메뉴 건너뛰기




Volumn 206, Issue 2, 2005, Pages 727-780

Local spectral time splitting method for first- and second-order partial differential equations

Author keywords

Discrete singular convolution; Local spectral method; Split step; Wavelet collocation

Indexed keywords

BOSE-EINSTEIN CONDENSATION; C (PROGRAMMING LANGUAGE); CONVOLUTION; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; STATISTICAL MECHANICS; WAVE PROPAGATION;

EID: 18144399959     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.01.010     Document Type: Article
Times cited : (47)

References (108)
  • 3
    • 70350504025 scopus 로고
    • Splitting and alternating direction methods
    • North-Holland, Amsterdam
    • G.I. Marchuk, Splitting and alternating direction methods, Handbook of Numerical Analysis, vol. I, North-Holland, Amsterdam, 1990, pp. 197-462
    • (1990) Handbook of Numerical Analysis , vol.1 , pp. 197-462
    • Marchuk, G.I.1
  • 5
    • 0025684066 scopus 로고
    • A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity
    • L. Demkowicz T.J. Oden W. Rachowicz A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and hp- adaptivity Comput. Methods Appl. Mech. Engng. 84 1990 275-326
    • (1990) Comput. Methods Appl. Mech. Engng. , vol.84 , pp. 275-326
    • Demkowicz, L.1    Oden, T.J.2    Rachowicz, W.3
  • 6
    • 0002615718 scopus 로고
    • An analysis of the fractional step method
    • J.B. Perot An analysis of the fractional step method J. Comput. Phys. 108 1993 51-58
    • (1993) J. Comput. Phys. , vol.108 , pp. 51-58
    • Perot, J.B.1
  • 7
    • 84966253400 scopus 로고
    • Intermediate boundary conditions for time split methods applied to hyperbolic partial differential equations
    • R.J. LeVeque Intermediate boundary conditions for time split methods applied to hyperbolic partial differential equations Math. Comput. 47 1986 37-54
    • (1986) Math. Comput. , vol.47 , pp. 37-54
    • LeVeque, R.J.1
  • 8
    • 0024470996 scopus 로고
    • Process splitting of the boundary conditions for the advection-dispersion equation
    • K.O. Aiyesimoju R.J. Sobey Process splitting of the boundary conditions for the advection-dispersion equation Int. J. Numer. Methods Fluids 9 1989 235-244
    • (1989) Int. J. Numer. Methods Fluids , vol.9 , pp. 235-244
    • Aiyesimoju, K.O.1    Sobey, R.J.2
  • 9
    • 0031677005 scopus 로고    scopus 로고
    • Numerical analyses of operator-splitting algorithms for the two-dimensional advection-diffusion equation
    • L.A. Khan P.L.-F. Liu Numerical analyses of operator-splitting algorithms for the two-dimensional advection-diffusion equation Comput. Meth. Appl. Mech. Engng. 152 1998 337-359
    • (1998) Comput. Meth. Appl. Mech. Engng. , vol.152 , pp. 337-359
    • Khan, L.A.1    Liu, P.L.-F.2
  • 10
    • 0001446261 scopus 로고    scopus 로고
    • An analysis of operator splitting techniques in the stiff case
    • B. Sportisse An analysis of operator splitting techniques in the stiff case J. Comput. Phys. 161 2000 140-168
    • (2000) J. Comput. Phys. , vol.161 , pp. 140-168
    • Sportisse, B.1
  • 11
    • 3142652006 scopus 로고    scopus 로고
    • Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: Singular perturbation and order reduction
    • S. Descombes M. Massot Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: Singular perturbation and order reduction Numer. Math. 97 2004 667-698
    • (2004) Numer. Math. , vol.97 , pp. 667-698
    • Descombes, S.1    Massot, M.2
  • 12
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • G. Strang On the construction and comparison of difference schemes SIAM J. Numer. Anal. 5 1968 506-517
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 506-517
    • Strang, G.1
  • 13
    • 0041184489 scopus 로고    scopus 로고
    • Nth-order operator splitting schemes and nonreversible systems
    • D. Goldman T.J. Kaper Nth-order operator splitting schemes and nonreversible systems SIAM J. Numer. Anal. 33 1996 349-367
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 349-367
    • Goldman, D.1    Kaper, T.J.2
  • 14
