메뉴 건너뛰기




Volumn 46, Issue 2-3, 2003, Pages 463-478

Asymptotic Numerical Methods for Singularly Perturbed Fourth-Order Ordinary Differential Equations of Reaction-Diffusion Type

Author keywords

Asymptotic expansion; Boundary layer; Boundary value technique; Exponentially fitted finite difference scheme; Finite difference scheme; Fitted mesh method; Fitted operator method; Fourth order ordinary differential equation; Singularly perturbed problems

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 0141639668     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)90039-3     Document Type: Article
Times cited : (19)

References (28)
  • 4
    • 0002841322 scopus 로고
    • Differential inequalities of higher order and the asymptotic solution of nonlinear boundary value problems
    • F.A. Howes, Differential inequalities of higher order and the asymptotic solution of nonlinear boundary value problems, SIAM J. Math. Anal. 13 (1), 61-80, (1982).
    • (1982) SIAM J. Math. Anal. , vol.13 , Issue.1 , pp. 61-80
    • Howes, F.A.1
  • 5
    • 0020830910 scopus 로고
    • The asymptotic solution of a class of third-order boundary value problem arising in the theory of thin film flow
    • F.A. Howes, The asymptotic solution of a class of third-order boundary value problem arising in the theory of thin film flow, SIAM J. Appl. Math. 43 (5), 993-1004, (1983).
    • (1983) SIAM J. Appl. Math. , vol.43 , Issue.5 , pp. 993-1004
    • Howes, F.A.1
  • 6
    • 44949286572 scopus 로고
    • Singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations
    • W. Zhao, Singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations, Journal of Differential Equations 88 (2), 265-278, (1990).
    • (1990) Journal of Differential Equations , vol.88 , Issue.2 , pp. 265-278
    • Zhao, W.1
  • 7
    • 43949158123 scopus 로고
    • Singularly perturbed higher order boundary value problems
    • M. Feckan, Singularly perturbed higher order boundary value problems, Journal of Differential Equations III (1), 79-102, (1994).
    • (1994) Journal of Differential Equations , vol.3 , Issue.1 , pp. 79-102
    • Feckan, M.1
  • 8
    • 0002621486 scopus 로고
    • A uniformly convergent discretization method for a fourth order singular perturbation problem
    • H.G. Roos and M. Stynes, A uniformly convergent discretization method for a fourth order singular perturbation problem, Bonner Math. Schriften 228, 30-40, (1991).
    • (1991) Bonner Math. Schriften , vol.228 , pp. 30-40
    • Roos, H.G.1    Stynes, M.2
  • 9
    • 0001417004 scopus 로고
    • The uniform stability of singularly perturbed discrete and continuous boundary value problems
    • K. Niederdrenk and H. Yserentant, The uniform stability of singularly perturbed discrete and continuous boundary value problems, Numer. Math. 41, 223-253, (1983).
    • (1983) Numer. Math. , vol.41 , pp. 223-253
    • Niederdrenk, K.1    Yserentant, H.2
  • 10
    • 84966250007 scopus 로고
    • Graded-mesh difference schemes for singularly perturbed two-point boundary value problems
    • E.C. Gartland, Graded-mesh difference schemes for singularly perturbed two-point boundary value problems, Math. Comput. 51, 631-657, (1988).
    • (1988) Math. Comput. , vol.51 , pp. 631-657
    • Gartland, E.C.1
  • 11
    • 21844493134 scopus 로고
    • Finite element methods for singularly perturbed higher order elliptic two point boundary value problems I: Reaction-diffusion type
    • G. Sun and M. Stynes,. Finite element methods for singularly perturbed higher order elliptic two point boundary value problems I: Reaction-diffusion type, IMA J. Numer. Anal. 15, 117-139, (1995).
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 117-139
    • Sun, G.1    Stynes, M.2
  • 12
    • 0002514558 scopus 로고
    • Locking in finite element approximation of long thin extensible beams
    • B. Semper, Locking in finite element approximation of long thin extensible beams, IMA J. Numer. Anal. 14, 97-109, (1994).
