I describe a software reliability growth model that yields accurate parameter estimates even with a small amount of input data. The model is based on a proposed discrete analog of a Gompertz equation that has an exact solution. The difference equation tends to a differential equation on which the Gompertz curve model is defined, when the time interval tends to zero. The exact solution also tend...

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite–difference equations approximating ordinary differential equations. Finite–difference equations are viewed as a system of algebraic equations with a small parameter, introduced through the definitions of finite–difference derivatives. I...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

In order to find a general framework for different combinatorial identities and identities that involve special functions, Bernshtein introduced in [1] a notion of holonomic functions. Let us recall this definition (in formulating it, we will follow [10]). A discrete holonomic function f(n) of one variable is defined as a solution of a homogeneous, linear difference equation with polynomial coe...

In this paper, we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.