메뉴 건너뛰기




Volumn 175, Issue 1, 2006, Pages 864-890

ε-Uniformly convergent non-standard finite difference methods for singularly perturbed differential difference equations with small delay

Author keywords

Boundary value problems; Differential difference equations; Non standard finite difference methods; Singular perturbations

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 33644911223     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.08.006     Document Type: Article
Times cited : (39)

References (29)
  • 1
    • 0035449292 scopus 로고    scopus 로고
    • Contributions to the mathematics of the nonstandard finite difference method and applications
    • R. Anguelov, and J.M.-S. Lubuma Contributions to the mathematics of the nonstandard finite difference method and applications Numerical Methods for Partial Differential Equations 17 2001 518 543
    • (2001) Numerical Methods for Partial Differential Equations , vol.17 , pp. 518-543
    • Anguelov, R.1    Lubuma, J.M.-S.2
  • 3
    • 0037472545 scopus 로고    scopus 로고
    • Nonstandard finite difference method by nonlocal approximation
    • R. Anguelov, and J.M.-S. Lubuma Nonstandard finite difference method by nonlocal approximation Mathematics and Computers in Simulation 61 3-6 2003 465 475
    • (2003) Mathematics and Computers in Simulation , vol.61 , Issue.3-6 , pp. 465-475
    • Anguelov, R.1    Lubuma, J.M.-S.2
  • 4
    • 0141957345 scopus 로고    scopus 로고
    • Applications of nonstandard finite difference models to computational electromagnetics
    • J.B. Cole, and S. Banerjee Applications of nonstandard finite difference models to computational electromagnetics Journal of Difference Equations and Applications 9 12 2003 1099 1112
    • (2003) Journal of Difference Equations and Applications , vol.9 , Issue.12 , pp. 1099-1112
    • Cole, J.B.1    Banerjee, S.2
  • 7
    • 0012701774 scopus 로고    scopus 로고
    • Non-standard discretization methods for some biological models
    • R.E. Mickens World Scientific Singapore
    • H. Al-Kahby, F. Dannan, and S. Elaydi Non-standard discretization methods for some biological models R.E. Mickens Applications of Nonstandard Finite Difference Schemes 2000 World Scientific Singapore 155 180
    • (2000) Applications of Nonstandard Finite Difference Schemes , pp. 155-180
    • Al-Kahby, H.1    Dannan, F.2    Elaydi, S.3
  • 10
    • 0141792568 scopus 로고    scopus 로고
    • A nonstandard finite difference scheme for nonlinear heat transfer in a thin finite rod
    • P.M. Jordan A nonstandard finite difference scheme for nonlinear heat transfer in a thin finite rod Journal of Difference Equations and Applications 9 11 2003 1015 1021
    • (2003) Journal of Difference Equations and Applications , vol.9 , Issue.11 , pp. 1015-1021
    • Jordan, P.M.1
  • 11
    • 0028369618 scopus 로고
    • Singular perturbation analysis of boundary-value problems for differential difference equations.V. Small shifts with layer behavior
    • C.G. Lange, and R.M. Miura Singular perturbation analysis of boundary-value problems for differential difference equations.V. Small shifts with layer behavior SIAM Journal on Applied Mathematics 54 1994 249 272
    • (1994) SIAM Journal on Applied Mathematics , vol.54 , pp. 249-272
    • Lange, C.G.1    Miura, R.M.2
  • 12
    • 0028370364 scopus 로고
    • Singular perturbation analysis of boundary-value problems for differential difference equations. VI. Small shifts with rapid oscillations
    • C.G. Lange, and R.M. Miura Singular perturbation analysis of boundary-value problems for differential difference equations. VI. Small shifts with rapid oscillations SIAM Journal on Applied Mathematics 54 1994 273 283
    • (1994) SIAM Journal on Applied Mathematics , vol.54 , pp. 273-283
    • Lange, C.G.1    Miura, R.M.2
  • 13
    • 0023718682 scopus 로고
    • Complex oscillations in the human pupil light reflex with mixed and delayed feedback
