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Volumn 205, Issue 1, 2005, Pages 72-97

Local discontinuous Galerkin methods for nonlinear Schrödinger equations

Author keywords

Local discontinuous Galerkin method; Nonlinear Schr dinger equation

Indexed keywords

GALERKIN METHODS; NUMERICAL METHODS;

EID: 16844366209     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.11.001     Document Type: Article
Times cited : (245)

References (34)
  • 1
    • 0001416032 scopus 로고    scopus 로고
    • A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
    • F. Bassi S. Rebay A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations J. Comput. Phys. 131 1997 267-279
    • (1997) J. Comput. Phys. , vol.131 , pp. 267-279
    • Bassi, F.1    Rebay, S.2
  • 2
    • 85163143647 scopus 로고
    • The propagation of nonlinear wave envelops
    • D.J. Benney A.C. Newll The propagation of nonlinear wave envelops J. Math. Phys. 46 1967 133-139
    • (1967) J. Math. Phys. , vol.46 , pp. 133-139
    • Benney, D.J.1    Newll, A.C.2
  • 3
    • 84864085736 scopus 로고
    • Gaussons: Solitons of the logarithmic Schrödinger equation
    • I. Białynicki-Birula J. Mycielski Gaussons: Solitons of the logarithmic Schrödinger equation Phys. Scripta 20 1979 539-544
    • (1979) Phys. Scripta , vol.20 , pp. 539-544
    • Białynicki-Birula, I.1    Mycielski, J.2
  • 5
    • 0001160015 scopus 로고    scopus 로고
    • Difference schemes for solving the generalized nonlinear Schrödinger equation
    • Q.S. Chang E. Jia W. Sun Difference schemes for solving the generalized nonlinear Schrödinger equation J. Comput. Phys. 148 1999 397-415
    • (1999) J. Comput. Phys. , vol.148 , pp. 397-415
    • Chang, Q.S.1    Jia, E.2    Sun, W.3
  • 6
    • 0003560721 scopus 로고
    • The finite element method for elliptic problem
    • Amsterdam: North-Holland
    • P. Ciarlet The finite element method for elliptic problem 1975 North-Holland Amsterdam
    • (1975)
    • Ciarlet, P.1
  • 8
    • 84966261380 scopus 로고
    • The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case
    • B. Cockburn S. Hou C.-W. Shu The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case Math. Comput. 54 1990 545-581
    • (1990) Math. Comput. , vol.54 , pp. 545-581
    • Cockburn, B.1    Hou, S.2    Shu, C.-W.3
  • 10
    • 45249130080 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems
    • B. Cockburn S.-Y. Lin C.-W. Shu TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one dimensional systems J. Comput. Phys. 84 1989 90-113
    • (1989) J. Comput. Phys. , vol.84 , pp. 90-113
    • Cockburn, B.1    Lin, S.-Y.2    Shu, C.-W.3
  • 11
    • 84966246413 scopus 로고
    • TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework
    • [11] B. Cockburn C.-W. Shu TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework Math. Comput. 52 1989 411-435
    • (1989) Math. Comput. , vol.52 , pp. 411-435
    • Cockburn, B.1    Shu, C.-W.2
  • 12
    • 0001690553 scopus 로고    scopus 로고
    • The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems
    • B. Cockburn C.-W. Shu The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems J. Comput. Phys. 141 1998 199-224
    • (1998) J. Comput. Phys. , vol.141 , pp. 199-224
    • Cockburn, B.1    Shu, C.-W.2
  • 13
    • 0344393366 scopus 로고    scopus 로고
    • The local discontinuous Galerkin method for time-dependent convection-diffusion systems
    • B. Cockburn C.-W. Shu The local discontinuous Galerkin method for time-dependent convection-diffusion systems SIAM J. Numer. Anal. 35 1998 2440-2463
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 2440-2463
    • Cockburn, B.1    Shu, C.-W.2
  • 14
