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...
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Boundary controllability of the finite-difference space semi-discretizations of the beam equation
We propose a finite difference semi-discrete scheme for the approximation of the boundary exact controllability problem of the 1-D beam equation modelling the transversal vibrations of a beam with fixed ends. First of all we show that, due to the high frequency spurious oscillations, the uniform (with respect to the mesh-size) controllability property of the semi-discrete model fails in the natural functional setting. We then prove that there are two ways of restoring the uniform controllability...
Boundary value problems for systems of functional differential equations
Algorithms for finding an approximate solution of boundary value problems for systems of functional ordinary differential equations are studied. Sufficient conditions for consistency and convergence of these methods are given. In the last section, a construction of methods of arbitrary order is presented.
Cubic spline difference scheme on a mesh of Bakhvalov type.
Derivation of BDF coefficients for equidistant time step
We present the derivation of the explicit formulae of BDF coefficients for equidistant time step.
Difference schemes for nonlinear BVPs using Runge-Kutta IVP-solvers.
Driver's influence on kinematics of articulated bus rear axle
This paper studies kinematic properties of the rear axle of the particle coach as function of driver’s activity. The main goals are the prediction of the trajectory, the computation of the vector of velocity of each wheel of the rear axle as a function of the real velocity vector of the front coach axle and the real curvature of the bus trajectory. The computer algebra system MAPLE was used for all necessary computations.
Euler approximation of nonconvex discontinuous differential inclusions.
Explicit Difference Approximations of the One-Dimensional Diffusion Equation, Using a Smoothing Technique.
Finite-difference method for parameterized singularly perturbed problem.