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Volumn 116, Issue 1, 2000, Pages 121-143

Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence

Author keywords

34E15; 65L10; 65L12; Adaptivity; Convergence analysis; Singular perturbation

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 0033888151     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00315-5     Document Type: Article
Times cited : (87)

References (21)
  • 1
    • 0000924189 scopus 로고    scopus 로고
    • Reliable and robust a posteriori error estimation for singularly perturbed reaction diffusion problems
    • Ainsworth M., Babuska I. Reliable and robust a posteriori error estimation for singularly perturbed reaction diffusion problems. SIAM J. Numer. Anal. 36:1999;331-353.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 331-353
    • Ainsworth, M.1    Babuska, I.2
  • 2
    • 0022145329 scopus 로고
    • Grading functions and mesh redistribution
    • Carey G.F., Dinh H.T. Grading functions and mesh redistribution. SIAM J. Numer. Anal. 22:1985;1028-1040.
    • (1985) SIAM J. Numer. Anal. , vol.22 , pp. 1028-1040
    • Carey, G.F.1    Dinh, H.T.2
  • 3
    • 0001121137 scopus 로고
    • Simple adaptive grids for 1-D initial value problems
    • Dorfi E.A., Drury L.O'C. Simple adaptive grids for 1-D initial value problems. J. Comput. Phys. 69:1987;175-195.
    • (1987) J. Comput. Phys. , vol.69 , pp. 175-195
    • Dorfi, E.A.1    Drury, L.o'C.2
  • 4
    • 0009522795 scopus 로고
    • Introduction to adaptive methods for differential equations
    • K. Eriksson, D. Estep, P. Hansbo, C. Johnson, Introduction to adaptive methods for differential equations, Acta Numerica (1995) 105-158.
    • (1995) Acta Numerica , pp. 105-158
    • Eriksson, K.1    Estep, D.2    Hansbo, P.3    Johnson, C.4
  • 5
    • 84966250007 scopus 로고
    • Graded-mesh difference schemes for singularly perturbed two-point boundary value problems
    • Gartland E.C. Graded-mesh difference schemes for singularly perturbed two-point boundary value problems. Math. Comp. 51:1988;631-657.
    • (1988) Math. Comp. , vol.51 , pp. 631-657
    • Gartland, E.C.1
  • 6
    • 0028446372 scopus 로고
    • Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle
    • Huang W., Ren Y., Russell R.D. Moving mesh partial differential equations (MMPDEs) based on the equidistribution principle. SIAM J. Numer. Anal. 31:1994;709-730.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 709-730
    • Huang, W.1    Ren, Y.2    Russell, R.D.3
  • 7
    • 0001354685 scopus 로고
    • A simple adaptive grid method in two dimensions
    • Huang W., Sloan D.M. A simple adaptive grid method in two dimensions. SIAM J. Sci. Comput. 15:1994;776-797.
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 776-797
    • Huang, W.1    Sloan, D.M.2
  • 8
    • 84966216257 scopus 로고
    • Analysis of some difference approximations for a singular perturbation problem without turning points
    • Kellogg R.B., Tsan A. Analysis of some difference approximations for a singular perturbation problem without turning points. Math. Comp. 32:1978;1025-1039.
    • (1978) Math. Comp. , vol.32 , pp. 1025-1039
    • Kellogg, R.B.1    Tsan, A.2
  • 9
    • 21844487877 scopus 로고
    • On piecewise-uniform meshes for upwind- And central-difference operators for solving singularly perturbed problems
    • Miller J.J.H., O'Riordan E., Shishkin G.I. On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems. IMA J. Numer. Anal. 15:1995;89-99.
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 89-99
    • Miller, J.J.H.1    O'Riordan, E.2    Shishkin, G.I.3
  • 11
    • 0000990612 scopus 로고    scopus 로고
    • Pseudospectral solutions of near-singular problems using numerical coordinate transformations based on adaptivity
    • Mulholland L.S., Huang W.-Z., Sloan D.M. Pseudospectral solutions of near-singular problems using numerical coordinate transformations based on adaptivity. SIAM J. Sci. Comput. 19(4):1998;1261-1289.
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.4 , pp. 1261-1289
    • Mulholland, L.S.1    Huang, W.-Z.2    Sloan, D.M.3
  • 12
    • 0000123829 scopus 로고    scopus 로고
    • Solution of evolutionary partial differential equations using adaptive finite differences with pseudospectral post-processing
    • Mulholland L.S., Qiu Y., Sloan D.M. Solution of evolutionary partial differential equations using adaptive finite differences with pseudospectral post-processing. J. Comput. Phys. 131:1997;280-298.
    • (1997) J. Comput. Phys. , vol.131 , pp. 280-298
    • Mulholland, L.S.1    Qiu, Y.2    Sloan, D.M.3
  • 13
    • 0032689583 scopus 로고    scopus 로고
    • Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid
    • Qiu Y., Sloan D.M. Analysis of difference approximations to a singularly perturbed two-point boundary value problem on an adaptively generated grid. J. Comput. Appl. Math. 101:1999;1-25.
    • (1999) J. Comput. Appl. Math. , vol.101 , pp. 1-25
    • Qiu, Y.1    Sloan, D.M.2
  • 14
    • 22044433064 scopus 로고    scopus 로고
    • Layer-adapted grids for singular perturbation problems
    • Roos H.-G. Layer-adapted grids for singular perturbation problems. Z. Angew. Math. Mech. 78:1998;291-309.
    • (1998) Z. Angew. Math. Mech. , vol.78 , pp. 291-309
    • Roos, H.-G.1
  • 21
    • 0000342281 scopus 로고
    • On selection of equidistribution meshes for two-point boundary value problems
    • White A.B. On selection of equidistribution meshes for two-point boundary value problems. SIAM J. Numer. Anal. 16:1979;472-502.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 472-502
    • White, A.B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.