    • 0000076512 scopus 로고    scopus 로고
    • Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
    • B. Cockburn C.-W. Shu Runge-Kutta discontinuous Galerkin methods for convection-dominated problems J. Sci. Comput. 16 2001 173-261
    • (2001) J. Sci. Comput. , vol.16 , pp. 173-261
    • Cockburn, B.1    Shu, C.-W.2
  • 15
    • 0012807790 scopus 로고
    • Quasi-soliton and other behaviour of the nonlinear cubic-quintic Schrödinger equation
    • S. Cowan R.H. Enns S.S. Rangnekar S.S. Sanghera Quasi-soliton and other behaviour of the nonlinear cubic-quintic Schrödinger equation Can. J. Phys. 64 1986 311-315
    • (1986) Can. J. Phys. , vol.64 , pp. 311-315
    • Cowan, S.1    Enns, R.H.2    Rangnekar, S.S.3    Sanghera, S.S.4
  • 16
    • 0036501083 scopus 로고    scopus 로고
    • Exponential time differencing for stiff systems
    • S.M. Cox P.C. Matthews Exponential time differencing for stiff systems J. Comput. Phys. 176 2002 430-455
    • (2002) J. Comput. Phys. , vol.176 , pp. 430-455
    • Cox, S.M.1    Matthews, P.C.2
  • 17
    • 0032666585 scopus 로고    scopus 로고
    • A quadratic B-spline finite element method for solving nonlinear Schrödinger equation
    • I. Daǧ A quadratic B-spline finite element method for solving nonlinear Schrödinger equation Comput. Methods Appl. Mech. Eng. 174 1999 247-258
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.174 , pp. 247-258
    • Daǧ, I.1
  • 18
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
    • [18] R.T. Glassey On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations J. Math. Phys. 18 1977 1794-1797
    • (1977) J. Math. Phys. , vol.18 , pp. 1794-1797
    • Glassey, R.T.1
  • 19
    • 0034920816 scopus 로고    scopus 로고
    • Numerical simulation of coupled nonlinear Schrödinger equation
    • M.S. Ismail T.R. Taha Numerical simulation of coupled nonlinear Schrödinger equation Math. Comput. Simulation 56 2001 547-562
    • (2001) Math. Comput. Simulation , vol.56 , pp. 547-562
    • Ismail, M.S.1    Taha, T.R.2
  • 20
    • 0039756618 scopus 로고    scopus 로고
    • A space-time finite element method for the nonlinear Schrödinger equation: The discontinuous Galerkin method
    • O. Karakashian C. Makridakis A space-time finite element method for the nonlinear Schrödinger equation: The discontinuous Galerkin method Math. Comput. 67 1998 479-499
    • (1998) Math. Comput. , vol.67 , pp. 479-499
    • Karakashian, O.1    Makridakis, C.2
  • 21
    • 0043232734 scopus 로고    scopus 로고
    • A space-time finite element method for the nonlinear Schrödinger equation: The continuous Galerkin method
    • O. Karakashian C. Makridakis A space-time finite element method for the nonlinear Schrödinger equation: The continuous Galerkin method SIAM J. Numer. Anal. 36 1999 1779-1807
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1779-1807
    • Karakashian, O.1    Makridakis, C.2
  • 22
    • 2442475431 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for nonlinear dispersive equations
    • D. Levy C.-W. Shu J. Yan Local discontinuous Galerkin methods for nonlinear dispersive equations J. Comput. Phys. 196 2004 751-772
    • (2004) J. Comput. Phys. , vol.196 , pp. 751-772
    • Levy, D.1    Shu, C.-W.2    Yan, J.3
  • 23
    • 0000471386 scopus 로고
    • An envelope soliton problem
    • J.W. Miles An envelope soliton problem SIAM J. Appl. Math. 41 1981 227-230
    • (1981) SIAM J. Appl. Math. , vol.41 , pp. 227-230
    • Miles, J.W.1
  • 24
    • 0003172958 scopus 로고
    • Pseudo-spectral solution of nonlinear Schrödinger equations
    • D. Pathria J.L. Morris Pseudo-spectral solution of nonlinear Schrödinger equations J. Comput. Phys. 87 1990 108-125
