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Volumn 80, Issue 1, 2009, Pages 151-163

A boundary value problem for the KdV equation: Comparison of finite-difference and Chebyshev methods

Author keywords

Boundary value problem; Chebyshev method; Finite difference method; KdV equation

Indexed keywords

CHEBYSHEV METHOD; CHEBYSHEV POLYNOMIALS; COLLOCATION METHOD; EXACT SOLUTION; FINITE DIFFERENCE; KDV EQUATION; KDV EQUATIONS; KORTEWEG-DE VRIES EQUATIONS;

EID: 70349186536     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2009.06.009     Document Type: Article
Times cited : (27)

References (29)
  • 2
    • 0141596147 scopus 로고    scopus 로고
    • A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain
    • Bona J.L., Sun S.M., and Zhang B.-Y. A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. Comm. Partial Diff. Eq. 28 (2003) 1391-1436
    • (2003) Comm. Partial Diff. Eq. , vol.28 , pp. 1391-1436
    • Bona, J.L.1    Sun, S.M.2    Zhang, B.-Y.3
  • 3
    • 0001864672 scopus 로고
    • Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond
    • Boussinesq J. Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. J. Math. Pures Appl. 17 (1872) 55-108
    • (1872) J. Math. Pures Appl. , vol.17 , pp. 55-108
    • Boussinesq, J.1
  • 4
    • 1842660660 scopus 로고
    • Benchmarking the propagator method for nonlinear systems: a Burgers-Korteweg-de Vries equation
    • Cacuci D.G., and Karakashian O.A. Benchmarking the propagator method for nonlinear systems: a Burgers-Korteweg-de Vries equation. J. Comput. Phys. 89 (1990) 63-79
    • (1990) J. Comput. Phys. , vol.89 , pp. 63-79
    • Cacuci, D.G.1    Karakashian, O.A.2
  • 6
    • 0042467377 scopus 로고
    • Approximations of the KdV equation by least squares finite elements
    • Carey G.F., and Shen Y. Approximations of the KdV equation by least squares finite elements. Comput. Methods Appl. Mech. Eng. 93 (1991) 1-11
    • (1991) Comput. Methods Appl. Mech. Eng. , vol.93 , pp. 1-11
    • Carey, G.F.1    Shen, Y.2
  • 7
    • 33646403441 scopus 로고    scopus 로고
    • Variable coefficient KdV equations and waves in elastic tubes, Evolution equations
    • Dekker, New York pp. 57-69
    • Cascaval R.C. Variable coefficient KdV equations and waves in elastic tubes, Evolution equations. Lecture Notes in Pure and Appl. Math. vol. 234 (2003), Dekker, New York pp. 57-69
    • (2003) Lecture Notes in Pure and Appl. Math. , vol.234
    • Cascaval, R.C.1
  • 8
    • 0012499847 scopus 로고    scopus 로고
    • An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval
    • Colin T., and Ghidaglia J.-M. An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval. Adv. Diff. Eq. 6 (2001) 1463-1492
    • (2001) Adv. Diff. Eq. , vol.6 , pp. 1463-1492
    • Colin, T.1    Ghidaglia, J.-M.2
  • 9
    • 0036956556 scopus 로고    scopus 로고
    • The generalized Korteweg-de Vries equation on the half line
    • Colliander J.E., and Kenig C.E. The generalized Korteweg-de Vries equation on the half line. Comm. Partial Diff. Eq. 27 (2002) 2187-2266
    • (2002) Comm. Partial Diff. Eq. , vol.27 , pp. 2187-2266
    • Colliander, J.E.1    Kenig, C.E.2
  • 10
    • 2342640689 scopus 로고
    • Applications of KdV
    • Crighton D.G. Applications of KdV. Acta Appl. Math. 39 (1995) 39-67
    • (1995) Acta Appl. Math. , vol.39 , pp. 39-67
    • Crighton, D.G.1
  • 11
    • 0000465701 scopus 로고
    • An easily implementable fourth-order method for the time integration of wave problems
    • de Frutos J., and Sanz-Serna J.M. An easily implementable fourth-order method for the time integration of wave problems. J. Comput. Phys. 103 (1992) 160-168
    • (1992) J. Comput. Phys. , vol.103 , pp. 160-168
    • de Frutos, J.1    Sanz-Serna, J.M.2
  • 12
    • 0029412261 scopus 로고
    • Numerical methods for the solution of the third- and fifth-order dispersive Korteweg-de Vries equations
    • Djidjeli K., Price W.G., Twizell E.H., and Wang Y. Numerical methods for the solution of the third- and fifth-order dispersive Korteweg-de Vries equations. J. Comput. Appl. Math. 58 (1995) 307-336
    • (1995) J. Comput. Appl. Math. , vol.58 , pp. 307-336
    • Djidjeli, K.1    Price, W.G.2    Twizell, E.H.3    Wang, Y.4
  • 14
    • 0001444952 scopus 로고    scopus 로고
    • A fast spectral algorithm for nonlinear wave equations with linear dispersion
    • Fornberg B., and Driscoll T. A fast spectral algorithm for nonlinear wave equations with linear dispersion. J. Comput. Phys. 155 (1999) 456-467
