메뉴 건너뛰기




Volumn , Issue , 2005, Pages 249-285

Reliable finite difference schemes with applications in mathematical ecology

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL SYSTEMS; NUTRIENTS; ORDINARY DIFFERENTIAL EQUATIONS; POPULATION STATISTICS; PREDATOR PREY SYSTEMS; RUNGE KUTTA METHODS;

EID: 84967663372     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812703316_0006     Document Type: Chapter
Times cited : (11)

References (27)
  • 4
    • 0036744729 scopus 로고    scopus 로고
    • Nonstandard finite difference schemes for differential equations
    • Mickens, R.E., Nonstandard finite difference schemes for differential equations, J. Differ. Equations Appl. 8:9, (2002) 823-847.
    • (2002) J. Differ. Equations Appl , vol.8 , Issue.9 , pp. 823-847
    • Mickens, R.E.1
  • 5
    • 0035449292 scopus 로고    scopus 로고
    • Contributions to the mathematics of the nonstandard finite difference method and applications
    • Anguelov R., Lubuma J.M.-S., Contributions to the mathematics of the nonstandard finite difference method and applications, Numer. Methods Partial Diff. Equations, 17:5 (2001) 518-543.
    • (2001) Numer. Methods Partial Diff. Equations , vol.17 , Issue.5 , pp. 518-543
    • Anguelov, R.1    Lubuma, J.M.-S.2
  • 6
    • 0141457690 scopus 로고    scopus 로고
    • An improved theta-method for systems of ordinary differential equations
    • Lubuma, J.M.-S. and Roux A., An improved theta-method for systems of ordinary differential equations, J. Differ. Equations Appl. 9:11, (2003) 1023-1035.
    • (2003) J. Differ. Equations Appl , vol.9 , Issue.11 , pp. 1023-1035
    • Lubuma, J.M.-S.1    Roux, A.2
  • 7
    • 18144420842 scopus 로고    scopus 로고
    • Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems
    • press
    • Dimitrov D.T., Kojouharov H.V., Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems, Appl. Math. Lett., (2005) in press.
    • (2005) Appl. Math. Lett
    • Dimitrov, D.T.1    Kojouharov, H.V.2
  • 8
    • 0037472545 scopus 로고    scopus 로고
    • Nonstandard finite difference method by nonlocal approximation
    • Anguelov R., Lubuma J.M.-S., Nonstandard finite difference method by nonlocal approximation, Math. Comput. Simulation 61:3-6, (2003) 465-475.
    • (2003) Math. Comput. Simulation , vol.61 , Issue.3-6 , pp. 465-475
    • Anguelov, R.1    Lubuma, J.M.-S.2
  • 9
    • 22344440721 scopus 로고    scopus 로고
    • A non-standard finite-difference scheme for a model of HIV transmission and control
    • Gumel A.B., Mickens R.E., Corbett B.D., A non-standard finite-difference scheme for a model of HIV transmission and control, J. Comput. Meth. Sci. Engin. 3:1, (2003) 91-98.
    • (2003) J. Comput. Meth. Sci. Engin , vol.3 , Issue.1 , pp. 91-98
    • Gumel, A.B.1    Mickens, R.E.2    Corbett, B.D.3
  • 10
    • 0032691079 scopus 로고    scopus 로고
    • Suppression of numerically induced chaos with nonstandard finite difference schemes
    • de Markus A.S., Mickens R.E., Suppression of numerically induced chaos with nonstandard finite difference schemes, J. Comput. Appl. Math. 106:2, (1999) 317-324.
    • (1999) J. Comput. Appl. Math , vol.106 , Issue.2 , pp. 317-324
    • de Markus, A.S.1    Mickens, R.E.2
  • 11
    • 0041736718 scopus 로고    scopus 로고
    • An unconditionally convergent finite-difference scheme for the SIR model
    • Piyawong W., Twizell E.H., Gumel A.B., An unconditionally convergent finite-difference scheme for the SIR model, Appl. Math. Comput. 146, (2003) 611-625.
    • (2003) Appl. Math. Comput , vol.146 , pp. 611-625
    • Piyawong, W.1    Twizell, E.H.2    Gumel, A.B.3
  • 12
    • 0036133051 scopus 로고    scopus 로고
    • An unconditionally convergent discretization of the SEIR model
    • Jansen H. and Twizell E.H., An unconditionally convergent discretization of the SEIR model, Math. Comput. Simulation 58, (2002) 147-158.
    • (2002) Math. Comput. Simulation , vol.58 , pp. 147-158
