shizgal, Properties of collocation third-derivative operators, J Comp Phys 105 (1993), 182-185.
11. W. Z. Huang and D. M. Sloan, The pseudo-spectral method for third-order differential equations, SIAM J Numer Anal 29 (1992), 1626-1647.
12. D. Gottlieb and S. Orszag, Numerical analysis of spectral methods: Theory and applications, SIAM-CBMS, Philadelphia, 1977.
13. J. Shen, Efficient spectral-Galerkin method, I. Direct solvers for second- and fourth-order equations using Legendre polynomials, SIAM J Sci Comp 15 (1994), 1489-1505.
14. J. Shen, Efficient spectral-Galerkin method, II. Direct solvers for second- and fourth-order equations using Chebyshev polynomials, SIAM J Sci Comp 16 (1995), 74-87.
15. G. Szegö, Orthogonal polynomials, American Mathematics Society, Providence, RI, 1975.
16. C. Bernardi and Y. Maday, Polynomial interpolation results in Sobolev space, J Comp Appl Math 43 (1992), 53-82.
17. Ben-Yu Guo, Difference methods for partial differential equations, Science Press, Beijing, 1988.
18. D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic, Dordrecht, 1991.
19. T. F. Chan and T. Kerkhoven, Fourier methods with extended stability intervals for the Korteweg-de Vries equation, SIAM J Numer Anal 22 (1985), 441-454.