Best constant for Hyers–Ulam stability of two step sizes linear difference equations

Reducibility and Stability Results for Linear System of Difference Equations

Stability of Stochastic Linear Difference Equations with Varying Delay

Many processes in automatic regulation, physics, mechanics, biology, economy, ecology etc. can be modelled by hereditary systems (see, e.g. [1-3]). One of the main problems for the theory of such systems and their applications is connected with stability [1,2]. Many stability results were obtained by the construction of appropriate Lyapunov functionals. In [4-8] the method is proposed allowing,...

Stability with Large Step Sizes for Multistep Discretizations of Stiff Ordinary Differential Equations

In this paper we consider a large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one. A small parameter t characterizes the stiffness of these systems. We approximate a system of ODE's in this set by a general class of multistep discretizations which includes both one-leg and linear multistep methods. ...

Two-step Spline Estimating Equations for Generalized Additive Partially Linear Models with Large Cluster Sizes by Shujie Ma

We propose a two-step estimating procedure for generalized additive partially linear models with clustered data using estimating equations. Our proposed method applies to the case that the number of observations per cluster is allowed to increase with the number of independent subjects. We establish oracle properties for the two-step estimator of each function component such that it performs as...

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...