메뉴 건너뛰기




Volumn 43, Issue 6, 2006, Pages 2607-2623

Galerkin methods based on Hermite splines for singular perturbation problems

Author keywords

Galerkin methods; Grid meshes; Hermite splines; Optimal order of uniform convergence; Singular perturbation

Indexed keywords

GRID MESHES; HERMITE SPLINES; OPTIMAL ORDER; SINGULAR PERTURBATION; UNIFORM CONVERGENCE;

EID: 33750306364     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040607411     Document Type: Article
Times cited : (20)

References (23)
  • 1
    • 0001238824 scopus 로고
    • K optimizacii methdov resenia kraevyh. zadac prinalicii pogranicnogo sloja
    • [B]
    • [B] A. S. BAKHVALOV, K optimizacii methdov resenia kraevyh. zadac prinalicii pogranicnogo sloja., Zh. Vychisl. Mat. Mat. Fiz., 9 (1969), pp. 841-859.
    • (1969) Zh. Vychisl. Mat. Mat. Fiz. , vol.9 , pp. 841-859
    • Bakhvalov, A.S.1
  • 3
    • 1842459288 scopus 로고    scopus 로고
    • A hybrid collocation method for Volterra integral equations with weakly singular kernels
    • [CHX]
    • [CHX] Y. Z. CAO, T. HERDMAN, AND Y. XU, A hybrid collocation method for Volterra integral equations with weakly singular kernels, SIAM J. Numer. Anal., 41 (2003), pp. 364-381.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 364-381
    • Cao, Y.Z.1    Herdman, T.2    Xu, Y.3
  • 4
    • 84966250007 scopus 로고
    • Graded-mesh difference schemes for singularly perturbed to-point boundary value problems
    • [G]
    • [G] E. C. GARTLAND, Graded-mesh difference schemes for singularly perturbed to-point boundary value problems, Math. Comp., 51 (1988), pp. 631-657.
    • (1988) Math. Comp. , vol.51 , pp. 631-657
    • Gartland, E.C.1
  • 7
    • 33745649909 scopus 로고    scopus 로고
    • Wavelet bases of Hermite cubic splines on the interval
    • [JL], to appear
    • [JL] R. Q. JIA AND S. T. Liu, Wavelet bases of Hermite cubic splines on the interval, Adv. Comput. Math., to appear.
    • Adv. Comput. Math.
    • Jia, R.Q.1    Liu, S.T.2
  • 8
    • 0034347979 scopus 로고    scopus 로고
    • Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem
    • [L]
    • [L] T. LINSS, Analysis of a Galerkin finite element method on a Bakhvalov-Shishkin mesh for a linear convection-diffusion problem, IMA J. Numer. Anal., 20 (2000), pp. 621-632
    • (2000) IMA J. Numer. Anal. , vol.20 , pp. 621-632
    • Linss, T.1
  • 9
    • 0035425658 scopus 로고    scopus 로고
    • Error analysis for a Galerkin-spectral method with coordinate transformation for solving singularly perturbed problems
    • [LT]
    • [LT] W. LIU AND T. TANG, Error analysis for a Galerkin-spectral method with coordinate transformation for solving singularly perturbed problems, Appl. Numer. Math., 38 (2001). pp. 315-345.
    • (2001) Appl. Numer. Math. , vol.38 , pp. 315-345
    • Liu, W.1    Tang, T.2
  • 12
    • 0032689583 scopus 로고    scopus 로고
    • Analysis of difference approximations to a singular perturbated two-point boundary value problem on an adaptively generated grid
    • [QS]
    • [QS] Y. QIU AND D. M. SLOAN, Analysis of difference approximations to a singular perturbated two-point boundary value problem on an adaptively generated grid, J. Comput. Appl. Math., 101 (1999), pp. 1-25.
    • (1999) J. Comput. Appl. Math. , vol.101 , pp. 1-25
    • Qiu, Y.1    Sloan, D.M.2
  • 13
    • 0033888151 scopus 로고    scopus 로고
    • Numerical solution of a singularly perturbated two-point boundary value problem using equidistribution: Analysis of convergence
    • [QST]
