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Volumn 41, Issue 5, 2003, Pages 1595-1619

A new dual-petrov-galerkin method for third and higher odd-order differential equations: Application to the KDV equation

Author keywords

Dual Petrov Galerkin; KDV equation; Legendre polynomials; Spectral approximation

Indexed keywords

DUAL-PETROV-GALERKIN; KDV EQUATIONS; LEGENDRE POLYNOMIALS; SPECTRAL APPROXIMATION;

EID: 9244255255     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902410271     Document Type: Conference Paper
Times cited : (129)

References (28)
  • 1
    • 0000944835 scopus 로고
    • A fast algorithm for the evaluation of Legendre expansions
    • B. K. ALPERT AND V. ROKHLIN, A fast algorithm for the evaluation of Legendre expansions, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 158-179.
    • (1991) SIAM J. Sci. Statist. Comput. , vol.12 , pp. 158-179
    • Alpert, B.K.1    Rokhlin, V.2
  • 2
    • 0001393582 scopus 로고
    • The Korteweg-de Vries equation, posed in a quarter-plane
    • J. BONA AND R. WINTHER, The Korteweg-de Vries equation, posed in a quarter-plane, SIAM J. Math. Anal., 14 (1983), pp. 1056-1106.
    • (1983) SIAM J. Math. Anal. , vol.14 , pp. 1056-1106
    • Bona, J.1    Winther, R.2
  • 4
    • 0141596147 scopus 로고    scopus 로고
    • A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain
    • J. L. BONA, S. M. SUN, AND B. Y. ZHANG, A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain, Comm. Partial Differential Equations, 28 (2003), pp. 1391-1436.
    • (2003) Comm. Partial Differential Equations , vol.28 , pp. 1391-1436
    • Bona, J.L.1    Sun, S.M.2    Zhang, B.Y.3
  • 5
    • 0035981911 scopus 로고    scopus 로고
    • A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane
    • J. L. BONA, S. M. SUN, AND B. Y. ZHANG, A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane, Trans. Amer. Math. Soc., 354 (2002), pp. 427-490.
    • (2002) Trans. Amer. Math. Soc. , vol.354 , pp. 427-490
    • Bona, J.L.1    Sun, S.M.2    Zhang, B.Y.3
  • 8
  • 9
    • 0012499847 scopus 로고    scopus 로고
    • An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval
    • T. COLIN AND J.-M. GHIDAGLIA, An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval, Adv. Differential Equations, 6 (2001), pp. 1463-1492.
    • (2001) Adv. Differential Equations , vol.6 , pp. 1463-1492
    • Colin, T.1    Ghidaglia, J.-M.2
  • 10
    • 0028750042 scopus 로고
    • The chebyshev-legendre method: Implementing legendre methods on chebyshev points
    • W. S. DON AND D. GOTTLIEB, The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points, SIAM J. Numer. Anal., 31 (1994), pp. 1519-1534.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1519-1534
    • Don, W.S.1    Gottlieb, D.2
  • 11
    • 0002193620 scopus 로고
    • Numerical analysis of spectral methods: Theory and applications
    • SIAM, Philadelphia
    • D. GOTTLIEB AND S. A. ORSZAG, Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conf. Ser. in Appl. Math. 26, SIAM, Philadelphia, 1977.
    • (1977) CBMS-NSF Regional Conf. Ser. in Appl. Math. , vol.26
    • Gottlieb, D.1    Orszag, S.A.2
  • 12
    • 0038868349 scopus 로고
    • Numerical solution of an initial-boundary value problem of the Korteweg-de Vries equation
    • B.-Y. GUO, Numerical solution of an initial-boundary value problem of the Korteweg-de Vries equation, Acta Math. Sci. (English Ed.), 5 (1985), pp. 337-348.
    • (1985) Acta Math. Sci. (English Ed.) , vol.5 , pp. 337-348
    • Guo, B.-Y.1
  • 13
    • 0041028677 scopus 로고    scopus 로고
    • On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line
    • Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000)
    • B.-Y. GUO AND J. SHEN, On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line, Indiana Univ. Math. J., 50 (2001), pp. 181-204. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000).
    • (2001) Indiana Univ. Math. J. , vol.50 , pp. 181-204
    • Guo, B.-Y.1    Shen, J.2
  • 15
    • 0034652883 scopus 로고    scopus 로고
    • Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations
    • B.-Y. GUO, Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations, J. Math. Anal. Appl., 243 (2000), pp. 373-408.
    • (2000) J. Math. Anal. Appl. , vol.243 , pp. 373-408
    • Guo, B.-Y.1
  • 16
    • 0347907385 scopus 로고
    • The korteweg-de vries equation and water waves. II, Comparison with experiments
