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Volumn 166, Issue 1, 2004, Pages 247-266

Discrete approximations of solutions and derivatives for a singularly perturbed parabolic convection-diffusion equation

Author keywords

Approximation of derivatives; Convection diffusion; Finite difference methods; Norms; Parameter uniform convergence; Piecewise uniform meshes; Singularly perturbed parabolic equation

Indexed keywords

APPROXIMATION THEORY; BOUNDARY LAYERS; FINITE DIFFERENCE METHOD; PERTURBATION TECHNIQUES; PIECEWISE LINEAR TECHNIQUES; PROBLEM SOLVING;

EID: 1542425092     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.09.023     Document Type: Article
Times cited : (13)

References (14)
  • 1
    • 0001238824 scopus 로고
    • On the optimization of the methods for solving boundary value problems in the presence of a boundary layer
    • Bakhvalov N.S. On the optimization of the methods for solving boundary value problems in the presence of a boundary layer Zh. Vychisl. Mat. Mat. Fiz. 9 4 1969 841-859
    • (1969) Zh. Vychisl. Mat. Mat. Fiz. , vol.9 , Issue.4 , pp. 841-859
    • Bakhvalov, N.S.1
  • 3
    • 1542408179 scopus 로고    scopus 로고
    • The ε-uniform convergence of the discrete derivatives for singularly perturbed problems
    • TCDMATH 99-07, The School of Mathematics, Trinity College, Dublin
    • P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin, The ε-uniform convergence of the discrete derivatives for singularly perturbed problems, TCDMATH Report Series, TCDMATH 99-07, The School of Mathematics, Trinity College, Dublin, 1999, 13 p.
    • (1999) TCDMATH Report Series , pp. 13
    • Farrell, P.A.1    Hegarty, A.F.2    Miller, J.J.H.3    O'Riordan, E.4    Shishkin, G.I.5
  • 5
    • 1842707147 scopus 로고
    • A difference scheme for a differential equation with a small parameter affecting the highest derivative
    • Il'in A.M. A difference scheme for a differential equation with a small parameter affecting the highest derivative Math. Notes 6 2 1969 596-602
    • (1969) Math. Notes , vol.6 , Issue.2 , pp. 596-602
    • Il'in, A.M.1
  • 6
    • 0003690985 scopus 로고
    • Nauka, Moscow, (in Russian) (translation in English: Translation of Math. Monographs, American Mathematical Society, Providence, RI)
    • O.A. Ladyzhenskaya, V.A. Solonnicov, N.N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (in Russian), (translation in English: Translation of Math. Monographs, Vol. 23, American Mathematical Society, Providence, RI, 1967).
    • (1967) Linear and Quasilinear Equations of Parabolic Type , vol.23
    • Ladyzhenskaya, O.A.1    Solonnicov, V.A.2    Ural'tseva, N.N.3
  • 9
    • 0003940419 scopus 로고
    • Nauka, Moscow, (in Russian), (translation in English: Marcel Dekker, Inc., New York, 2001)
    • A.A. Samarskii, The Theory of Difference Schemes, Nauka, Moscow, 1989 (in Russian), (translation in English: Marcel Dekker, Inc., New York, 2001).
    • (1989) The Theory of Difference Schemes
    • Samarskii, A.A.1
  • 12
    • 1542617404 scopus 로고    scopus 로고
    • Approximation of solutions and of diffusion flows in the case of singularly perturbed boundary value problems with discontinuous initial conditions
    • Shishkin G.I. Approximation of solutions and of diffusion flows in the case of singularly perturbed boundary value problems with discontinuous initial conditions Zh. Vychisl. Mat. Mat. Fiz. 36 9 1996 83-104
    • (1996) Zh. Vychisl. Mat. Mat. Fiz. , vol.36 , Issue.9 , pp. 83-104
    • Shishkin, G.I.1
  • 13
    • 1542408175 scopus 로고    scopus 로고
    • Approximation of solutions and derivatives for a singularly perturbed elliptic convection-diffusion equation
    • Shishkin G.I. Approximation of solutions and derivatives for a singularly perturbed elliptic convection-diffusion equation Zh. Vychisl. Mat. Mat. Fiz. 43 5 2003 671-687
    • (2003) Zh. Vychisl. Mat. Mat. Fiz. , vol.43 , Issue.5 , pp. 671-687
    • Shishkin, G.I.1
  • 14
    • 1542722624 scopus 로고    scopus 로고
    • Approximation of solutions and derivatives for singularly perturbed elliptic convection-diffusion equations
    • Shishkin G.I. Approximation of solutions and derivatives for singularly perturbed elliptic convection-diffusion equations Math. Proc. Royal Irish Acad. 103A 2 2003 169-207
    • (2003) Math. Proc. Royal Irish Acad. , vol.103 A , Issue.2 , pp. 169-207
    • Shishkin, G.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.