    • (1999) J. Comput. Phys. , vol.155 , pp. 456-467
    • Fornberg, B.1    Driscoll, T.2
  • 15
    • 0017901962 scopus 로고
    • A numerical and theoretical study of certain nonlinear phenomena
    • Fornberg B., and Whitham G.B. A numerical and theoretical study of certain nonlinear phenomena. Philos. Trans. R. Soc. Lond. Ser. A 289 (1978) 373-404
    • (1978) Philos. Trans. R. Soc. Lond. Ser. A , vol.289 , pp. 373-404
    • Fornberg, B.1    Whitham, G.B.2
  • 17
    • 0033300307 scopus 로고    scopus 로고
    • Spectral approximation of third-order problems
    • Heinrichs W. Spectral approximation of third-order problems. J. Sci. Comput. 14 (1999) 275-289
    • (1999) J. Sci. Comput. , vol.14 , pp. 275-289
    • Heinrichs, W.1
  • 18
    • 33746816587 scopus 로고    scopus 로고
    • The initial-boundary value problem for the Korteweg-de Vries equation
    • Holmer J. The initial-boundary value problem for the Korteweg-de Vries equation. Comm. Partial Diff. Eq. 31 (2006) 1151-1190
    • (2006) Comm. Partial Diff. Eq. , vol.31 , pp. 1151-1190
    • Holmer, J.1
  • 19
    • 0015419996 scopus 로고
    • Weak nonlinear dispersive waves: a discussion centered around the Korteweg-de Vries equation
    • Jeffrey A., and Kakutani T. Weak nonlinear dispersive waves: a discussion centered around the Korteweg-de Vries equation. SIAM Rev. 14 (1972) 582-643
    • (1972) SIAM Rev. , vol.14 , pp. 582-643
    • Jeffrey, A.1    Kakutani, T.2
  • 20
    • 34547440371 scopus 로고    scopus 로고
    • On the rate of convergence of a collocation projection of the KdV equation
    • Kalisch H., and Raynaud X. On the rate of convergence of a collocation projection of the KdV equation. Math. Model. Numer. Anal. 41 (2007) 95-110
    • (2007) Math. Model. Numer. Anal. , vol.41 , pp. 95-110
    • Kalisch, H.1    Raynaud, X.2
  • 21
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular channel and on a new type of long stationary wave
    • Korteweg D.J., and de Vries G. On the change of form of long waves advancing in a rectangular channel and on a new type of long stationary wave. Philos. Mag. 39 (1895) 422-443
    • (1895) Philos. Mag. , vol.39 , pp. 422-443
    • Korteweg, D.J.1    de Vries, G.2
  • 22
    • 0034543430 scopus 로고    scopus 로고
    • A Legendre-Petrov-Galerkin method and Chebyshev collocation method for the third-order differential equations
    • Ma H., and Sun W. A Legendre-Petrov-Galerkin method and Chebyshev collocation method for the third-order differential equations. SIAM J. Numer. Anal. 38 (2000) 1425-1438
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1425-1438
    • Ma, H.1    Sun, W.2
  • 23
    • 0039004073 scopus 로고
    • Error analysis for spectral approximation of the Korteweg-de Vries equation
    • Maday Y., and Quarteroni A. Error analysis for spectral approximation of the Korteweg-de Vries equation. RAIRO Modl. Math. Anal. Num. 22 (1988) 499-529
    • (1988) RAIRO Modl. Math. Anal. Num. , vol.22 , pp. 499-529
    • Maday, Y.1    Quarteroni, A.2
  • 24
    • 51249175469 scopus 로고
    • Single and multidomain Chebyshev collocation methods for the Korteweg-de Vries equation
    • Pavoni D. Single and multidomain Chebyshev collocation methods for the Korteweg-de Vries equation. Calcolo 25 (1988) 311-346
    • (1988) Calcolo , vol.25 , pp. 311-346
    • Pavoni, D.1
  • 25
    • 9244255255 scopus 로고    scopus 로고
    • A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: application to the KDV equation
    • Shen J. A new dual-Petrov-Galerkin method for third and higher odd-order differential equations: application to the KDV equation. SIAM J. Numer. Anal. 41 (2003) 1595-1619
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 1595-1619
    • Shen, J.1
  • 26
    • 48549108442 scopus 로고
    • Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation
    • Taha T., and Ablowitz M. Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation. J. Comput. Phys. 55 (1984) 231-253
    • (1984) J. Comput. Phys. , vol.55 , pp. 231-253
    • Taha, T.1    Ablowitz, M.2
  • 29
    • 33846361348 scopus 로고
    • Interaction of solutions in a collisionless plasma and the recurrence of initial states
    • Zabusky N.J., and Kruskal M.D. Interaction of solutions in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240-243
    • (1965) Phys. Rev. Lett. , vol.15 , pp. 240-243
    • Zabusky, N.J.1    Kruskal, M.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.