메뉴 건너뛰기




Volumn 39, Issue 2, 2002, Pages 647-667

Numerical methods for time-periodic solutions of nonlinear parabolic boundary value problems

Author keywords

Convergence; Error estimates; Finite difference equations; Monotone iterations; Reaction diffusion convection equation; Time periodic solution

Indexed keywords


EID: 0035322502     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142999361396     Document Type: Article
Times cited : (25)

References (27)
  • 1
    • 0002312007 scopus 로고
    • Periodic solutions of semilinear parabolic equations
    • Academic Press, New York
    • H. AMANN, Periodic solutions of semilinear parabolic equations, in Nonlinear Analysis, Academic Press, New York, 1978, pp. 1-29.
    • (1978) Nonlinear Analysis , pp. 1-29
    • Amann, H.1
  • 3
    • 0002360528 scopus 로고
    • Periodic solutions of a quasilinear parabolic differential equation
    • D. W. BANGE, Periodic solutions of a quasilinear parabolic differential equation, J. Differential Equations, 17 (1975), pp. 61-72.
    • (1975) J. Differential Equations , vol.17 , pp. 61-72
    • Bange, D.W.1
  • 4
    • 0016327621 scopus 로고
    • On least squares methods for parabolic equations and the computation of time-periodic solutions
    • A. CARASSO, On least squares methods for parabolic equations and the computation of time-periodic solutions, SIAM J. Numer. Anal., 11 (1974), pp. 1181-1192.
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 1181-1192
    • Carasso, A.1
  • 6
    • 0000755977 scopus 로고    scopus 로고
    • Asymptotic periodicity in logistic equations with discrete delays
    • W. FENG AND X. LU, Asymptotic periodicity in logistic equations with discrete delays, Nonlinear Anal., 26 (1996), pp. 171-178.
    • (1996) Nonlinear Anal. , vol.26 , pp. 171-178
    • Feng, W.1    Lu, X.2
  • 7
    • 0001703525 scopus 로고
    • Solutions of parabolic boundary problems existing for all times
    • P. FIVE, Solutions of parabolic boundary problems existing for all times, Arch. Ration. Mech. Anal., 16 (1964), pp. 155-186.
    • (1964) Arch. Ration. Mech. Anal. , vol.16 , pp. 155-186
    • Five, P.1
  • 8
    • 0042755616 scopus 로고
    • Fast numerical solution of time-periodic parabolic problems by a multigrid method
    • W. HACKBUSCH, Fast numerical solution of time-periodic parabolic problems by a multigrid method, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 198-206.
    • (1981) SIAM J. Sci. Statist. Comput. , vol.2 , pp. 198-206
    • Hackbusch, W.1
  • 11
    • 0001210677 scopus 로고
    • Periodic solutions of quasilinear parabolic equations of second order
    • Ju. S. KOLESOV, Periodic solutions of quasilinear parabolic equations of second order, Trans. Moscow Math. Soc., 21 (1970), pp. 114-146.
    • (1970) Trans. Moscow Math. Soc. , vol.21 , pp. 114-146
    • Kolesov, Ju.S.1
  • 12
    • 0041753684 scopus 로고
    • Periodic solutions of the first boundary value problem for quasilinear parabolic equations of second order
    • T. KUSANO, Periodic solutions of the first boundary value problem for quasilinear parabolic equations of second order, Funkcial. Ekvac., 9 (1966), pp. 129-137.
    • (1966) Funkcial. Ekvac. , vol.9 , pp. 129-137
    • Kusano, T.1
  • 13
    • 0001639797 scopus 로고    scopus 로고
    • An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions
    • K. LUST, D. ROOSE, A. SPENCE, AND A. R. CHAMPNEYS, An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions, SIAM J. Sci. Comp., 19 (1998), pp. 1188-1209.
    • (1998) SIAM J. Sci. Comp. , vol.19 , pp. 1188-1209
    • Lust, K.1    Roose, D.2    Spence, A.3    Champneys, A.R.4
  • 14
    • 0007187862 scopus 로고
    • On boundedness, periodicity, and almost periodicity of solutions of some nonlinear parabolic equations
    • M. NAKAO, On boundedness, periodicity, and almost periodicity of solutions of some nonlinear parabolic equations, J. Differential Equations, 19 (1975), pp. 371-385.
    • (1975) J. Differential Equations , vol.19 , pp. 371-385
    • Nakao, M.1
  • 16
    • 0043256726 scopus 로고
    • The numerical solution of a periodic parabolic problem subject to a nonlinear boundary condition, II
    • M. R. OSBORNE, The numerical solution of a periodic parabolic problem subject to a nonlinear boundary condition, II, Numer. Math., 12 (1968), pp. 280-287.
    • (1968) Numer. Math. , vol.12 , pp. 280-287
    • Osborne, M.R.1
  • 18
    • 0001978569 scopus 로고    scopus 로고
    • Blowing-up and asymptotic behavior of solutions for a finite difference system
    • C. V. PAO, Blowing-up and asymptotic behavior of solutions for a finite difference system, J. Appl. Anal., 62 (1996), pp. 29-38.
    • (1996) J. Appl. Anal. , vol.62 , pp. 29-38
    • Pao, C.V.1
  • 19
    • 0023288133 scopus 로고
    • Numerical methods for semilinear parabolic equations
    • C. V. PAO, Numerical methods for semilinear parabolic equations, SIAM J. Numer. Anal., 24 (1987), pp. 24-35.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 24-35
    • Pao, C.V.1
  • 20
    • 84985415686 scopus 로고
    • Finite difference reaction diffusion equations with nonlinear boundary conditions
    • C. V. PAO, Finite difference reaction diffusion equations with nonlinear boundary conditions, Numer. Methods Partial Differential Equations, 11 (1995), pp. 355-374.
    • (1995) Numer. Methods Partial Differential Equations , vol.11 , pp. 355-374
    • Pao, C.V.1
  • 21
    • 0001326901 scopus 로고    scopus 로고
    • Periodic solutions of parabolic systems with nonlinear boundary conditions
    • C. V. PAO, Periodic solutions of parabolic systems with nonlinear boundary conditions, J. Math. Anal. Appl., 36 (1999), pp. 393-416.
    • (1999) J. Math. Anal. Appl. , vol.36 , pp. 393-416
    • Pao, C.V.1
  • 23
    • 0042755609 scopus 로고
    • The existence, computation, and number of solutions of periodic parabolic problems
    • M. STEUERWALT, The existence, computation, and number of solutions of periodic parabolic problems, SIAM J. Numer. Anal., 16 (1979), pp. 402-420.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 402-420
    • Steuerwalt, M.1
  • 24
    • 0007249039 scopus 로고
    • Periodic solutions of nonlinear parabolic differential equations
    • L. Y. TSAI, Periodic solutions of nonlinear parabolic differential equations, Bull. Inst. Math. Acad Sinica, 5 (1977), pp. 219-247.
    • (1977) Bull. Inst. Math. Acad Sinica , vol.5 , pp. 219-247
    • Tsai, L.Y.1
  • 25
    • 0027543989 scopus 로고
    • On dynamic iteration methods for solving time-periodic differential equations
    • S. VANDEWALLE AND R. PIESSENS, On dynamic iteration methods for solving time-periodic differential equations, SIAM J. Numer. Anal., 30 (1993), pp. 286-303.
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 286-303
    • Vandewalle, S.1    Piessens, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.