A GENERALIZED SEMICONJUGACY IN DIFFERENCE EQUATIONS

Difference equations arise in many fields.This article is concerned to generalization of semiconjugacy in difference equations.In fact,H.Sedaghat in [7] investigated the semiconjugacy in difference equations where the factor maps are one-dimensional.We generalize the definition of semiconjugacy of maps,where the factor map is multi-dimensional.This generalization is very useful.By this generalization,we can investigate the dynamics of many difference equations especially the dynamics of systems of higher order difference equations.Some systems of difference equations are investigated using the semiconjugacy property.

The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws:An Alternative Technique

To solve conservation laws,efficient schemes such as essentially nonoscillatory(ENO)and weighted ENO(WENO)have been introduced to control the Gibbs oscillations.Based on radial basis functions(RBFs)with the classical WENO-JS weights,a new type of WENO schemes has been proposed to solve conservation laws[J.Guo et al.,J.Sci.Comput.,70(2017),pp.551–575].The purpose of this paper is to introduce a new formulation of conservative finite difference RBFWENO schemes to solve conservation laws.Unlike the usual method for reconstructing the flux functions,the flux function is generated directly with the conservative variables.Comparing with Guo and Jung(2017),the main advantage of this framework is that arbitrary monotone fluxes can be employed,while in Guo and Jung(2017)only smooth flux splitting can be used to reconstruct flux functions.Several 1D and 2D benchmark problems are prepared to demonstrate the good performance of the new scheme.

LOCAL GAUSSIAN-COLLOCATION SCHEME TO APPROXIMATE THE SOLUTION OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS USING VOLTERRA INTEGRAL EQUATIONS

This work describes an accurate and effective method for numerically solving a class of nonlinear fractional differential equations.To start the method,we equivalently convert these types of differential equations to nonlinear fractional Volterra integral equations of the second kind by integrating from both sides of them.Afterward,the solution of the mentioned Volterra integral equations can be estimated using the collocation method based on locally supported Gaussian functions.The local Gaussian-collocation scheme estimates the unknown function utilizing a small set of data instead of all points in the solution domain,so the proposed method uses much less computer memory and volume computing in comparison with global cases.We apply the composite non-uniform Gauss-Legendre quadrature formula to estimate singular-fractional integrals in the method.Because of the fact that the proposed scheme requires no cell structures on the domain,it is a meshless method.Furthermore,we obtain the error analysis of the proposed method and demon-strate that the convergence rate of the approach is arbitrarily high.Illustrative examples clearly show the reliability and efficiency of the new technique and confirm the theoretical error estimates.

Modeling of Propagation of Road Hazard Information in Sparse Vehicular ad hoc Networks

In this paper, we study the propagation of road hazard information to vehicles which enter the hazard segment of a highway in a sparse 1D vehicular ad hoc network(VANET) with store-and-forward mechanism. Store-and-forward is an option for message propagation in sparse vehicular networks where connectivity is intermittent. Upon receiving the message, the vehicle becomes an informed vehicle, it carries the message for a while and then forwards it to the approaching vehicles which are about to enter the highway segment. In this way, a platoon of informed vehicles is formed. We establish an analytical model to obtain the probability that a vehicle receives the message and joins the informed platoon. Moreover, we prove that traffic dynamics increase the reception probability of messages. We find the expected message propagation delay in the platoon using the store-and-forward policy. We also show that the propagation delay in store-and-forward inter-vehicle communications is tightly related to traffic parameters such as traffic flow rate and vehicle speeds on the highway. Results show that for smaller transmission ranges, smaller platoons are formed, the expected message propagation delay in the platoon is low, and it increases very slightly as the traffic flow rate increases. But for larger transmission ranges, larger platoons are formed, the expected delay is high, and it increases remarkably with a small increase in the traffic flow rate. The impacts of some network and traffic parameters such as transmission range, speed of vehicles, and highway speed limits on the message propagation are investigated as well. Finally, the accuracy of the analytical results is evaluated by an extensive simulation study.