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Volumn 188, Issue 1, 2007, Pages 720-733

High order parameter uniform numerical method for singular perturbation problems

Author keywords

Boundary value problems; Finite difference methods; Ordinary differential equations; Shishkin Mesh; Singular perturbation problems

Indexed keywords

BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; NUMERICAL METHODS; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; PIECEWISE LINEAR TECHNIQUES;

EID: 34247604986     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.10.040     Document Type: Article
Times cited : (26)

References (44)
  • 1
    • 0001533213 scopus 로고
    • Relaxation methods applied to determine the motion in 2-D of a viscous fluid past a fixed cylinder
    • Allen D., and Southwell R.V. Relaxation methods applied to determine the motion in 2-D of a viscous fluid past a fixed cylinder. Q. J. Mech. Appl. Math. VIII 2 (1955) 129-145
    • (1955) Q. J. Mech. Appl. Math. , vol.VIII , Issue.2 , pp. 129-145
    • Allen, D.1    Southwell, R.V.2
  • 2
    • 0001238824 scopus 로고
    • Towards optimization of methods for solving boundary value problems in the presence of a boundary layer
    • (in Russian)
    • Bakhvalov N.S. Towards optimization of methods for solving boundary value problems in the presence of a boundary layer. Zh. Vychisl. Mat. Mat. Fiz. 9 (1969) 841-859 (in Russian)
    • (1969) Zh. Vychisl. Mat. Mat. Fiz. , vol.9 , pp. 841-859
    • Bakhvalov, N.S.1
  • 3
    • 0038536333 scopus 로고
    • A variational difference scheme for a boundary value problem with a small parameter in the highest derivative
    • Boglaev I.P. A variational difference scheme for a boundary value problem with a small parameter in the highest derivative. USSR Comput. Math. Math. Phys. 21 4 (1981) 71-81
    • (1981) USSR Comput. Math. Math. Phys. , vol.21 , Issue.4 , pp. 71-81
    • Boglaev, I.P.1
  • 7
    • 0038197646 scopus 로고
    • Uniform fourth order difference scheme for a singular perturbation problem
    • Herceg D. Uniform fourth order difference scheme for a singular perturbation problem. Numer. Math. 56 (1990) 675-693
    • (1990) Numer. Math. , vol.56 , pp. 675-693
    • Herceg, D.1
  • 8
    • 0037102857 scopus 로고    scopus 로고
    • A survey of numerical techniques for solving singulalry perturbed ordinary differential equations
    • Kadalbajoo M.K., and Patidar K.C. A survey of numerical techniques for solving singulalry perturbed ordinary differential equations. Appl. Math. Comp. 130 2-3 (2002) 457-510
    • (2002) Appl. Math. Comp. , vol.130 , Issue.2-3 , pp. 457-510
    • Kadalbajoo, M.K.1    Patidar, K.C.2
  • 9
    • 0037169644 scopus 로고    scopus 로고
    • Singularly perturbed problems in partial differential equations: a survey
    • Kadalbajoo M.K., and Patidar K.C. Singularly perturbed problems in partial differential equations: a survey. Appl. Math. Comp. 134 2-3 (2003) 371-429
    • (2003) Appl. Math. Comp. , vol.134 , Issue.2-3 , pp. 371-429
    • Kadalbajoo, M.K.1    Patidar, K.C.2
  • 13
    • 34247643014 scopus 로고    scopus 로고
    • W. Liniger, R.A. Willoughby, Efficient numerical integration methods for stiff system of differential equations, IBM Research Report RC-1970, 1967.
  • 14
    • 0034436597 scopus 로고    scopus 로고
    • Uniform pointwise convergence on Shishkin type meshes for quasiliner convection diffusion problems
    • Linss T., Roos H.-G., and Vulanović R. Uniform pointwise convergence on Shishkin type meshes for quasiliner convection diffusion problems. SIAM J. Numer. Anal. 38 (2000) 897-912
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 897-912
    • Linss, T.1    Roos, H.-G.2    Vulanović, R.3
  • 15
    • 34247636501 scopus 로고    scopus 로고