    • 0001724114 scopus 로고
    • Symplectic integrators for long-term integrations in celestial mechanics
    • B. Gladman M. Duncan J. Candy Symplectic integrators for long-term integrations in celestial mechanics Celest. Mech. Dyn. Astro. 52 1991 221-240
    • (1991) Celest. Mech. Dyn. Astro. , vol.52 , pp. 221-240
    • Gladman, B.1    Duncan, M.2    Candy, J.3
  • 15
    • 33646388286 scopus 로고
    • Fourth order symplectic integration
    • E. Forest R.D. Ruth Fourth order symplectic integration Physica D 43 1990 105-117
    • (1990) Physica D , vol.43 , pp. 105-117
    • Forest, E.1    Ruth, R.D.2
  • 16
    • 0001005075 scopus 로고
    • Construction of higher order symplectic integrators
    • H. Yoshida Construction of higher order symplectic integrators Phys. Lett. A 150 1990 262-268
    • (1990) Phys. Lett. A , vol.150 , pp. 262-268
    • Yoshida, H.1
  • 17
    • 0013366568 scopus 로고    scopus 로고
    • High order symplectic integrators for perturbed Hamiltonian systems
    • J. Laskar P. Robutel High order symplectic integrators for perturbed Hamiltonian systems Celestial Mech. Dynam. Astr. 80 2001 39-62
    • (2001) Celestial Mech. Dynam. Astr. , vol.80 , pp. 39-62
    • Laskar, J.1    Robutel, P.2
  • 18
    • 0000300459 scopus 로고
    • Numerically induced chaos in the nonlinear Schrödinger equation
    • B.M. Herbst M.J. Ablowitz Numerically induced chaos in the nonlinear Schrödinger equation Phys. Rev. Lett. 62 1989 2065-2068
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 2065-2068
    • Herbst, B.M.1    Ablowitz, M.J.2
  • 19
    • 16144366227 scopus 로고    scopus 로고
    • On the numerical solution of the sine-Gordon equation. 1. Integrable discretizations and homoclinic manifolds
    • M.J. Ablowitz B.M. Herbst C. Schober On the numerical solution of the sine-Gordon equation. 1. Integrable discretizations and homoclinic manifolds J. Comput. Phys. 126 1996 299-314
    • (1996) J. Comput. Phys. , vol.126 , pp. 299-314
    • Ablowitz, M.J.1    Herbst, B.M.2    Schober, C.3
  • 20
    • 0347945239 scopus 로고    scopus 로고
    • Discrete singular convolution for the sine-Gordon equation
    • G.W. Wei Discrete singular convolution for the sine-Gordon equation Physica D 137 2000 247-259
    • (2000) Physica D , vol.137 , pp. 247-259
    • Wei, G.W.1
  • 21
    • 0001668244 scopus 로고
    • Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations
    • R.H. Hardin F.D. Tappert Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations SIAM Review 15 1973 423
    • (1973) SIAM Review , vol.15 , pp. 423
    • Hardin, R.H.1    Tappert, F.D.2
  • 22
    • 0343676826 scopus 로고
    • Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion
    • A. Hasegawa F. Tappert Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion Appl. Phys. Lett. 23 1973 142-144
    • (1973) Appl. Phys. Lett. , vol.23 , pp. 142-144
    • Hasegawa, A.1    Tappert, F.2
  • 23
    • 0039071563 scopus 로고
    • A novel method for simulating the complex Ginzburg-Landau equation
    • D. Goldman L. Sirovich A novel method for simulating the complex Ginzburg-Landau equation Quart. Appl. Math. 53 1995 315-333
    • (1995) Quart. Appl. Math. , vol.53 , pp. 315-333
    • Goldman, D.1    Sirovich, L.2
  • 24
    • 0001444952 scopus 로고    scopus 로고
    • A fast spectral algorithm for nonlinear wave equations with linear dispersion
    • B. Fornberg T.A. Driscoll 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.A.2
  • 25
    • 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
  • 26
    • 48549108442 scopus 로고
    • Analytical and numerical aspects of certain nonlinear evolution equations, III. Numerical, Korteweg-de Vries equation
    • T.R. Taha M.J. Ablowitz 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.R.1    Ablowitz, M.J.2
  • 27
    • 0043256997 scopus 로고    scopus 로고
    • Operator splitting methods for generalized Korteweg-de Vries equations
    • H. Holden K.H. Karlsen N.H. Risebro Operator splitting methods for generalized Korteweg-de Vries equations J. Comput. Phys. 153 1999 203-222
