메뉴 건너뛰기




Volumn 50, Issue SUPPL., 2001, Pages 181-203

On spectral approximations using modified Legendre rational functions: Application to the Korteweg-de Vries equation on the half line

(2)  Guo, Ben Yu a   Shen, Jie a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0041028677     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2001.50.2090     Document Type: Article
Times cited : (60)

References (31)
  • 2
    • 67349095304 scopus 로고    scopus 로고
    • Spectral method
    • (P.G. Ciarlet & L.L. Lions, eds), North-Holland
    • C. BERNARDI & Y. MADAY, Spectral method, In: Handbook of Numerical Analysis, Volume 5 (Part 2) (P.G. Ciarlet & L.L. Lions, eds), North-Holland, 1997.
    • (1997) Handbook of Numerical Analysis , vol.5 , Issue.PART 2
    • Bernardi, C.1    Maday, Y.2
  • 4
    • 0002717130 scopus 로고
    • Orthogonal rational functions on a semi-infinite interval
    • J.P. BOYD, Orthogonal rational functions on a semi-infinite interval, J. Comput. Phys. 70 (1987), 63-88.
    • (1987) J. Comput. Phys. , vol.70 , pp. 63-88
    • Boyd, J.P.1
  • 5
    • 0001718791 scopus 로고
    • Spectral methods using rational basis functions on an infinite interval
    • _, Spectral methods using rational basis functions on an infinite interval, J. Comput. Phys. 69 (1987), 112-142.
    • (1987) J. Comput. Phys. , vol.69 , pp. 112-142
  • 6
    • 0040215429 scopus 로고
    • The soliton and its history
    • (R.K. Bullough & P.J. Caudrey, eds), Springer-Verlag
    • R. K. BULLOUGH & P.J. CAUDREY, The soliton and its history, In: Solitons (R.K. Bullough & P.J. Caudrey, eds), Springer-Verlag, 1980.
    • (1980) Solitons
    • Bullough, R.K.1    Caudrey, P.J.2
  • 9
    • 84990581566 scopus 로고
    • Solitary waves induced by boundary motion
    • C.K. CHU, L.W. XIANG & Y. BARANSKY, Solitary waves induced by boundary motion, CPAM 36 (1983), 495-504.
    • (1983) CPAM , vol.36 , pp. 495-504
    • Chu, C.K.1    Xiang, L.W.2    Baransky, Y.3
  • 11
    • 84966205570 scopus 로고
    • Approximation of some diffusion evolution equations in unbounded domains by Hermite function
    • D. FUNARO & O. KAVIAN, Approximation of some diffusion evolution equations in unbounded domains by Hermite function, Math. Comp. 57 (1990), 597-619.
    • (1990) Math. Comp. , vol.57 , pp. 597-619
    • Funaro, D.1    Kavian, O.2
  • 13
    • 0038868349 scopus 로고
    • Numerical solution of an initial-boundary value problem of the Korteweg-de Vries equation
    • BEN-YU GUO, Numerical solution of an initial-boundary value problem of the Korteweg-de Vries equation, Acta Math. Sci. 5 (1985), 377-348.
    • (1985) Acta Math. Sci. , vol.5 , pp. 377-348
    • Guo, B.-Y.1
  • 14
    • 0000587852 scopus 로고    scopus 로고
    • Gegenbauer approximation and its applications to differential equations on the whole line
    • _, 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
  • 15
    • 0003902398 scopus 로고    scopus 로고
    • World Scientific Publishing Co. Inc., River Edge, NJ
    • _, Spectral methods and their applications, World Scientific Publishing Co. Inc., River Edge, NJ, 1998.
    • (1998) Spectral Methods and their Applications
  • 16
    • 0040633278 scopus 로고    scopus 로고
    • Error estimation of Hermite spectral method for nonlinear partial differential equations
    • _, 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
  • 17
    • 0034652883 scopus 로고    scopus 로고
    • Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations
    • _, Jacobi approximations in certain Hilbert spaces 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
  • 18
    • 0002665809 scopus 로고    scopus 로고