    • J.J.H. Miller, Construction of a FEM for a singularly perturbed problem in 2 dimensions, in Numerische Behandlung von Differentialgleichungen, Band 2 (Tagung, Math. Forschungsinst., Oberwolfach, 1975), Int. Ser. Numer. Math., Birkhaüser, Basel, 31 (1976), 165-169.
  • 21
    • 0037859912 scopus 로고
    • On a three-point difference scheme for a singular perturbation problem without a first derivative term I
    • Niijima K. On a three-point difference scheme for a singular perturbation problem without a first derivative term I. Mem. Numer. Math. 7 (1980) 1-10
    • (1980) Mem. Numer. Math. , vol.7 , pp. 1-10
    • Niijima, K.1
  • 24
    • 84966211358 scopus 로고
    • A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion problem
    • O'Riordan E., and Stynes M. 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
  • 25
    • 28444453616 scopus 로고    scopus 로고
    • High order fitted operator numerical method for self-adjoint singular perturbation problems
    • Patidar K.C. High order fitted operator numerical method for self-adjoint singular perturbation problems. Appl. Math. Comp. 171 (2005) 547-566
    • (2005) Appl. Math. Comp. , vol.171 , pp. 547-566
    • Patidar, K.C.1
  • 26
    • 0025208498 scopus 로고
    • Global uniformly convergent schemes for a singularly perturbed boundary-value problem using patched base spline-functions
    • Roos H.-G. Global uniformly convergent schemes for a singularly perturbed boundary-value problem using patched base spline-functions. J. Comput. Appl. Math. 29 1 (1990) 69-77
    • (1990) J. Comput. Appl. Math. , vol.29 , Issue.1 , pp. 69-77
    • Roos, H.-G.1
  • 28
    • 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
  • 29
    • 0344718020 scopus 로고    scopus 로고
    • Sufficient conditions for uniform convergence on layer adapted grids
    • Roos H.-G., and Linss T. Sufficient conditions for uniform convergence on layer adapted grids. Computing 64 (1999) 27-45
    • (1999) Computing , vol.64 , pp. 27-45
    • Roos, H.-G.1    Linss, T.2
  • 30
    • 84966220357 scopus 로고
    • On the finite element method for singularly perturbed reaction diffusion problems in two and one dimension
    • Schatz A.H., and Wahlbin L.B. On the finite element method for singularly perturbed reaction diffusion problems in two and one dimension. Math. Comp. 40 (1983) 47-89
    • (1983) Math. Comp. , vol.40 , pp. 47-89
    • Schatz, A.H.1    Wahlbin, L.B.2
  • 31
    • 0001588439 scopus 로고
    • A difference scheme for a singularly perturbed parabolic equation with a discontinuous boundary condition
    • (in Russian)
    • Shishkin G.I. A difference scheme for a singularly perturbed parabolic equation with a discontinuous boundary condition. Zh. Vychisl. Mat. Mat. Fiz. 28 (1988) 1679-1692 (in Russian)
    • (1988) Zh. Vychisl. Mat. Mat. Fiz. , vol.28 , pp. 1679-1692
    • Shishkin, G.I.1
  • 32
    • 51249175649 scopus 로고
    • A uniformly accurate spline collocation method for a singular perturbation problem
    • Stojanović M. A uniformly accurate spline collocation method for a singular perturbation problem. Calcolo 27 1-2 (1990) 81-88
    • (1990) Calcolo , vol.27 , Issue.1-2 , pp. 81-88
    • Stojanović, M.1
  • 33
    • 0026257239 scopus 로고
    • Exponential splines difference scheme for singular perturbation problem with mixed boundary conditions
    • Stojanović M. Exponential splines difference scheme for singular perturbation problem with mixed boundary conditions. Comm. Appl. Numer. Meth. 7 8 (1991) 625-632
    • (1991) Comm. Appl. Numer. Meth. , vol.7 , Issue.8 , pp. 625-632
    • Stojanović, M.1
  • 34
    • 0031141256 scopus 로고    scopus 로고
    • The midpoint upwind scheme
    • Stynes M., and Roos H.-G. The midpoint upwind scheme. Appl. Numer. Math. 23 (1997) 361-374