    • (1999) J. Comput. Phys. , vol.153 , pp. 203-222
    • Holden, H.1    Karlsen, K.H.2    Risebro, N.H.3
  • 28
    • 0037284595 scopus 로고    scopus 로고
    • A split-step Fourier method for the complex modified Korteweg-de Vries equation
    • G.M. Muslu H.A. Erbay A split-step Fourier method for the complex modified Korteweg-de Vries equation Comput. Math. Appl. 45 2003 503-514
    • (2003) Comput. Math. Appl. , vol.45 , pp. 503-514
    • Muslu, G.M.1    Erbay, H.A.2
  • 29
    • 0141849302 scopus 로고    scopus 로고
    • A split step approach for the 3-D Maxwell's equations
    • J. Lee B. Fornberg A split step approach for the 3-D Maxwell's equations J. Comput. Appl. Math. 158 2003 485-505
    • (2003) J. Comput. Appl. Math. , vol.158 , pp. 485-505
    • Lee, J.1    Fornberg, B.2
  • 30
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • G.S. Jiang C.W. Shu Efficient implementation of weighted ENO schemes J. Comput. Phys. 126 2003 202-228
    • (2003) J. Comput. Phys. , vol.126 , pp. 202-228
    • Jiang, G.S.1    Shu, C.W.2
  • 31
    • 13844262830 scopus 로고    scopus 로고
    • Numerical simulation of a generalized Zakharov system
    • S. Jin P.A. Markowich C. Zheng Numerical simulation of a generalized Zakharov system J. Comput. Phys. 201 2004 376-395
    • (2004) J. Comput. Phys. , vol.201 , pp. 376-395
    • Jin, S.1    Markowich, P.A.2    Zheng, C.3
  • 32
    • 18144389899 scopus 로고    scopus 로고
    • A Fourth-order time-splitting Laguerre-Hermite pseudo-spectral method for Bose-Einstein condensates
    • in press
    • W. Bao, J. Shen, A Fourth-order time-splitting Laguerre-Hermite pseudo-spectral method for Bose-Einstein condensates, SIAM J. Sci. Comput. in press (2005)
    • (2005) SIAM J. Sci. Comput
    • Bao, W.1    Shen, J.2
  • 33
    • 6344289363 scopus 로고    scopus 로고
    • Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow
    • W. Bao Q. Du Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow SIAM J. Sci. Comput. 25 2004 1674-1697
    • (2004) SIAM J. Sci. Comput. , vol.25 , pp. 1674-1697
    • Bao, W.1    Du, Q.2
  • 34
    • 0037138007 scopus 로고    scopus 로고
    • On time-splitting spectral approximation for the Schrödinger equation in the semiclassical regime
    • W. Bao S. Jin P.A. Markowich On time-splitting spectral approximation for the Schrödinger equation in the semiclassical regime J. Comput. Phys. 175 2002 487-524
    • (2002) J. Comput. Phys. , vol.175 , pp. 487-524
    • Bao, W.1    Jin, S.2    Markowich, P.A.3
  • 36
    • 0036504849 scopus 로고    scopus 로고
    • Split-step wavelet collocation method for nonlinear optical pulse propagation
    • T. Kremp A. Killi A. Rieder W. Freude Split-step wavelet collocation method for nonlinear optical pulse propagation IEICE Trans. Electron. 3 2002 534-543
    • (2002) IEICE Trans. Electron. , vol.3 , pp. 534-543
    • Kremp, T.1    Killi, A.2    Rieder, A.3    Freude, W.4
  • 38
    • 84966248629 scopus 로고
    • The stability of pseudospectral-Chebyshev methods
    • D. Gottlieb The stability of pseudospectral-Chebyshev methods Math. Comput. 36 1981 107-118
    • (1981) Math. Comput. , vol.36 , pp. 107-118
    • Gottlieb, D.1
  • 39
    • 84966205028 scopus 로고
    • Stability of pseudospectral and finite-difference methods for variable coefficient problems
    • D. Gottlieb S.A. Orszag E. Turkel Stability of pseudospectral and finite-difference methods for variable coefficient problems Math. Comput. 37 1981 293-305
    • (1981) Math. Comput. , vol.37 , pp. 293-305
    • Gottlieb, D.1    Orszag, S.A.2    Turkel, E.3
  • 40
    • 84966236671 scopus 로고
    • Essentially nonoscillatory spectral Fourier methods for shock wave calculations
    • W. Cai D. Gottlieb C.W. Shu Essentially nonoscillatory spectral Fourier methods for shock wave calculations Math. Comput. 52 1989 389-410
    • (1989) Math. Comput. , vol.52 , pp. 389-410
    • Cai, W.1    Gottlieb, D.2    Shu, C.W.3
  • 41
    • 84966257131 scopus 로고
    • The CFL condition for spectral approximations to hyperbolic initial-boundary value problems