    • J. L. HAMMACK AND H. SEGUR, The Korteweg-de Vries equation and water waves. II, Comparison with experiments, J. Fluid Mech., 65 (1974), pp. 289-313.
    • (1974) J. Fluid Mech. , vol.65 , pp. 289-313
    • Hammack, J.L.1    Segur, H.2
  • 17
    • 0026972778 scopus 로고
    • The pseudospectral method for third-order differential equations
    • W. Z. HUANG AND D. M. SLOAN, The pseudospectral method for third-order differential equations, SIAM J. Numer. Anal., 29 (1992), pp. 1626-1647.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1626-1647
    • Huang, W.Z.1    Sloan, D.M.2
  • 18
    • 0000106540 scopus 로고
    • Existence and nonexistence of solitary wave solutions to higher-order model evolution equations
    • S. KICHENASSAMY AND P. J. OLVER, Existence and nonexistence of solitary wave solutions to higher-order model evolution equations, SIAM J. Math. Anal., 23 (1992), pp. 1141-1166.
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 1141-1166
    • Kichenassamy, S.1    Olver, P.J.2
  • 19
    • 0034543430 scopus 로고    scopus 로고
    • A Legendre-Petrov-Galerkin method and Chebyshev collocation method for the third-order differential equations
    • H. MA AND W. SUN, A Legendre-Petrov-Galerkin method and Chebyshev collocation method for the third-order differential equations, SIAM J. Numer. Anal., 38 (2000), pp. 1425-1438.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1425-1438
    • Ma, H.1    Sun, W.2
  • 20
    • 0042922604 scopus 로고    scopus 로고
    • Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation
    • H. MA AND W. SUN, Optimal error estimates of the Legendre-Petrov-Galerkin method for the Korteweg-de Vries equation, SIAM J. Numer. Anal., 39 (2001), pp. 1380-1394.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 1380-1394
    • Ma, H.1    Sun, W.2
  • 21
    • 38249003800 scopus 로고
    • Properties of collocation third-derivative operators
    • W. J. MERRYFIELD AND B. SHIZGAL, Properties of collocation third-derivative operators, J. Comput. Phys., 105 (1993), pp. 182-185.
    • (1993) J. Comput. Phys. , vol.105 , pp. 182-185
    • Merryfield, W.J.1    Shizgal, B.2
  • 22
    • 0000567049 scopus 로고
    • Efficient spectral-Galerkin method I: Direct solvers of second- And fourth-order equations using Legendre polynomials
    • J. SHEN, Efficient spectral-Galerkin method I: Direct solvers of second- and fourth-order equations using Legendre polynomials, SIAM J. Sci. Comput., 15 (1994), pp. 1489-1505.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1489-1505
    • Shen, J.1
  • 23
    • 0002543392 scopus 로고
    • Efficient spectral-Galerkin method II: Direct solvers of second- And fourth-order equations using Chebyshev polynomials
    • J. SHEN, Efficient spectral-Galerkin method II: Direct solvers of second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comput., 16 (1994), pp. 74-87.
    • (1994) SIAM J. Sci. Comput. , vol.16 , pp. 74-87
    • Shen, J.1
  • 24
    • 0002043336 scopus 로고    scopus 로고
    • Efficient Chebyshev-Legendre galerkin methods for elliptic problems, in
    • Proceedings of ICOSAHOM'95, A. V. Ilin and R. Scott, eds., Houston, TX
    • J. SHEN, Efficient Chebyshev-Legendre Galerkin methods for elliptic problems, in Proceedings of ICOSAHOM'95, A. V. Ilin and R. Scott, eds., Houston J. Math., Houston, TX, 1996, pp. 233-240.
    • (1996) Houston J. Math. , pp. 233-240
    • Shen, J.1
  • 25
    • 0031261340 scopus 로고    scopus 로고
    • Efficient spectral-Galerkin methods III: Polar and cylindrical geometries
    • J. SHEN, Efficient spectral-Galerkin methods III: Polar and cylindrical geometries, SIAM J. Sci. Comput., 18 (1997), pp. 1583-1604.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1583-1604
    • Shen, J.1
  • 26
    • 0033279023 scopus 로고    scopus 로고
    • Efficient spectral-Galerkin methods IV: Spherical geometries
    • J. SHEN, Efficient spectral-Galerkin methods IV: Spherical geometries, SIAM J. Sci. Comput., 20 (1999), pp. 1438-1455.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1438-1455
    • Shen, J.1
  • 28
    • 0000783351 scopus 로고
    • Shallow water waves, the Korteveg-de-Vries equation and solitons
    • N. J. ZABUSKY AND C. J. GALVIN, Shallow water waves, the Korteveg-de-Vries equation and solitons, J. Fluid Mech., 47 (1971), pp. 811-824.
    • (1971) J. Fluid Mech. , vol.47 , pp. 811-824
    • Zabusky, N.J.1    Galvin, C.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.