A comparison of four- and five-point difference approximations for stabilizing the one-dimensional stationary convection-diffusion equation.
A higher-order method for nonlinear singular two-point boundary value problems.
A nonstandard dynamically consistent numerical scheme applied to obesity dynamics.
A note on numerically consistent initial values for high index differential-algebraic equations.
A numerical method for a singularly perturbed three-point boundary value problem.
A parameter robust method for singularly perturbed delay differential equations.
An Analysis and Improvement of the El~mistikawy and Werle Scheme
An exponentially fitted method for singularly perturbed delay differential equations.
An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination
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
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...