    • D. Gottlieb E. Tadmor The CFL condition for spectral approximations to hyperbolic initial-boundary value problems Math. Comput. 56 1991 565-588
    • (1991) Math. Comput. , vol.56 , pp. 565-588
    • Gottlieb, D.1    Tadmor, E.2
  • 43
    • 0242511111 scopus 로고    scopus 로고
    • A multidomain spectral method for supersonic reactive flows
    • W.S. Don D. Gottlieb J.H. Jung A multidomain spectral method for supersonic reactive flows J. Comput. Phys. 192 2003 325-354
    • (2003) J. Comput. Phys. , vol.192 , pp. 325-354
    • Don, W.S.1    Gottlieb, D.2    Jung, J.H.3
  • 48
    • 0141750667 scopus 로고    scopus 로고
    • A note on the numerical solution of high-order differential equations
    • Ying Wang Y.B. Zhao G.W. Wei A note on the numerical solution of high-order differential equations J. Comput. Appl. Math. 159 2003 387-398
    • (2003) J. Comput. Appl. Math. , vol.159 , pp. 387-398
    • Ying, W.1    Zhao, Y.B.2    Wei, G.W.3
  • 49
    • 48549109395 scopus 로고
    • A spectral element method for fluid dynamics - Laminar flow in a channel expansion
    • A.T. Patera A spectral element method for fluid dynamics - laminar flow in a channel expansion J. Comput. Phys. 54 1984 468-488
    • (1984) J. Comput. Phys. , vol.54 , pp. 468-488
    • Patera, A.T.1
  • 50
    • 28144457683 scopus 로고
    • High order splitting methods for the incompressible Navier-Stokes equations
    • G.E. Karniadakis M. Iseraeli S.A. Orszag High order splitting methods for the incompressible Navier-Stokes equations J. Comput. Phys. 97 1991 414-443
    • (1991) J. Comput. Phys. , vol.97 , pp. 414-443
    • Karniadakis, G.E.1    Iseraeli, M.2    Orszag, S.A.3
  • 51
    • 26444583020 scopus 로고    scopus 로고
    • Discrete singular convolution for the Fokker-Planck equation
    • G.W. Wei Discrete singular convolution for the Fokker-Planck equation J. Chem. Phys. 110 1999 8930-8942
    • (1999) J. Chem. Phys. , vol.110 , pp. 8930-8942
    • Wei, G.W.1
  • 52
    • 0037145686 scopus 로고    scopus 로고
    • Discrete singular convolution and its application to the analysis of plates with internal supports. I. Theory and algorithm
    • G.W. Wei Y.B. Zhao Y. Xiang Discrete singular convolution and its application to the analysis of plates with internal supports. I. Theory and algorithm Int. J. Numer. Methods Engng. 55 2002 913-946
    • (2002) Int. J. Numer. Methods Engng. , vol.55 , pp. 913-946
    • Wei, G.W.1    Zhao, Y.B.2    Xiang, Y.3
  • 53
    • 0034647354 scopus 로고    scopus 로고
    • A unified approach for the solution of the Fokker-Planck equation
    • G.W. Wei A unified approach for the solution of the Fokker-Planck equation J. Phys. A, Math. General 33 2000 4935-4953
    • (2000) J. Phys. A, Math. General , vol.33 , pp. 4935-4953
    • Wei, G.W.1
  • 54
    • 1842616207 scopus 로고    scopus 로고
    • Comparison of the discrete singular convolution and three other numerical schemes for Fisher's equation
    • S. Zhao G.W. Wei Comparison of the discrete singular convolution and three other numerical schemes for Fisher's equation SIAM J. Sci. Comput. 25 2003 127-147
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 127-147
    • Zhao, S.1    Wei, G.W.2
  • 55
    • 0035850205 scopus 로고    scopus 로고
    • Vibration analysis by discrete singular convolution
    • G.W. Wei Vibration analysis by discrete singular convolution J. Sound Vibr. 244 2001 535-553
    • (2001) J. Sound Vibr. , vol.244 , pp. 535-553
    • Wei, G.W.1
  • 56
    • 0035808191 scopus 로고    scopus 로고
    • A new algorithm for solving some mechanical problems
    • G.W. Wei A new algorithm for solving some mechanical problems Comput. Methods Appl. Mech. Engng. 190 2001 2017-2030
    • (2001) Comput. Methods Appl. Mech. Engng. , vol.190 , pp. 2017-2030
    • Wei, G.W.1
  • 57
    • 17444422521 scopus 로고    scopus 로고
    • DSC analysis of free-edged beams by an iteratively matched boundary method
    • in press
    • S. Zhao, G.W. Wei, Y. Xiang, DSC analysis of free-edged beams by an iteratively matched boundary method, J. Sound Vib., in press (2005)
    • (2005) J. Sound Vib.
