A ‎nonstandard finite difference (NSFD) scheme has been constructed and analyzed for a mathematical model that describes Lotka–Volterra food web model‎. ‎This new discrete system has the same stability properties as the continuous model and,‎on the whole‎, ‎it preserves‎the same local asymptotic stability properties‎. ‎Linearized stability theory and Schur–Cohn criteria are used for local asymp...

In this work, a novel second-order nonstandard finite difference (NSFD) method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced analyzed. This based on non-local approximations for right-hand side functions differential equations in combination with denominator functions. The obtained results not only resol...

Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit, and a nonstandard finite difference scheme (Mickens 1991). We solve a 1D numerical experiment with spe...

In this study, we implement a Nonstandard Finite Difference (NSFD) scheme for predator-prey model involving cannibalism and refuge in predator. The which is considered as discrete dynamical system analyzed. performed analysis includes the determination of equilibrium point its local stability. has four points, namely origin, prey extinction point, predator coexistence have exactly same form exi...

The hepatitis B infection is a global epidemic disease which huge risk to the public health. In this paper, transmission dynamics of deterministic model are presented and studied. basic reproduction number attained by applying it, local as well stability disease-free endemic equilibria continuous discussed. To better understand disease, discrete nonstandard finite difference (NSFD) scheme produ...

In this paper, the Black–Scholes equation is solved using a new technique. This scheme derived by combining Laplace transform method and nonstandard finite difference (NSFD) strategy. The qualitative properties of are discussed, it shown that positive, stable, consistent when low volatility assumed. efficiency demonstrated numerical example.

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

The honey bees play a role of unquestioned relevance in nature and the comprehension of the mechanisms affecting their population dynamic is of fundamental importance. As experimentally documented, the proper development of a colony is related to the nest temperature, whose value is maintained around the optimal value if the colony population is sufficiently large. Then, the environmental tempe...

This work is devoted to constructing reliable numerical schemes for some computer virus and malware propagation models. We apply the Mickens' methodology formulate nonstandard finite difference (NSFD) epidemiological models describing spread of viruses malware. Positivity, boundedness global asymptotic stability (GAS) proposed NSFD are studied rigorously. It should be emphasized that GAS establ...