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Exact finite-difference schemes for first order differential equations having three distinct fixed-points. (English) Zbl 1131.65061

Summary: We construct nonstandard finite-difference (NSFD) schemes that provide exact numerical methods for a first-order differential equation having three distinct fixed-points. An explicit, but also nonexact, NSFD scheme is also constructed. It has the feature of preserving the critical properties of the original differential equation such as the positivity of the solutions and the stability behavior of the three fixed-points.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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References:

[1] Bender C.M., Advanced Mathematical Methods for Scientists and Engineers I (1999) · Zbl 0938.34001
[2] Gradshteyn I.S., Tables of Integrals, Series and Products (1965)
[3] Mickens R.E., Nonstandard Finite Difference Models of Differential Equations (1994) · Zbl 0810.65083
[4] DOI: 10.1142/9789812813251
[5] DOI: 10.1142/9789812703316
[6] Morse P.M., Methods of Theoretical Physics, Vols. I and II (1953)
[7] Rucker S.A., Journal of Difference Equations and Applications 9 pp 1007– (2006) · Zbl 1040.65077
[8] Strogatz S.H., Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering (1994)
[9] Thieme H.R., Mathematics in Population Biology (2003) · Zbl 1054.92042
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