    • (1994) IMA J. Numer. Anal. , vol.14 , pp. 97-109
    • Semper, B.1
  • 13
    • 0024067689 scopus 로고
    • Further examples of the boundary value technique in singular perturbation problems
    • S.M. Roberts, Further examples of the boundary value technique in singular perturbation problems, Journal of Mathematical Analysis and Applications 133, 411-436, (1988).
    • (1988) Journal of Mathematical Analysis and Applications , vol.133 , pp. 411-436
    • Roberts, S.M.1
  • 14
    • 0020148074 scopus 로고
    • A boundary value technique for singular perturbation problems
    • S.M. Roberts, A boundary value technique for singular perturbation problems, J. of Mathematical Analysis and Applications 87, 489-508, (1982).
    • (1982) J. of Mathematical Analysis and Applications , vol.87 , pp. 489-508
    • Roberts, S.M.1
  • 15
    • 38249001630 scopus 로고
    • A computational method for solving singular perturbation problems
    • J. Jayakumar and N. Ramanujam, A computational method for solving singular perturbation problems, Applied Mathematics and Computation 55, 31-48, (1993).
    • (1993) Applied Mathematics and Computation , vol.55 , pp. 31-48
    • Jayakumar, J.1    Ramanujam, N.2
  • 16
    • 38149145154 scopus 로고
    • A numerical method for singular perturbation problems arising in chemical reactor theory
    • J. Jayakumar and N. Ramanujam, A numerical method for singular perturbation problems arising in chemical reactor theory, Computers Math. Applic. 27 (5), 83-99, (1994).
    • (1994) Computers Math. Applic. , vol.27 , Issue.5 , pp. 83-99
    • Jayakumar, J.1    Ramanujam, N.2
  • 17
    • 0001113796 scopus 로고    scopus 로고
    • A computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers
    • S. Natesan and N. Ramanujam, A computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers, Appl. Math. Computation 93, 259-275, (1998).
    • (1998) Appl. Math. Computation , vol.93 , pp. 259-275
    • Natesan, S.1    Ramanujam, N.2
  • 22
    • 38249038259 scopus 로고
    • Numerical treatment of singularly perturbed two-point boundary-value problems
    • M.K. Khadalbajoo and Y.N. Reddy, Numerical treatment of singularly perturbed two-point boundary-value problems, Applied Mathematics and Computation 21, 93-110, (1987).
    • (1987) Applied Mathematics and Computation , vol.21 , pp. 93-110
    • Khadalbajoo, M.K.1    Reddy, Y.N.2
  • 23
    • 0001504930 scopus 로고
    • Approximate methods for the numerical solution of singular perturbation problems
    • M.K. Khadalbajoo and Y.N. Reddy, Approximate methods for the numerical solution of singular perturbation problems, Applied Mathematics and Computation 21, 85-199, (1987).
    • (1987) Applied Mathematics and Computation , vol.21 , pp. 85-199
    • Khadalbajoo, M.K.1    Reddy, Y.N.2
  • 25
    • 0001125929 scopus 로고
    • Sufficient conditions for uniform convergence of a class of difference schemes for a singular perturbation problem
    • P.A. Farrell, Sufficient conditions for uniform convergence of a class of difference schemes for a singular perturbation problem, IMA J. Numer. Anal. 7, 459-472, (1987).
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 459-472
    • Farrell, P.A.1
  • 27
    • 0003223008 scopus 로고
    • Singular perturbation problems for systems of PDEs of elliptic type
    • September
    • N. Ramanujam and U.N. Srivastava, Singular perturbation problems for systems of PDEs of elliptic type, JMAA 71 (1), (September 1979).
    • (1979) JMAA , vol.71 , Issue.1
    • Ramanujam, N.1    Srivastava, U.N.2
  • 28
    • 0003213179 scopus 로고
    • Singular perturbation problems for systems of partial differential equations of parabolic type
    • December
    • N. Ramanujam and U.N. Srivastava, Singular perturbation problems for systems of partial differential equations of parabolic type, Funkcialaj Ekvacioj 23 (3), (December 1980).
    • (1980) Funkcialaj Ekvacioj , vol.23 , Issue.3
    • Ramanujam, N.1    Srivastava, U.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.