    • Zhao, S.1    Wei, G.W.2    Xiang, Y.3
  • 58
    • 0037142940 scopus 로고    scopus 로고
    • Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows
    • D.C. Wan B.S.V. Patnaik G.W. Wei Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows J. Comput. Phys. 180 2002 229-255
    • (2002) J. Comput. Phys. , vol.180 , pp. 229-255
    • Wan, D.C.1    Patnaik, B.S.V.2    Wei, G.W.3
  • 59
    • 0038454600 scopus 로고    scopus 로고
    • High-resolution conjugate filters for the simulation of flows
    • Y.C. Zhou G.W. Wei High-resolution conjugate filters for the simulation of flows J. Comput. Phys. 189 2003 150-179
    • (2003) J. Comput. Phys. , vol.189 , pp. 150-179
    • Zhou, Y.C.1    Wei, G.W.2
  • 61
    • 1442315655 scopus 로고    scopus 로고
    • Numerical solution of the Helmholtz equation with high wave numbers
    • G. Bao G.W. Wei S. Zhao Numerical solution of the Helmholtz equation with high wave numbers Int. J. Numer. Meth. Engng. 59 2004 389-408
    • (2004) Int. J. Numer. Meth. Engng. , vol.59 , pp. 389-408
    • Bao, G.1    Wei, G.W.2    Zhao, S.3
  • 62
    • 0042405039 scopus 로고    scopus 로고
    • DSC time-domain solution of Maxwell's equations
    • Z.H. Shao G.W. Wei S. Zhao DSC time-domain solution of Maxwell's equations J. Comput. Phys. 189 2003 427-453
    • (2003) J. Comput. Phys. , vol.189 , pp. 427-453
    • Shao, Z.H.1    Wei, G.W.2    Zhao, S.3
  • 63
    • 0038678165 scopus 로고    scopus 로고
    • Local spectral time-domain method for electromagnetic wave propagation
    • G. Bao G.W. Wei S. Zhao Local spectral time-domain method for electromagnetic wave propagation Opt. Lett. 28 2003 513-515
    • (2003) Opt. Lett. , vol.28 , pp. 513-515
    • Bao, G.1    Wei, G.W.2    Zhao, S.3
  • 64
    • 0036643310 scopus 로고    scopus 로고
    • A new approach for edge detection
    • Z.J. Hou G.W. Wei A new approach for edge detection Pattern Recogn. 35 2002 1559-1570
    • (2002) Pattern Recogn. , vol.35 , pp. 1559-1570
    • Hou, Z.J.1    Wei, G.W.2
  • 65
    • 0037126467 scopus 로고    scopus 로고
    • A novel approach for the analysis of high frequency vibrations
    • G.W. Wei Y.B. Zhao Y. Xiang A novel approach for the analysis of high frequency vibrations J. Sound Vib. 257 2002 207-246
    • (2002) J. Sound Vib. , vol.257 , pp. 207-246
    • Wei, G.W.1    Zhao, Y.B.2    Xiang, Y.3
  • 66
    • 0035861785 scopus 로고    scopus 로고
    • Discrete singular convolution for the prediction of high frequency vibration of plates
    • Y.B. Zhao G.W. Wei Y. Xiang Discrete singular convolution for the prediction of high frequency vibration of plates Int. J. Solids Struct. 39 2002 65-88
    • (2002) Int. J. Solids Struct. , vol.39 , pp. 65-88
    • Zhao, Y.B.1    Wei, G.W.2    Xiang, Y.3
  • 67
    • 0041355423 scopus 로고    scopus 로고
    • Numerical methods for the generalized Zakharov system
    • W. Bao F. Sun G.W. Wei Numerical methods for the generalized Zakharov system J. Comput. Phys. 190 2003 201-228
    • (2003) J. Comput. Phys. , vol.190 , pp. 201-228
    • Bao, W.1    Sun, F.2    Wei, G.W.3
  • 68
    • 0037383937 scopus 로고    scopus 로고
    • On the regularized Whittaker-Kotel'nikov-Shannon sampling formula
    • L.W. Qian On the regularized Whittaker-Kotel'nikov-Shannon sampling formula Proc. Amer. Math. Soc. 131 2003 1169-1176
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 1169-1176
    • Qian, L.W.1
  • 69
    • 0037082931 scopus 로고    scopus 로고
    • Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral methods for solving partial differential equations