    • [QST] Y. QIU, D.M. SLOAN, AND T. TANG, Numerical solution of a singularly perturbated two-point boundary value problem using equidistribution: Analysis of convergence, J. Comput. Appl. Math., 116 (2000), pp. 121-143.
    • (2000) J. Comput. Appl. Math. , vol.116 , pp. 121-143
    • Qiu, Y.1    Sloan, D.M.2    Tang, T.3
  • 14
    • 0344718020 scopus 로고    scopus 로고
    • Sufficient conditions for uniform convergence on layer-adapted grids
    • [RL]
    • [RL] H. G. ROOS AND T. LINSS, Sufficient conditions for uniform convergence on layer-adapted grids, Computing, 63 (1999), pp. 27-45.
    • (1999) Computing , vol.63 , pp. 27-45
    • Roos, H.G.1    Linss, T.2
  • 17
    • 84961479437 scopus 로고
    • Grid approximation of singularly perturbed parabolic equations with internal layers
    • [S]
    • [S] G. I. SHISHKIN, Grid approximation of singularly perturbed parabolic equations with internal layers, Sov. J. Numer. Anal. Math. Model., 3 (1988), pp. 393-407.
    • (1988) Sov. J. Numer. Anal. Math. Model. , vol.3 , pp. 393-407
    • Shishkin, G.I.1
  • 18
    • 0002945582 scopus 로고
    • A finite element method for a singularly perturbed boundary value problem
    • [SO1I]
    • [SO1I] M. STYNES AND E. O'RIORDAN, A finite element method for a singularly perturbed boundary value problem, Numer. Math., 50 (1986), pp. 1-15.
    • (1986) Numer. Math. , vol.50 , pp. 1-15
    • Stynes, M.1    O'Riordan, E.2
  • 19
    • 84966249957 scopus 로고
    • An analysis of a singularly perturbed two-point boundary value problem using only finite element techniques
    • [SO2]
    • [SO2] M. STYNES AND E. O'RIORDAN, An analysis of a singularly perturbed two-point boundary value problem using only finite element techniques, Math. Comp., 56 (1991), pp. 663-675.
    • (1991) Math. Comp. , vol.56 , pp. 663-675
    • Stynes, M.1    O'Riordan, E.2
  • 20
    • 21844493134 scopus 로고
    • Finite element methods for singularly perturbed high-order elliptic two-point boundary problems, I: Reaction-diffusion-type problems
    • [SS1]
    • [SS1] G. SUN AND M. STYNES, Finite element methods for singularly perturbed high-order elliptic two-point boundary problems, I: Reaction-diffusion-type problems, IMA J. Numer. Anal., 15 (1995), pp. 117-139.
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 117-139
    • Sun, G.1    Stynes, M.2
  • 21
    • 21844506775 scopus 로고
    • Finite element methods for singularly perturbed high-order elliptic two-point boundary problems, II: Convection-diffusion-type problems
    • [SS2]
    • [SS2] G. SUN AND M. STYNES, Finite element methods for singularly perturbed high-order elliptic two-point boundary problems, II: Convection-diffusion-type problems, IMA J. Numer. Anal., 15 (1995), pp. 197-219.
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 197-219
    • Sun, G.1    Stynes, M.2
  • 22
    • 0001581262 scopus 로고    scopus 로고
    • Boundary layer resolving pseudospectral methods for singular perturbation problems
    • [TT]
    • [TT] T. TANG AND M. R. TRUMMER, Boundary layer resolving pseudospectral methods for singular perturbation problems, SIAM J. Sci. Comput., 17 (1996), pp. 430-438.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 430-438
    • Tang, T.1    Trummer, M.R.2
  • 23
    • 84983920897 scopus 로고
    • Non-equidistant generalizations of the Gushchin-Shchennikov scheme
    • [V]
    • [V] R. VULANOVIC, Non-equidistant generalizations of the Gushchin-Shchennikov scheme, Z. Angew. Math. Mec., 67 (1987), pp. 625-632.
    • (1987) Z. Angew. Math. Mec. , vol.67 , pp. 625-632
    • Vulanovic, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.