    • (1990) J. Comput. Phys. , vol.87 , pp. 108-125
    • Pathria, D.1    Morris, J.L.2
  • 25
    • 0347708733 scopus 로고    scopus 로고
    • Solving the generalized nonlinear Schrödinger equation via quartic spline approximation
    • Q. Sheng A.Q.M. Khaliq E.A. Al-Said Solving the generalized nonlinear Schrödinger equation via quartic spline approximation J. Comput. Phys. 166 2001 400-417
    • (2001) J. Comput. Phys. , vol.166 , pp. 400-417
    • Sheng, Q.1    Khaliq, A.Q.M.2    Al-Said, E.A.3
  • 26
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes
    • C.-W. Shu S. Osher Efficient implementation of essentially non-oscillatory shock-capturing schemes J. Comput. Phys. 77 1988 439-471
    • (1988) J. Comput. Phys. , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 27
    • 84990553244 scopus 로고
    • Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation
    • P.L. Sulem C. Sulem A. Patera Numerical simulation of singular solutions to the two-dimensional cubic Schrödinger equation Commun. Pure Appl. Math. 37 1984 755-778
    • (1984) Commun. Pure Appl. Math. , vol.37 , pp. 755-778
    • Sulem, P.L.1    Sulem, C.2    Patera, A.3
  • 28
    • 0142216144 scopus 로고    scopus 로고
    • Multi-symplectic methods for the coupled 1D nonlinear Schrödinger system
    • J.Q. Sun M.Z. Qin Multi-symplectic methods for the coupled 1D nonlinear Schrödinger system Comput. Phys. Commun. 155 2003 221-235
    • (2003) Comput. Phys. Commun. , vol.155 , pp. 221-235
    • Sun, J.Q.1    Qin, M.Z.2
  • 29
    • 48549114390 scopus 로고
    • Analytical and numerical aspects of certain nonlinear evolution equations II. Numerical, nonlinear Schrödinger equation
    • T.R. Taha M.J. Ablowitz Analytical and numerical aspects of certain nonlinear evolution equations II. Numerical, nonlinear Schrödinger equation J. Comput. Phys. 55 1984 203-230
    • (1984) J. Comput. Phys. , vol.55 , pp. 203-230
    • Taha, T.R.1    Ablowitz, M.J.2
  • 30
    • 3042791844 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for three classes of nonlinear wave equations
    • Y. Xu C.-W. Shu Local discontinuous Galerkin methods for three classes of nonlinear wave equations J. Comput. Math. 22 2004 250-274
    • (2004) J. Comput. Math. , vol.22 , pp. 250-274
    • Xu, Y.1    Shu, C.-W.2
  • 31
    • 0038693389 scopus 로고    scopus 로고
    • A local discontinuous Galerkin method for KdV type equations
    • J. Yan C.-W. Shu A local discontinuous Galerkin method for K dV type equations SIAM J. Numer. Anal. 40 2002 769-791
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 769-791
    • Yan, J.1    Shu, C.-W.2
  • 32
    • 1942475854 scopus 로고    scopus 로고
    • Local discontinuous Galerkin methods for partial differential equations with higher order derivatives
    • J. Yan C.-W. Shu Local discontinuous Galerkin methods for partial differential equations with higher order derivatives J. Sci. Comput. 17 2002 27-47
    • (2002) J. Sci. Comput. , vol.17 , pp. 27-47
    • Yan, J.1    Shu, C.-W.2
  • 33
    • 0002591433 scopus 로고    scopus 로고
    • Classification of the solitary waves in coupled nonlinear Schrödinger equations
    • J.K. Yang Classification of the solitary waves in coupled nonlinear Schrödinger equations Physica D 108 1997 92-112
    • (1997) Physica D , vol.108 , pp. 92-112
    • Yang, J.K.1
  • 34
    • 36749114276 scopus 로고
    • On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
    • R.T. Glassey On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations J. Math. Phys. 18 1977 1794-1797
    • (1977) J. Math. Phys. , vol.18 , pp. 1794-1797
    • Glassey, R.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.