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Displaying 141 –
160 of
882
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 step. Our...
We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical...
This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee...
This paper provides new results of consistence and convergence of the
lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed,
lumped parameter models (exploiting the electric circuit analogy for the circulatory system)
are shown to discretize continuous 1D models
at first order in space.
We derive the complete set of equations useful for the blood flow networks,
new schemes for electric circuit analogy,
the stability criteria that...
In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis and A. Zagaris,
SIAM J. Appl. Dyn. Syst. 4 (2005) 711–732],
we developed
a class of iterative algorithms
within the context
of equation-free methods
to approximate
low-dimensional,
attracting,
slow manifolds
in systems
of differential equations
with multiple time scales.
For user-specified values
of a finite number
of the observables,
the mth member
of the class
of algorithms
()
finds iteratively
an approximation
of the appropriate zero
of the (m+1)st...
A method for solving second order matrix differential equations avoiding the increase of the dimension of the problem is presented. Explicit approximate solutions and an error bound of them in terms of data are given.
Currently displaying 141 –
160 of
882