Henryk Leszczyński, Piotr Zwierkowski (2004)
Applicationes Mathematicae
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We consider a generalized 1-D von Foerster equation. We present two discretization methods for the initial value problem and study stability of finite difference schemes on regular meshes.
Ciegis, R., Starikovicius, V. (2001)
Computational Methods in Applied Mathematics
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T. Lewiński (1984)
Applicationes Mathematicae
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T.I. SEIDMAN (1963)
Numerische Mathematik
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Matus, P., Zyuzina, E. (2001)
Computational Methods in Applied Mathematics
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Deqiong Ding, Qiang Ma, Xiaohua Ding (2014)
International Journal of Applied Mathematics and Computer Science
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In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time...
Gordeziani, E., Gordeziani, D. (2000)
Bulletin of TICMI
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Raimondas Čiegis, Aleksas Mirinavičius (2011)
Open Mathematics
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We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430], and [Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649] to solve an initial-boundary...
Michael Breuß (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We are concerned with the structure of the operator corresponding to the Lax–Friedrichs method. At first, the phenomenae which may arise by the naive use of the Lax–Friedrichs scheme are analyzed. In particular, it turns out that the correct definition of the method has to include the details of the discretization of the initial condition and the computational domain. Based on the results of the discussion, we give a recipe that ensures that the number of extrema within the discretized...