    • A. Longtin, and J. Milton Complex oscillations in the human pupil light reflex with mixed and delayed feedback Mathematical Biosciences 90 1988 183 199
    • (1988) Mathematical Biosciences , vol.90 , pp. 183-199
    • Longtin, A.1    Milton, J.2
  • 14
    • 0017714604 scopus 로고
    • Oscillations and chaos in physiological control systems
    • M.C. Mackey, and L. Glass Oscillations and chaos in physiological control systems Science 197 1977 287 289
    • (1977) Science , vol.197 , pp. 287-289
    • MacKey, M.C.1    Glass, L.2
  • 17
    • 0037035145 scopus 로고    scopus 로고
    • Numerical study of a non-standard finite difference scheme for the van der pol equation
    • R.E. Mickens, and A.B. Gumel Numerical study of a non-standard finite difference scheme for the van der pol equation Journal of Sound and Vibration 250 5 2002 955 963
    • (2002) Journal of Sound and Vibration , vol.250 , Issue.5 , pp. 955-963
    • Mickens, R.E.1    Gumel, A.B.2
  • 18
    • 0037207002 scopus 로고    scopus 로고
    • Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equation
    • R.E. Mickens, and A.B. Gumel Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equation Journal of Sound and Vibration 257 4 2002 791 797
    • (2002) Journal of Sound and Vibration , vol.257 , Issue.4 , pp. 791-797
    • Mickens, R.E.1    Gumel, A.B.2
  • 19
    • 0041380942 scopus 로고    scopus 로고
    • A non-standard finite difference scheme for the equations modelling stellar structure
    • R.E. Mickens A non-standard finite difference scheme for the equations modelling stellar structure Journal of Sound and Vibration 265 5 2003 1116 1120
    • (2003) Journal of Sound and Vibration , vol.265 , Issue.5 , pp. 1116-1120
    • Mickens, R.E.1
  • 23
    • 0347476983 scopus 로고    scopus 로고
    • A non-standard numerical scheme for a generalized Gause-type predator-prey model
    • S.M. Moghadas, M.E. Alexander, and B.D. Corbett A non-standard numerical scheme for a generalized Gause-type predator-prey model Physica D: Nonlinear Phenomena 188 1-2 2004 134 151
    • (2004) Physica D: Nonlinear Phenomena , vol.188 , Issue.1-2 , pp. 134-151
    • Moghadas, S.M.1    Alexander, M.E.2    Corbett, B.D.3
  • 25
    • 0001782371 scopus 로고    scopus 로고
    • Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization
    • J.I. Ramos, and C.M. GarcIÍa-López Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization Applied Mathematics and Computation 86 1 1997 11 36
    • (1997) Applied Mathematics and Computation , vol.86 , Issue.1 , pp. 11-36
    • Ramos, J.I.1    Garciía-López, C.M.2
  • 26
    • 0141922932 scopus 로고    scopus 로고
    • An efficient non-standard finite difference scheme for an ionic model of cardiac action potentials
    • R.J. Spiteri, and M.C. MacLachlan An efficient non-standard finite difference scheme for an ionic model of cardiac action potentials Journal of Difference Equations and Applications 9 12 2003 1069 1081
    • (2003) Journal of Difference Equations and Applications , vol.9 , Issue.12 , pp. 1069-1081
    • Spiteri, R.J.1    MacLachlan, M.C.2
  • 27
    • 11844290435 scopus 로고
    • A theoretical analysis of neuronal variability
    • R.B. Stein A theoretical analysis of neuronal variability Biophysical Journal 5 1965 173 194
    • (1965) Biophysical Journal , vol.5 , pp. 173-194
    • Stein, R.B.1
  • 28
    • 84954086574 scopus 로고
    • Some models of neuronal variability
    • R.B. Stein Some models of neuronal variability Biophysical Journal 7 1967 37 68
    • (1967) Biophysical Journal , vol.7 , pp. 37-68
    • Stein, R.B.1
  • 29
    • 0001995554 scopus 로고
    • Mathematical models of the red cell system
    • M. Wazewska-Czyzewska, and A. Lasota Mathematical models of the red cell system Mat. Stos. 6 1976 25 40
    • (1976) Mat. Stos. , vol.6 , pp. 25-40
    • Wazewska-Czyzewska, M.1    Lasota, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.