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Volumn 54, Issue 1, 2007, Pages 136-146

A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions

Author keywords

Collocation; Multiquadrics (MQ); Radial Basis Function (RBF); Thin Plate Splines (TPS); Two dimensional Schr dinger equation

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; RADIAL BASIS FUNCTION NETWORKS;

EID: 34347347254     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.01.038     Document Type: Article
Times cited : (162)

References (24)
  • 1
    • 0031632570 scopus 로고    scopus 로고
    • Numerically absorbing boundary conditions for quantum evolution equations
    • Arnold A. Numerically absorbing boundary conditions for quantum evolution equations. VLSI Design 6 (1998) 313-319
    • (1998) VLSI Design , vol.6 , pp. 313-319
    • Arnold, A.1
  • 3
    • 0000978807 scopus 로고
    • The parabolic approximation method
    • Wave Propagation and Underwater Acoustics. Keller J.B., and Papadakis J.S. (Eds), Springer, Berlin
    • Tappert F.D. The parabolic approximation method. In: Keller J.B., and Papadakis J.S. (Eds). Wave Propagation and Underwater Acoustics. Lecture Notes in Physics vol. 70 (1977), Springer, Berlin 224-287
    • (1977) Lecture Notes in Physics , vol.70 , pp. 224-287
    • Tappert, F.D.1
  • 4
    • 0026834954 scopus 로고
    • The finite-difference vector beam propagation method
    • Huang W., Xu C., Chu S.T., and Chaudhuri S.K. The finite-difference vector beam propagation method. J. Lightwave Technol. 10 3 (1992) 295-304
    • (1992) J. Lightwave Technol. , vol.10 , Issue.3 , pp. 295-304
    • Huang, W.1    Xu, C.2    Chu, S.T.3    Chaudhuri, S.K.4
  • 5
    • 0042936309 scopus 로고
    • Solution of the Schrodinger equation in two and three dimensions
    • Hajj F.Y. Solution of the Schrodinger equation in two and three dimensions. J. Phys. B At. Mol. Phys. 18 (1985) 1-11
    • (1985) J. Phys. B At. Mol. Phys. , vol.18 , pp. 1-11
    • Hajj, F.Y.1
  • 6
    • 0031237961 scopus 로고    scopus 로고
    • Operations on oscillatory functions
    • Ixaru L.Gr. Operations on oscillatory functions. Comput. Phys. Comm. 105 (1997) 1-9
    • (1997) Comput. Phys. Comm. , vol.105 , pp. 1-9
    • Ixaru, L.Gr.1
  • 7
    • 0000538578 scopus 로고    scopus 로고
    • A review of dispersive limits of (non) linear Schrödinger type equations
    • Gasser I., Lin C.K., and Markowich P.A. A review of dispersive limits of (non) linear Schrödinger type equations. Taiwanese J. Math. 4 4 (2000) 501-529
    • (2000) Taiwanese J. Math. , vol.4 , Issue.4 , pp. 501-529
    • Gasser, I.1    Lin, C.K.2    Markowich, P.A.3
  • 8
    • 33746827431 scopus 로고    scopus 로고
    • A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrödinger equation
    • Kalita J.C., Chhabra P., and Kumar S. A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrödinger equation. J. Comput. Appl. Math. 197 (2006) 141-149
    • (2006) J. Comput. Appl. Math. , vol.197 , pp. 141-149
    • Kalita, J.C.1    Chhabra, P.2    Kumar, S.3
  • 9
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
    • Dehghan M. Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Math. Comput. Simulation 71 (2006) 16-30
    • (2006) Math. Comput. Simulation , vol.71 , pp. 16-30
    • Dehghan, M.1
  • 10
    • 0036844275 scopus 로고    scopus 로고
    • On the finite-difference schemes for the numerical solution of two dimensional Schrödinger equation
    • Subaşi M. On the finite-difference schemes for the numerical solution of two dimensional Schrödinger equation. Numer. Methods Partial Differential Equations 18 (2002) 752-758
    • (2002) Numer. Methods Partial Differential Equations , vol.18 , pp. 752-758
    • Subaşi, M.1
  • 11
    • 0036466644 scopus 로고    scopus 로고
    • Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition
    • Dehghan M. Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition. Nonlinear Anal., TMA 48 5(A) (2002) 637-650
    • (2002) Nonlinear Anal., TMA , vol.48 , Issue.5 A , pp. 637-650
    • Dehghan, M.1
  • 12
    • 0032644351 scopus 로고    scopus 로고
    • Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition
    • Dehghan M. Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition. J. Comput. Appl. Math. 106 2 (1999) 255-269
    • (1999) J. Comput. Appl. Math. , vol.106 , Issue.2 , pp. 255-269
    • Dehghan, M.1
  • 13
    • 5644226324 scopus 로고    scopus 로고
    • Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions
    • Antoine X., Besse C., and Mouysett V. Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions. Math. Comput. 73 (2004) 1779-1799
    • (2004) Math. Comput. , vol.73 , pp. 1779-1799
    • Antoine, X.1    Besse, C.2    Mouysett, V.3
  • 14
    • 33645862277 scopus 로고    scopus 로고
    • A local discontinuous Galerkin method for the Korteweg de Vries equation with boundary effect
    • Liu H., and Yan J. A local discontinuous Galerkin method for the Korteweg de Vries equation with boundary effect. J. Comput. Phys. 215 1 (2005) 197-218
    • (2005) J. Comput. Phys. , vol.215 , Issue.1 , pp. 197-218
    • Liu, H.1    Yan, J.2
  • 15
    • 0025229330 scopus 로고
    • Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics-I
    • Kansa E.J. Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics-I. Comput. Math. Appl. 19 (1990) 127-145
    • (1990) Comput. Math. Appl. , vol.19 , pp. 127-145
    • Kansa, E.J.1
  • 16
    • 0025210711 scopus 로고
    • Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics-II
    • Kansa E.J. Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics-II. Comput. Math. Appl. 19 (1990) 147-161
    • (1990) Comput. Math. Appl. , vol.19 , pp. 147-161
    • Kansa, E.J.1
  • 17
    • 0002879831 scopus 로고    scopus 로고
    • An efficient numerical scheme for Burgers equation
    • Hon Y.C., and Mao X.Z. An efficient numerical scheme for Burgers equation. Appl. Math. Comput. 95 1 (1998) 37-50
    • (1998) Appl. Math. Comput. , vol.95 , Issue.1 , pp. 37-50
    • Hon, Y.C.1    Mao, X.Z.2
  • 19
    • 0032529187 scopus 로고
    • A numerical method for heat transfer problem using collocation and radial basis functions
    • Zerroukat M., Power H., and Chen C.S. A numerical method for heat transfer problem using collocation and radial basis functions. Internat. J. Numer. Meth. Engrg. 42 (1992) 1263-1278
    • (1992) Internat. J. Numer. Meth. Engrg. , vol.42 , pp. 1263-1278
    • Zerroukat, M.1    Power, H.2    Chen, C.S.3
  • 20
    • 0001291977 scopus 로고    scopus 로고
    • A radial basis function method for solving options pricing model
    • Hon Y.C., and Mao X.Z. A radial basis function method for solving options pricing model. Financial Engrg. 8 1 (1999) 31-49
    • (1999) Financial Engrg. , vol.8 , Issue.1 , pp. 31-49
    • Hon, Y.C.1    Mao, X.Z.2
  • 21
    • 0001764927 scopus 로고    scopus 로고
    • On the use of boundary conditions for variational formulations arising in financial mathematics
    • Marcozzi M., Choi S., and Chen C.S. On the use of boundary conditions for variational formulations arising in financial mathematics. Appl. Math. Comput. 124 (2001) 197-214
    • (2001) Appl. Math. Comput. , vol.124 , pp. 197-214
    • Marcozzi, M.1    Choi, S.2    Chen, C.S.3
  • 22
    • 0003028016 scopus 로고
    • The parameter R2 in multiquadric interpolation
    • Carlson R.E., and Foley T.A. The parameter R2 in multiquadric interpolation. Comput. Math. Appl. 21 (1991) 29-42
    • (1991) Comput. Math. Appl. , vol.21 , pp. 29-42
    • Carlson, R.E.1    Foley, T.A.2
  • 23
    • 34347349802 scopus 로고    scopus 로고
    • A.E. Tarwater, A parameter study of Hardys multiquadric method for scattered data interpolation, Technical report UCRL-54670, Lawrence Livermore National Laboratory, 1985
  • 24
    • 33749559910 scopus 로고    scopus 로고
    • The one-dimensional heat equation subject to a boundary integral specification
    • Dehghan M. The one-dimensional heat equation subject to a boundary integral specification. Chaos Solitons Fractals 32 (2007) 661-675
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 661-675
    • Dehghan, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.