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Volumn 274, Issue 1, 2002, Pages 374-403

A rational approximation and its applications to nonlinear partial differential equations on the whole line

Author keywords

Differential equation on the whole line; Pseudospectral method; Rational approximation; Spectral method

Indexed keywords


EID: 0036815013     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00334-7     Document Type: Article
Times cited : (27)

References (20)
  • 1
    • 0003796630 scopus 로고
    • Sobolev Spaces
    • Academic Press, New York
    • R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
    • (1975)
    • Adams, R.A.1
  • 2
    • 67349095304 scopus 로고    scopus 로고
    • Spectral methods
    • P.G. Ciarlet, J.L. Lions (Eds.), Techniques of Scientific Computing, Elsevier, Amsterdam
    • C. Bernardi, Y. Maday, Spectral methods, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, Vol. 5, Techniques of Scientific Computing, Elsevier, Amsterdam, 1997, pp. 209-486.
    • (1997) Handbook of Numerical Analysis , vol.5 , pp. 209-486
    • Bernardi, C.1    Maday, Y.2
  • 3
    • 0001718791 scopus 로고
    • Spectral method using rational basis functions on an infinite interval
    • J.P. Boyd, Spectral method using rational basis functions on an infinite interval, J. Comp. Phys. 69 (1987) 112-142.
    • (1987) J. Comp. Phys. , vol.69 , pp. 112-142
    • Boyd, J.P.1
  • 4
    • 0002717130 scopus 로고
    • Orthogonal rational functions on a semi-infinite interval
    • J.P. Boyd, Orthogonal rational functions on a semi-infinite interval, J. Comp. Phys. 70 (1987) 63-88.
    • (1987) J. Comp. Phys. , vol.70 , pp. 63-88
    • Boyd, J.P.1
  • 7
    • 84966205570 scopus 로고
    • Approximation of some diffusion evolution equations in unbounded domains by Hermite functions
    • D. Funaro, O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions, Math. Comp. 57 (1990) 597-619.
    • (1990) Math. Comp. , vol.57 , pp. 597-619
    • Funaro, D.1    Kavian, O.2
  • 8
    • 0003600453 scopus 로고
    • Numerical Analysis of Spectral Methods: Theory and Applications
    • SIAM-CBMS, Philadelphia
    • D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM-CBMS, Philadelphia, 1977.
    • (1977)
    • Gottlieb, D.1    Orszag, S.A.2
  • 9
    • 0003902398 scopus 로고    scopus 로고
    • Spectral Methods and Their Applications
    • World Scientific, Singapore
    • Guo Ben-yu, Spectral Methods and Their Applications, World Scientific, Singapore, 1998.
    • (1998)
    • Guo Ben-yu, A.1
  • 10
    • 0000587852 scopus 로고    scopus 로고
    • Gegenbauer approximation and its applications to differential equations on the whole line
    • Guo Ben-yu, Gegenbauer approximation and its applications to differential equations on the whole line, J. Math. Anal. Appl. 226 (1998) 180-206.
    • (1998) J. Math. Anal. Appl. , vol.226 , pp. 180-206
    • Guo Ben-yu, A.1
  • 11
    • 0040633278 scopus 로고    scopus 로고
    • Error estimation of Hermite spectral method for nonlinear partial differential equations
    • Guo Ben-yu, Error estimation of Hermite spectral method for nonlinear partial differential equations, Math. Comp. 68 (1999) 1067-1078.
    • (1999) Math. Comp. , vol.68 , pp. 1067-1078
    • Guo Ben-yu, A.1
  • 12
    • 0002665809 scopus 로고    scopus 로고
    • Jacobi spectral approximation and its applications to differential equations on the half line
    • Guo Ben-yu, Jacobi spectral approximation and its applications to differential equations on the half line, J. Comput. Math. 18 (2000) 95-112.
    • (2000) J. Comput. Math. , vol.18 , pp. 95-112
    • Guo Ben-yu, A.1
  • 13
    • 0000784542 scopus 로고    scopus 로고
    • Gegenbauer approximation in certain Hilbert spaces and its applications to singular differential equations
    • Guo Ben-yu, Gegenbauer approximation in certain Hilbert spaces and its applications to singular differential equations, SIAM J. Numer. Anal. 37 (2000) 621-645.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 621-645
    • Guo Ben-yu, A.1
  • 14
    • 0034652883 scopus 로고    scopus 로고
    • Jacobi approximation in certain Hilbert space and their applications to singular differential equations
    • Guo Ben-yu, Jacobi approximation in certain Hilbert space and their applications to singular differential equations, J. Math. Anal. Appl. 243 (2000) 373-408.
    • (2000) J. Math. Anal. Appl. , vol.243 , pp. 373-408
    • Guo Ben-yu, A.1
  • 15
    • 0011832388 scopus 로고    scopus 로고
    • Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval
    • to appear
    • Guo Ben-yu, Jie Shen, Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval, Numer. Math., to appear.
    • Numer. Math.
    • Guo Ben-yu, A.1    Jie Shen, A.2
  • 16
    • 0011837596 scopus 로고    scopus 로고
    • A rational approximation and its applications to differential equations on the half line
    • to appear
    • Ben-yu Guo, Jie Shen, Zhong-qing Wang, A rational approximation and its applications to differential equations on the half line, J. Sci. Comp., to appear.
    • J. Sci. Comp.
    • Ben-yu Guo, A.1    Jie Shen, A.2    Zhong-qing Wang, A.3
  • 17
    • 0003543733 scopus 로고
    • Inequalities
    • Cambridge University Press, Cambridge
    • G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, Cambridge University Press, Cambridge, 1952.
    • (1952)
    • Hardy, G.H.1    Littlewood, J.E.2    Pólya, G.3
  • 19
    • 0003401602 scopus 로고
    • Theory of Approximation of Functions of a Real Variable
    • Pergamon, Oxford
    • A.F. Timan, Theory of Approximation of Functions of a Real Variable, Pergamon, Oxford, 1963.
    • (1963)
    • Timan, A.F.1
  • 20
    • 0000818701 scopus 로고
    • The eigenvalues of Hermite and rational spectral differential matrices
    • J.A.C. Weideman, The eigenvalues of Hermite and rational spectral differential matrices, Numer. Math. 61 (1992) 409-432.
    • (1992) Numer. Math. , vol.61 , pp. 409-432
    • Weideman, J.A.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.