    • S.Y. Yang Y.C. Zhou G.W. Wei Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral methods for solving partial differential equations Comput. Phys. Commun. 143 2002 113-135
    • (2002) Comput. Phys. Commun. , vol.143 , pp. 113-135
    • Yang, S.Y.1    Zhou, Y.C.2    Wei, G.W.3
  • 71
    • 0001742419 scopus 로고
    • Probability density estimation using delta sequences
    • G.G. Walter J. Blum Probability density estimation using delta sequences Ann. Statist. 7 1977 328-340
    • (1977) Ann. Statist. , vol.7 , pp. 328-340
    • Walter, G.G.1    Blum, J.2
  • 73
    • 0004706024 scopus 로고
    • Pansions and the theory of Fourier transforms
    • J. Korevaar Pansions and the theory of Fourier transforms Amer. Math. Soc. Trans. 91 1959 53-101
    • (1959) Amer. Math. Soc. Trans. , vol.91 , pp. 53-101
    • Korevaar, J.1
  • 74
    • 0001169579 scopus 로고
    • Analytic banded approximation for the discretized free propagator
    • D.K. Hoffman N. Nayar O.A. Sharafeddin D.J. Kouri Analytic banded approximation for the discretized free propagator J. Phys. Chem. 95 1991 8299-8305
    • (1991) J. Phys. Chem. , vol.95 , pp. 8299-8305
    • Hoffman, D.K.1    Nayar, N.2    Sharafeddin, O.A.3    Kouri, D.J.4
  • 75
    • 0009254650 scopus 로고    scopus 로고
    • Distributed approximating functional approach to the Fokker-Planck equation: Time propagation
    • G.W. Wei D.S. Zhang D.J. Kouri D.K. Hoffman Distributed approximating functional approach to the Fokker-Planck equation: Time propagation J. Chem. Phys. 107 1997 3239-3246
    • (1997) J. Chem. Phys. , vol.107 , pp. 3239-3246
    • Wei, G.W.1    Zhang, D.S.2    Kouri, D.J.3    Hoffman, D.K.4
  • 78
    • 0000612277 scopus 로고
    • Numerical evaluation of path-integral solutions to Fokker-Planck equations
    • M.F. Wehner W.G. Wolfer Numerical evaluation of path-integral solutions to Fokker-Planck equations Phys. Rev. A 27 1983 2663-2670
    • (1983) Phys. Rev. A , vol.27 , pp. 2663-2670
    • Wehner, M.F.1    Wolfer, W.G.2
  • 79
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • F. Black M.S. Scholes The pricing of options and corporate liabilities J. Polit. Econ. 81 1973 637-654
    • (1973) J. Polit. Econ. , vol.81 , pp. 637-654
    • Black, F.1    Scholes, M.S.2
  • 82
    • 84901286863 scopus 로고
    • Finite-difference methods and jump processes arising in the pricing of contingent claims: A synthesis
    • M.J. Brennan E.S. Schwartz Finite-difference methods and jump processes arising in the pricing of contingent claims: A synthesis J. Financ. Quant. Anal. 13 1978 461-474
    • (1978) J. Financ. Quant. Anal. , vol.13 , pp. 461-474
    • Brennan, M.J.1    Schwartz, E.S.2
  • 83
    • 84978565583 scopus 로고
    • A modified lattice approach to option pricing
    • Y. Tian A modified lattice approach to option pricing J. Futures Markets 13 1993 563-577
    • (1993) J. Futures Markets , vol.13 , pp. 563-577
    • Tian, Y.1
  • 84
    • 0000268135 scopus 로고
    • The wave of advantage of advantageous genes
    • R.A. Fisher The wave of advantage of advantageous genes Ann. Eugenics 7 1937 355-369
    • (1937) Ann. Eugenics , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 85
    • 0002722044 scopus 로고
    • Étude de l'équation de la diffusion aveccroissance de la quanitité de matière et son application è un problème biologique
    • A. Kolmogorov I. Petrovshy N. Piscounoff Étude de l'équation de la diffusion aveccroissance de la quanitité de matière et son application à un problème biologique Bull. Univ. Etat Moscou Ser. Int. Sect. A Math. et Mecan. 1 1937 1-25