    • Jacobi spectral approximation and its applications to differential equations on the half line
    • _, 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
  • 19
    • 0034369460 scopus 로고    scopus 로고
    • Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval
    • BEN-YU GUO & JIE SHEN, Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval, Numer. Math. 86 (2000), 635-654.
    • (2000) Numer. Math. , vol.86 , pp. 635-654
    • Guo, B.-Y.1    Shen, J.I.E.2
  • 20
    • 0034197003 scopus 로고    scopus 로고
    • A rational approximation and its applications to differential equations on the half line
    • BEN-YU GUO, JIE SHEN & ZHONG-QING WANG, A rational approximation and its applications to differential equations on the half line, J. Sci. Comput. 15 (2000), 117-147.
    • (2000) J. Sci. Comput. , vol.15 , pp. 117-147
    • Guo, B.-Y.1    Shen, J.I.E.2    Wang, Z.-Q.3
  • 21
    • 84875085046 scopus 로고
    • Solitary solution of an initial-boundary value problem of the Korteweg-de Vries equation
    • (C.W. Zang, Z.H. Guo & K.Y. Yeh, eds.), Scientific Press, Beijing
    • BEN-YU GUO & J.C. WEIDEMAN, Solitary solution of an initial-boundary value problem of the Korteweg-de Vries equation, In: Proc. Inter. Conference on Nonlinear Mechanics (C.W. Zang, Z.H. Guo & K.Y. Yeh, eds.), Scientific Press, Beijing, 1985.
    • (1985) Proc. Inter. Conference on Nonlinear Mechanics
    • Guo, B.-Y.1    Weideman, J.C.2
  • 23
    • 0039461207 scopus 로고
    • Convergence of methods for the numerical solution of Korteweg-de Vries equation
    • PEN-YU KUO & J.M. SANZ SERNA, Convergence of methods for the numerical solution of Korteweg-de Vries equation, IMA J. Numer. Anal. 1 (1981), 215-221.
    • (1981) IMA J. Numer. Anal. , vol.1 , pp. 215-221
    • Kuo, P.-Y.1    Serna, J.M.S.2
  • 24
    • 0011622839 scopus 로고
    • Numerical solution of K.d.V. Equation
    • PEN-YU KUO & HUA-MO WU, Numerical solution of K.d.V. equation, J. Math. Anal. Appl. 81 (1981), 334-345.
    • (1981) J. Math. Anal. Appl. , vol.81 , pp. 334-345
    • Kuo, P.-Y.1    Wu, H.-M.2
  • 25
    • 0000991407 scopus 로고
    • Almost periodic solutions of the K.d.V. Equation
    • P.D. LAX, Almost periodic solutions of the K.d.V. equation, SIAM Review 18 (1976), 351-375.
    • (1976) SIAM Review , vol.18 , pp. 351-375
    • Lax, P.D.1
  • 27
    • 0034432262 scopus 로고    scopus 로고
    • Stable and efficient spectral methods in unbounded domains using Laguerre functions
    • JIE SHEN, Stable and efficient spectral methods in unbounded domains using Laguerre functions, SIAM J. Numer Anal. 38 (2000), 1113-1133.
    • (2000) SIAM J. Numer Anal. , vol.38 , pp. 1113-1133
    • Shen, J.I.E.1
  • 29
    • 0000600898 scopus 로고
    • Sur un problème non linéaire
    • R. TEMAM, Sur un problème non linéaire, J. Math. Pures Appl. 48 (1969). 159-172.
    • (1969) J. Math. Pures Appl. , vol.48 , pp. 159-172
    • Temam, R.1
  • 30
    • 0009389147 scopus 로고
    • Initial-boundary value problem of the Korteweg-de Vries equation
    • BUI AN TON, Initial-boundary value problem of the Korteweg-de Vries equation, J. of Differential Equations 25 (1977), 288-309.
    • (1977) J. of Differential Equations , vol.25 , pp. 288-309
    • Bui An, T.O.N.1
  • 31
    • 33846361348 scopus 로고
    • Interaction of solitons in a collisionlessplasma and the recurrence of initial states
    • N.J. ZABUSKY & M.D. KRUSKAL, Interaction of solitons in a collisionlessplasma and the recurrence of initial states, Phys. Lett. 15 (1965), 240-243.
    • (1965) Phys. Lett. , vol.15 , pp. 240-243
    • Zabusky, N.J.1    Kruskal, M.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.