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An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

Deqiong Ding, Qiang Ma, Xiaohua Ding (2014)

International Journal of Applied Mathematics and Computer Science

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...

An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection

Hasim A. Obaid, Rachid Ouifki, Kailash C. Patidar (2013)

International Journal of Applied Mathematics and Computer Science

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...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

Vuk Milišić, Alfio Quarteroni (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Analysis of the accuracy and convergence of equation-free projection to a slow manifold

Antonios Zagaris, C. William Gear, Tasso J. Kaper, Yannis G. Kevrekidis (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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 ( m = 0 , 1 , ... ) finds iteratively an approximation of the appropriate zero of the (m+1)st...

Approximate solutions of matrix differential equations.

Lucas Jódar Sánchez, A. Hervás, D. García Sala (1986)

Stochastica

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 177