    • (1937) Bull. Univ. Etat. Moscou Ser. Int. Sect. A Math. Et Mecan. , vol.1 , pp. 1-25
    • Kolmogorov, A.1    Petrovshy, I.2    Piscounoff, N.3
  • 86
    • 0000110286 scopus 로고
    • On a nonlinear diffusion equation describing population growth
    • J. Canosa On a nonlinear diffusion equation describing population growth IBM J. Res. Develop. 17 1973 307-313
    • (1973) IBM J. Res. Develop. , vol.17 , pp. 307-313
    • Canosa, J.1
  • 87
    • 0002820133 scopus 로고
    • Transient bounds and time-asymptotic behavior of solutions to nonlinear equations of Fisher type
    • D.A. Larson Transient bounds and time-asymptotic behavior of solutions to nonlinear equations of Fisher type SIAM J. Appl. Math. 34 1978 93-103
    • (1978) SIAM J. Appl. Math. , vol.34 , pp. 93-103
    • Larson, D.A.1
  • 88
    • 0010052770 scopus 로고
    • Traveling wave and multiple traveling wave solutions of parabolic equations
    • P.S. Hagan Traveling wave and multiple traveling wave solutions of parabolic equations SIAM J. Math. Anal. 13 1982 717-738
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 717-738
    • Hagan, P.S.1
  • 89
    • 0010015652 scopus 로고
    • The numerical calculation of traveling wave solutions of nonlinear parabolic equations
    • T. Hagstrom H.B. Keller The numerical calculation of traveling wave solutions of nonlinear parabolic equations SIAM J. Sci. Stat. Comput. 7 1986 978-988
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 978-988
    • Hagstrom, T.1    Keller, H.B.2
  • 90
    • 0000688482 scopus 로고
    • Numerical solution of Fisher's equation
    • J. Gazdag J. Canosa Numerical solution of Fisher's equation J. Appl. Probab. 11 1974 445-457
    • (1974) J. Appl. Probab. , vol.11 , pp. 445-457
    • Gazdag, J.1    Canosa, J.2
  • 91
    • 84985407466 scopus 로고
    • Least-squares finite element approximation of Fisher's reaction diffusion equation
    • G.F. Carey Y. Shen Least-squares finite element approximation of Fisher's reaction diffusion equation Numer. Meth. Partial Differential Equations 11 1995 175-186
    • (1995) Numer. Meth. Partial Differential Equations , vol.11 , pp. 175-186
    • Carey, G.F.1    Shen, Y.2
  • 92
    • 0032228619 scopus 로고    scopus 로고
    • Stability of moving mesh systems of partial differential equations
    • S. Li L.R. Petzold Y. Ren Stability of moving mesh systems of partial differential equations SIAM J. Sci. Comput. 20 1998 719-738
    • (1998) SIAM J. Sci. Comput. , vol.20 , pp. 719-738
    • Li, S.1    Petzold, L.R.2    Ren, Y.3
  • 93
    • 0002840078 scopus 로고
    • Numerical study of Fisher's equation by Adomian's method
    • T. Mavoungou Y. Cherruault Numerical study of Fisher's equation by Adomian's method Math. Comput. Model. 19 1994 89-95
    • (1994) Math. Comput. Model. , vol.19 , pp. 89-95
    • Mavoungou, T.1    Cherruault, Y.2
  • 94
    • 18144369752 scopus 로고
    • Gaussons: Solutions of the logarithmic Schrödinger equations
    • I. Blalynickl-Birdla J. Mycielski Gaussons: Solutions of the logarithmic Schrödinger equations Sci. Sinica Ser. A 26 1983 687
    • (1983) Sci. Sinica Ser. A , vol.26 , pp. 687
    • Blalynickl-Birdla, I.1    Mycielski, J.2
  • 96
    • 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
  • 97
    • 0001160015 scopus 로고    scopus 로고
    • Difference schemes for solving the generalized nonlinear Schrödinger equation
    • Q. 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.1    Jia, E.2    Sun, W.3