    • (1997) Appl. Numer. Math. , vol.23 , pp. 361-374
    • Stynes, M.1    Roos, H.-G.2
  • 35
    • 84977749153 scopus 로고    scopus 로고
    • A jejune heuristic mesh theorem
    • Stynes M. A jejune heuristic mesh theorem. Comput. Meth. Appl. Math. 3 (2003) 488-492
    • (2003) Comput. Meth. Appl. Math. , vol.3 , pp. 488-492
    • Stynes, M.1
  • 36
    • 21844521577 scopus 로고
    • An almost fourth order uniformly convergent difference scheme for a semilinear singlularly perturbed reaction diffusion problem
    • Sun G., and Stynes M. An almost fourth order uniformly convergent difference scheme for a semilinear singlularly perturbed reaction diffusion problem. Numer. Math. 17 (1995) 487-500
    • (1995) Numer. Math. , vol.17 , pp. 487-500
    • Sun, G.1    Stynes, M.2
  • 37
    • 0001741172 scopus 로고
    • On a numerical solution of a type of singularly perturbed boundary value problem by using a special discretization mesh
    • Vulanović R. On a numerical solution of a type of singularly perturbed boundary value problem by using a special discretization mesh. Univ. Novom. Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat 13 (1983) 187-201
    • (1983) Univ. Novom. Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat , vol.13 , pp. 187-201
    • Vulanović, R.1
  • 38
    • 0002560723 scopus 로고
    • A uniform method for quasilinear singular perturbation problems without turning points
    • Vulanović R. A uniform method for quasilinear singular perturbation problems without turning points. Computing 41 (1989) 97-106
    • (1989) Computing , vol.41 , pp. 97-106
    • Vulanović, R.1
  • 39
    • 44949284985 scopus 로고
    • A second order numerical method for nonlinear singular perturbation problems without turning points
    • Vulanović R. A second order numerical method for nonlinear singular perturbation problems without turning points. J. Comput. Math. Math. Phys. 31 (1991) 522-532
    • (1991) J. Comput. Math. Math. Phys. , vol.31 , pp. 522-532
    • Vulanović, R.1
  • 40
    • 34247625880 scopus 로고    scopus 로고
    • R. Vulanović, A uniform numerical method for a class of quasilinear turning point problems, in: J.J.H. Miller, R. Vichnevetsky (Eds.), Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, Dublin, IMACS, 1991, pp. 493.
  • 41
    • 0027677339 scopus 로고
    • Continuous and numerical analysis of a multiple boundary turning point problems
    • Vulanović R., and Farrell P.A. Continuous and numerical analysis of a multiple boundary turning point problems. SIAM J. Numer. Anal. 30 (1993) 1400-1418
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 1400-1418
    • Vulanović, R.1    Farrell, P.A.2
  • 42
    • 21944444650 scopus 로고    scopus 로고
    • Fourth order algorithms for a semilinear singular perturbation problem
    • Vulanović R. Fourth order algorithms for a semilinear singular perturbation problem. Numer. Algor. 16 (1997) 117-128
    • (1997) Numer. Algor. , vol.16 , pp. 117-128
    • Vulanović, R.1
  • 43
    • 0035529772 scopus 로고    scopus 로고
    • A priori meshes for singularly perturbed quasilinear two-point boundary value problems
    • Vulanović R. A priori meshes for singularly perturbed quasilinear two-point boundary value problems. IMA J. Numer. Anal. 21 (2001) 349-366
    • (2001) IMA J. Numer. Anal. , vol.21 , pp. 349-366
    • Vulanović, R.1
  • 44
    • 0035657939 scopus 로고    scopus 로고
    • A higher order scheme for quasilinear boundary value problems with two small parameters
    • Vulanović R. A higher order scheme for quasilinear boundary value problems with two small parameters. Computing 67 (2001) 287-303
    • (2001) Computing , vol.67 , pp. 287-303
    • Vulanović, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.