Discrete-time Lotka-Volterra competition models are obtained by applying nonstandard finite difference (NSFD) schemes to the continuous-time counterparts of the model. The NSFD methods are noncanonical symplectic numerical schemes when applying to the predator-prey model x = x − xy and y = −y + xy. The local dynamics of the discrete-time model are analyzed and compared with the continuous model...

In this paper, we proposed an unconditionally stable NonStandard Finite Difference (NSFD) scheme to solve nonlinear Riccati differential equation. The accuracy and efficiency of the proposed scheme is verified by comparing the results with other numerical techniques such as Euler and RK-4 and semi analytical technique DTM. The obtained results show that the performance of NSFD scheme is more ac...

We design nonstandard finite difference (NSFD) schemes which are unconditionally dynamically consistent with respect to the positivity property of solutions of cross-diffusion equations in biosciences. This settles a problem that was open for quite some time. The study is done in the setting of three concrete and highly relevant cross-diffusion systems regarding tumor growth, convective predato...

We consider the basic SIR epidemiological model with the Michaelis-Menten formulation of the contact rate. From the study of Michaelis-Menten basic enzymatic reaction, we design two types of Nonstandard Finite Difference (NSFD) schemes for the SIR model: Exact-related schemes based on the Lambert W function and schemes obtained by using Mickens’s rules of more complex denominator functions for ...

We construct a nonstandard finite difference (NSFD) scheme for an SIRS mathematical model of respiratory virus transmission. This discretization is in full compliance with the NSFD methodology as formulated by R. E. Mickens. By use of an exact conservation law satisfied by the SIRS differential equations, we are able to determine the corresponding denominator function for the discrete first-ord...

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 positivit...

‎In this paper‎, ‎the fractional--order form of three dimensional chemostat model with variable yields is introduced‎. ‎The stability analysis of this fractional system is discussed in detail‎. ‎In order to study the dynamic behaviours of the mentioned fractional system‎, ‎the well known nonstandard (NSFD) scheme is implemented‎. ‎The proposed NSFD scheme is compared with the forward Euler and ...

We consider a complex autonomously driven single limit cycle oscillator with delayed feedback.The original model is translated to a two-dimensional system.Through a nonstandard finite-difference (NSFD) schemewe study the dynamics of this resulting system. The stability of the equilibriumof themodel is investigated by analyzing the characteristic equation. In the two-dimensional discrete model, ...

PROTOSOLID is a solid modeler that represents solids with planar surfaces and manipulates the solids with regularized set operations. This paper looks at the internal structures and operations of PROTOSOLID and is intended as a programmer user guide. A boundary of a solid is represented by a/edge-based data structure. It is developed in ComrnonLisp. IThill work hILS been supported in part by an...