  • 99
    • 0000196586 scopus 로고
    • Vortex lines in an imperfect Bose gas
    • L.P. Pitaevskii Vortex lines in an imperfect Bose gas Sov. Phys. JETP 13 1961 451-454
    • (1961) Sov. Phys. JETP , vol.13 , pp. 451-454
    • Pitaevskii, L.P.1
  • 100
    • 0037075612 scopus 로고    scopus 로고
    • Bose-Einstein condensation of atomic gases
    • J.R. Anglin W. Ketterle Bose-Einstein condensation of atomic gases Nature 416 2002 211-218
    • (2002) Nature , vol.416 , pp. 211-218
    • Anglin, J.R.1    Ketterle, W.2
  • 101
    • 0001308051 scopus 로고    scopus 로고
    • Very cold indeed: The nanokelvin physics of Bose-Einstein condensation
    • E. Cornell Very cold indeed: The nanokelvin physics of Bose-Einstein condensation J. Res. Natl. Inst. Stan. 101 1996 419-434
    • (1996) J. Res. Natl. Inst. Stan. , vol.101 , pp. 419-434
    • Cornell, E.1
  • 103
    • 0034676963 scopus 로고    scopus 로고
    • Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms
    • S.K. Adhikari Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms Phys. Lett. A 265 2000 91-96
    • (2000) Phys. Lett. A , vol.265 , pp. 91-96
    • Adhikari, S.K.1
  • 104
    • 0034318663 scopus 로고    scopus 로고
    • Ground state of trapped interacting Bose-Einstein condensates by an explicit imaginary-time algorithm
    • M.L. Chiofalo S. Succi M.P. Tosi Ground state of trapped interacting Bose-Einstein condensates by an explicit imaginary-time algorithm Phys. Rev. E 62 2000 7438-7444
    • (2000) Phys. Rev. E , vol.62 , pp. 7438-7444
    • Chiofalo, M.L.1    Succi, S.2    Tosi, M.P.3
  • 105
    • 0347107495 scopus 로고    scopus 로고
    • Bosons in a trap: A rigorous derivation of the Gross-Pitaevski energy functional
    • E.H. Lieb R. Seiringer J. Yngvason Bosons in a trap: A rigorous derivation of the Gross-Pitaevski energy functional Phys. Rev. A 61 2000 043602
    • (2000) Phys. Rev. A , vol.61 , pp. 043602
    • Lieb, E.H.1    Seiringer, R.2    Yngvason, J.3
  • 106
    • 0034229732 scopus 로고    scopus 로고
    • Numerical solution of the Gross-Pitaevskii equation using an explicit finite-difference scheme: An application to trapped Bose-Einstein condensates
    • M.M. Cerimele M.L. Chiofalo F. Pistella S. Succi M.P. Tosi Numerical solution of the Gross-Pitaevskii equation using an explicit finite-difference scheme: An application to trapped Bose-Einstein condensates Phys. Rev. E 62 2000 1382-1389
    • (2000) Phys. Rev. E , vol.62 , pp. 1382-1389
    • Cerimele, M.M.1    Chiofalo, M.L.2    Pistella, F.3    Succi, S.4    Tosi, M.P.5
  • 107
    • 6344269406 scopus 로고    scopus 로고
    • Numerical computations of quantized vortices in Bose-Einstein condensate
    • T. Chan et al. (Eds.) Kluwer Academic Dordrecht, The Netherlands
    • Q. Du Numerical computations of quantized vortices in Bose-Einstein condensate In: T. Chan et al. (Eds.) Recent progress in computational and applied PDEs 2002 Kluwer Academic Dordrecht, The Netherlands 155
    • (2002) Recent Progress in Computational and Applied PDEs , pp. 155
    • Du, Q.1
  • 108
    • 0033480955 scopus 로고    scopus 로고
    • Numerical approximation of quadratic obsevables of Schrödinger-type equations in the semi-classical limit
    • P.A. Markowich P. Pietra C. Pohl Numerical approximation of quadratic obsevables of Schrödinger-type equations in the semi-classical limit Numer. Math. 81 1999 595-630
    • (1999) Numer. Math. , vol.81 , pp. 595-630
    • Markowich, P.A.1    Pietra, P.2    Pohl, C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.