Preservation of local dynamics when applying central difference methods: Application to SIR model

Journal of Difference Equations and Applications

Volumn 13, Issue 4, 2007, Pages 333-340

  Roeger, Lih Ing W ^a   Barnard, Roger W ^a  

^a TEXAS TECH UNIVERSITY   (United States)

Author keywords

Central difference method; Conformal mapping; Difference equations; Local dynamics

Indexed keywords

EID: 34047197289     PISSN: 10236198     EISSN: 15635120     Source Type: Journal    
DOI: 10.1080/10236190601079134     Document Type: Article

References (12)

1. Ascher, U.M. and Petzold, L.R., 1998, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (Philadelphia, PA: SIAM).
2. Elaydi, S. and Jang, S., 2003, Difference equations from discretization of continuous epidemic models with disease in the prey. Canadian Applied Mathematics Quaterly, 11(1), 93-105.
3. Gerald, C.F. and Wheatley, P.O., 1999, Applied Numerical Analysis (Reading, MA: Addison-Wesley).
4. Hethcote, H.W., 1989, Three basic epidemiological models. In: S.A. Levin, T.G. Hallam and L. Gross (Eds.) Applied Mathematical Ecology (Berlin: Springer-Verlag).
5. Mickens, R.E., 1994, Nonstandard Finite Difference Models of Differential Equations (Singapore: World Scientific).
6. Mickens, R.E., 2000, Applications of Nonstandard Finite Difference Schemes (Hackensack, NJ: World Scientific).
7. Roeger, L.-I.W, 2004, Discrete May-Leonard competition models III. Journal of Difference Equations and Applications, 10, 773-790.
8. Roeger, L.-I.W., 2005, Discrete May-Leonard competition models II. Discrete and Continuous Dynamical Systems Series B, 5(3), 841-860.
9. Roeger, L.-I.W., 2005, A nonstandard discretization method for Lotka-Volterra models that preserves periodic solutions. Journal of Difference Equations and Applications, 11, 721 -733.
10. Roeger, L.-I.W. and Allen, L.J.S., 2004, Discrete May-Leonard competition models. Journal of Difference Equations and Applications, 10, 77-98.
11. Ushiki. S., 1982, Central difference scheme and chaos. Physica, 4D, 407-424.
12. Yamaguti, M. and Ushiki, S., 1981, Chaos in numerical analysis of ordinary differential equations. Physica, 3D, 618-626.