    • Jansen, H.1    Twizell, E.H.2
  • 13
    • 11044227566 scopus 로고    scopus 로고
    • On non-standard finite difference models of reaction-diffusion equations
    • Anguelov R., Kama P., Lubuma J.M.-S., On non-standard finite difference models of reaction-diffusion equations, J. Comput. Appl. Math. 175:1, (2005) 11-29.
    • (2005) J. Comput. Appl. Math , vol.175 , Issue.1 , pp. 11-29
    • Anguelov, R.1    Kama, P.2    Lubuma, J.M.-S.3
  • 14
    • 0008515570 scopus 로고    scopus 로고
    • Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation
    • Mickens, R.E., Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation, Numer. Methods Partial Differential Equations 13:1, (1997) 51-55.
    • (1997) Numer. Methods Partial Differential Equations , vol.13 , Issue.1 , pp. 51-55
    • Mickens, R.E.1
  • 15
    • 0012741562 scopus 로고    scopus 로고
    • Nonstandard Eulerian-Lagrangian Methods for Advection-Diffusion-Reaction Equations
    • (R.E. Mickens, Editor), World Scientific Publishing, River Edge, NJ
    • Kojouharov H.V., Chen B.M., Nonstandard Eulerian-Lagrangian Methods for Advection-Diffusion-Reaction Equations, Applications of Nonstandard Finite Difference Schemes, (R.E. Mickens, Editor) (World Scientific Publishing, River Edge, NJ, 2000), 55-108.
    • (2000) Applications of Nonstandard Finite Difference Schemes , pp. 55-108
    • Kojouharov, H.V.1    Chen, B.M.2
  • 20
    • 0022856174 scopus 로고
    • The interaction of physical and biological process in a model of the vertical distribution of phytoplankton under stratification
    • editor
    • Taylor A.H., Harris J.R.W. and Aiken J., The interaction of physical and biological process in a model of the vertical distribution of phytoplankton under stratification, Mar. Int. Ecohyrd., Jacques C. Nihoul (editor) 42, (1986) 313-330.
    • (1986) Mar. Int. Ecohyrd., Jacques C.Nihoul , vol.42 , pp. 313-330
    • Taylor, A.H.1    Harris, J.R.W.2    Aiken, J.3
  • 21
    • 0002366911 scopus 로고
    • The functional response of predators to prey density and its role in mimicry and population regulation
    • Holling C.S., The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Entomol. Soc. Canada 45, (1965) 1-60.
    • (1965) Mem. Entomol. Soc. Canada , vol.45 , pp. 1-60
    • Holling, C.S.1
  • 22
    • 23744457175 scopus 로고    scopus 로고
    • Analysis and numerical simulation of phytoplankton-nutrient systems with nutrient loss
    • accepted
    • Dimitrov D.T., Kojouharov H.V., Analysis and numerical simulation of phytoplankton-nutrient systems with nutrient loss, Math. Comput. Simulation, (2005) accepted.
    • (2005) Math. Comput. Simulation
    • Dimitrov, D.T.1    Kojouharov, H.V.2
  • 25
    • 10444225454 scopus 로고    scopus 로고
    • Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response
    • Dimitrov D.T., Kojouharov H.V., Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response, Appl. Math. Comput., 162:2, (2005) 523-538.
    • (2005) Appl. Math. Comput , vol.162 , Issue.2 , pp. 523-538
    • Dimitrov, D.T.1    Kojouharov, H.V.2
  • 26
    • 0343238366 scopus 로고    scopus 로고
    • A simple vaccination model with multiple endemic states
    • Kribs-Zaleta C.M. and Velasco-Hernandez J.X., A simple vaccination model with multiple endemic states, Math. Biosci. 164, (2000) 183-201.
    • (2000) Math. Biosci , vol.164 , pp. 183-201
    • Kribs-Zaleta, C.M.1    Velasco-Hernandez, J.X.2
  • 27
    • 0041361873 scopus 로고    scopus 로고
    • A high-order conservative Patankar-type discretization for stiff systems of production-destruction equations
    • Burchard H., Deleersnijder E., Meister A., A high-order conservative Patankar-type discretization for stiff systems of production-destruction equations, Appl. Numer. Math. 47:1, (2003) 1-30.
    • (2003) Appl. Numer. Math , vol.47 , Issue.1 , pp. 1-30
    • Burchard, H.1    Deleersnijder, E.2    Meister, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.