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Volumn 98, Issue 2-3, 1999, Pages 119-137

Improvement of numerical solution of self-adjoint singular perturbation problems by incorporation of asymptotic approximations

Author keywords

Asymptotic approximation; Boundary layer; Finite difference scheme; Self adjoint boundary value problem; Singular perturbation

Indexed keywords

BOUNDARY LAYERS; BOUNDARY VALUE PROBLEMS; FINITE DIFFERENCE METHOD; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; DIFFERENTIAL EQUATIONS;

EID: 28844504374     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(97)10167-9     Document Type: Article
Times cited : (17)

References (19)
  • 2
    • 0037859915 scopus 로고
    • On the convergence, uniformly in ε, of difference schemes for a two-point boundary value singular perturbation problem
    • P.W. Hemker, J.J.H. Miller (Eds.), Academic Press, New York
    • J.J.H. Miller, On the convergence, uniformly in ε, of difference schemes for a two-point boundary value singular perturbation problem, in:P.W. Hemker, J.J.H. Miller (Eds.), Numerical Analysis of Singular Perturbation Problem, Academic Press, New York, 1979, pp. 467-474.
    • (1979) Numerical Analysis of Singular Perturbation Problem , pp. 467-474
    • Miller, J.J.H.1
  • 4
    • 0037859912 scopus 로고
    • On a three-point difference scheme for a singular perturbation problem without a first derivative term I
    • K. Niijima, On a three-point difference scheme for a singular perturbation problem without a first derivative term I, Mere. Numer. Math. 7 (1980) 1-10.
    • (1980) Mere. Numer. Math. , vol.7 , pp. 1-10
    • Niijima, K.1
  • 5
    • 0038536333 scopus 로고
    • A variational difference scheme for a boundary value problem with a small parameter in the highest derivative
    • I.P. Boglaev, A variational difference scheme for a boundary value problem with a small parameter in the highest derivative, U.S.S.R. Comput. Math. Math. Phys. 21 (4) (1981) 71-81.
    • (1981) U.S.S.R. Comput. Math. Math. Phys. , vol.21 , Issue.4 , pp. 71-81
    • Boglaev, I.P.1
  • 6
    • 0038536334 scopus 로고
    • A difference scheme on a non-uniform mesh for a differential equation with a small parameter in the highest derivative
    • G.I. Shishkin, A difference scheme on a non-uniform mesh for a differential equation with a small parameter in the highest derivative, U.S.S.R. Comput. Math. Math. Phys. 23 (3) (1983) 59-66.
    • (1983) U.S.S.R. Comput. Math. Math. Phys. , vol.23 , Issue.3 , pp. 59-66
    • Shishkin, G.I.1
  • 8
    • 84966211358 scopus 로고
    • A uniformly accurate finite element method for a singularly perturbed one-dimensional reaction diffusion problem
    • E. O'Riordan, M. Stynes, A uniformly accurate finite element method for a singularly perturbed one-dimensional reaction diffusion problem, Math. Comp. 47 (1986) 555-570.
    • (1986) Math. Comp. , vol.47 , pp. 555-570
    • O'Riordan, E.1    Stynes, M.2
  • 9
    • 0002597533 scopus 로고
    • Solving singularly perturbed boundary value problems by spline in tension
    • K. Surla, M. Stojanovic, Solving singularly perturbed boundary value problems by spline in tension, J. Comput. Appl. Math. 24 (1988) 355-363.
    • (1988) J. Comput. Appl. Math. , vol.24 , pp. 355-363
    • Surla, K.1    Stojanovic, M.2
  • 10
    • 21844521577 scopus 로고
    • An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction-diffusion problem
    • G. Sun, M. Stynes, An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction-diffusion problem, Numer. Math. 70 (1995) 487-500.
    • (1995) Numer. Math. , vol.70 , pp. 487-500
    • Sun, G.1    Stynes, M.2
  • 11
    • 0010962908 scopus 로고
    • Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations
    • M. Israeli, M. Ungarish, Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations, Numer. Math. 39 (1982) 309-324.
    • (1982) Numer. Math. , vol.39 , pp. 309-324
    • Israeli, M.1    Ungarish, M.2
  • 12
    • 84965000983 scopus 로고
    • The numerical solution of boundary value problems for stiff differential equations
    • J.E. Flaherty, R.E. O'Malley, The numerical solution of boundary value problems for stiff differential equations, Math. Comp. 31 (1977) 66-93.
    • (1977) Math. Comp. , vol.31 , pp. 66-93
    • Flaherty, J.E.1    O'Malley, R.E.2
  • 15
    • 0038197646 scopus 로고
    • Uniform fourth order difference scheme for a singular perturbation problem
    • D. Herceg, Uniform fourth order difference scheme for a singular perturbation problem, Numer. Math. 56 (1990) 675493.
    • (1990) Numer. Math. , vol.56 , pp. 675493
    • Herceg, D.1
  • 16
    • 85171875513 scopus 로고
    • On a differential equation of boundary layer type
    • C.E. Pearson, On a differential equation of boundary layer type, J. Math Phys. 47 (1968) 134-154.
    • (1968) J. Math Phys. , vol.47 , pp. 134-154
  • 17
    • 0025468490 scopus 로고
    • Initial value methods for second order singularly perturbed boundary value problems
    • M.G. Gasparo, M. Macconi, Initial value methods for second order singularly perturbed boundary value problems, J. Optim. Theory Appl. 66 (2) (1990) 197-210.
    • (1990) J. Optim. Theory Appl. , vol.66 , Issue.2 , pp. 197-210
    • Gasparo, M.G.1    Macconi, M.2
  • 18
    • 0026883117 scopus 로고
    • Parallel initial value algorithms for singularly perturbed boundary value problems
    • M.G. Gasparo, M. Macconi, Parallel initial value algorithms for singularly perturbed boundary value problems, J. Optim. Theory Appl. 73 (3) (1992) 501-517.
    • (1992) J. Optim. Theory Appl. , vol.73 , Issue.3 , pp. 501-517
    • Gasparo, M.G.1    Macconi, M.2
  • 19
    • 0020148074 scopus 로고
    • A boundary value technique for singular perturbation problems
    • S.M. Roberts, A boundary value technique for singular perturbation problems, J. Math. Anal. Appl. 87 (1982) 489-508.
    • (1982) J. Math. Anal. Appl. , vol.87 , pp. 489-508
    • Roberts, S.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.