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The generalized hypergeometric difference equation

Bohner M., Cuchta T.

Demonstratio Mathematica

2018

Vol. 51, nr 1

62--75

A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special functions are demonstrated.

Persistence and global attractivity for a discretized version of a general model of glucose-insulin interaction

Huong D. C.

Demonstratio Mathematica

2016

Vol. 49, nr 3

302--318

In this paper, we construct a non-standard finite difference scheme for a general model of glucose-insulin interaction. We establish some new sufficient conditions to ensure that the discretized model preserves the persistence and global attractivity of the continuous model. One of the main findings in this paper is that we derive two important propositions (Proposition 3.1 and Proposition 3.2) which are used to prove the global attractivity of the discretized model. Furthermore, when investigating the persistence and, in some cases, the global attractivity of the discretized model, the nonlinear functions f and h are not required to be differentiable. Hence, our results are more realistic because the statistical data of glucose and insulin are collected and reported in discrete time. We also present some numerical examples and their simulations to illustrate our results.

On a linear difference equation with several infinite lags

Čermák J.

Fasciculi Mathematici

2010

Nr 44

19-28

This paper deals with asymptotic properties of the solutions of a variable order linear difference equation. As the main result, we derive the effective asymptotic estimate valid for all solutions of this equation. Moreover, we are going to discuss some consequences of this theoretical result, especially with respect to the numerical analysis of the multi-pantograph differential equation.