Abstract: The approximate analytical solution of the fractional Cahn-Hilliard and Gardner equations has been acquired successfully via residual power series method (RPSM). The approximate solutions obtained by RPSM are compared with the exact solutions as well as the solutions obtained by homotopy perturbation method (HPM) and q-homotopy analysis method (q-HAM). Numerical results are known through different graphs and tables. The fractional derivatives are described in the Caputo sense. The results light the power, efficiency, simplicity, and reliability of the proposed method. PubDate: Wed, 04 Jul 2018 00:00:00 +000

Abstract: We consider the standard affine discontinuous Galerkin method approximation of the second-order linear elliptic equation in divergence form with coefficients in and the right-hand side belongs to ; we extend the results where the case of linear finite elements approximation is considered. We prove that the unique solution of the discrete problem converges in for every with ( or ) to the unique renormalized solution of the problem. Statements and proofs remain valid in our case, which permits obtaining a weaker result when the right-hand side is a bounded Radon measure and, when the coefficients are smooth, an error estimate in when the right-hand side belongs to verifying for every , for some PubDate: Mon, 02 Jul 2018 00:00:00 +000

Abstract: This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The RPS algorithm is significant and straightforward tool for creating a fractional power series solution without linearization, limitation on the problem’s nature, sort of classification, or perturbation. Some illustrative examples are provided to demonstrate the feasibility of the RPS scheme. The results obtained show that the scheme is simple and reliable and there is good agreement with exact solution. PubDate: Mon, 02 Jul 2018 00:00:00 +000

Abstract: This paper is concerned with the analysis of the linear -method and compact -method for solving delay reaction-diffusion equation. Solvability, consistence, stability, and convergence of the two methods are studied. When , sufficient and necessary conditions are given to show that the two methods are asymptotically stable. When , the two methods are proven to be unconditionally asymptotically stable. Finally, several examples are carried out to confirm the theoretical results. PubDate: Mon, 11 Jun 2018 09:43:55 +000

Abstract: This paper is concerned with stability analysis of additive Runge-Kutta methods for delay-integro-differential equations. We show that if the additive Runge-Kutta methods are algebraically stable, the perturbations of the numerical solutions are controlled by the initial perturbations from the system and the methods. PubDate: Mon, 11 Jun 2018 00:00:00 +000

Abstract: This article discusses the evolution of Benjamin-Bona-Mahony (BBM) wave packet’s envelope. The envelope equation is derived by applying the asymptotic series up to the third order and choosing appropriate fast-to-slow variable transformations which eliminate the resonance terms that occurred. It is obtained that the envelope evolves satisfying the Nonlinear Schrodinger (NLS) equation. The evolution of NLS envelope is investigated through its exact solution, Soliton on Finite Background, which undergoes modulational instability during its propagation. The resulting wave may experience phase singularity indicated by wave splitting and merging and causing amplification on its amplitude. Some parameter values take part in triggering this phenomenon. The amplitude amplification can be analyzed by employing Maximal Temporal Amplitude (MTA) which is a quantity measuring the maximum wave elevation at each spatial position during the observation time. Wavenumber value affects the extreme position of the wave but not the amplitude amplification. Meanwhile, modulational frequency value affects both terms. Comparison of the evolution of the BBM wave packet to the previous results obtained from KdV equation gives interesting outputs regarding the extreme position and the maximum wave peaking. PubDate: Sun, 03 Jun 2018 00:00:00 +000

Abstract: This paper presents a computational study of the stability of the steady state solutions of a biological model with negative feedback and time delay. The motivation behind the construction of our system comes from biological gene networks and the model takes the form of an integro-delay differential equation (IDDE) coupled to a partial differential equation. Linear analysis shows the existence of a critical delay where the stable steady state becomes unstable. Closed form expressions for the critical delay and associated frequency are found and confirmed by approximating the IDDE model with a system of delay differential equations (DDEs) coupled to ordinary differential equations. An example is then given that shows how the critical delay for the DDE system approaches the results for the IDDE model as becomes large. PubDate: Wed, 02 May 2018 00:00:00 +000

Abstract: The mathematical simulation of water contaminant measurement is often used to assess the water quality. The monitoring point placement for water quality measurement in an opened-closed reservoir can give accurate or inaccurate assessment. In this research, the mathematical model of the approximated water quality in an opened-closed reservoir with removal mechanism system is proposed. The water quality model consists of the hydrodynamic model and the dispersion model. The hydrodynamic model is used to describe the water current in the opened-closed reservoir. The transient advection-diffusion equation with removal mechanism provides the water pollutant concentration. The water velocity from the hydrodynamic model is plugged into the dispersion model. The finite difference techniques are used to approximate the solution of the water quality model. The proposed numerical simulations give a suitable area of zonal removal mechanism placement. The proposed simulations also give the overall and specified approximated water quality for each point and time when the exit gate is opened on the different periods of time. In addition, the proposed techniques can give a suitable period of time to open the exit gate to achieve a good agreement water quality by using contaminant removal mechanism. PubDate: Wed, 02 May 2018 00:00:00 +000

Abstract: We study the equations governing the high-speed transmission in long-haul electrical systems , , , where , and is the Fourier transformation. Our purpose in this paper is to obtain the large time asymptotics for the solutions under the nonzero mass condition PubDate: Wed, 18 Apr 2018 00:00:00 +000

Abstract: Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton’s cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit the prices well and the forecasting ability of the best model is acceptable even though the martingale forecasts the prices slightly better. To increase the forecasting ability and to broaden the scope of applications of the dynamic models, we will model the coefficients of the dynamic models in the future. Applying the models to the market without the price limit is also our future work. PubDate: Thu, 12 Apr 2018 00:00:00 +000

Abstract: An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms. The analytic solution is represented by an infinite series. We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method. The result of the theorem will be used to solve a weakly singular Volterra integral equation later on. PubDate: Sun, 01 Apr 2018 00:00:00 +000

Abstract: We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination. PubDate: Thu, 15 Mar 2018 00:00:00 +000

Abstract: We propose and analyse an human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two threshold parameters that are the basic reproduction number and the CTL immune response reproduction number . The stability of the last equilibrium depends on and as well as time delay in the CTL activation. We prove that the chronic infection equilibrium is locally asymptotically stable when the time delay is sufficiently small, while it loses its stability and a Hopf bifurcation occurs when passes through a certain critical value. PubDate: Thu, 01 Mar 2018 00:00:00 +000

Abstract: We prove some uniqueness results for the solution of two kinds of Dirichlet boundary value problems for second- and fourth-order linear elliptic differential equations with discontinuous coefficients in polyhedral angles, in weighted Sobolev spaces. PubDate: Thu, 01 Mar 2018 00:00:00 +000

Abstract: We consider the following nonlinear parabolic equation: , where and the exponent of nonlinearity are given functions. By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions. PubDate: Thu, 01 Mar 2018 00:00:00 +000

Abstract: It is known that power series expansion of certain functions such as diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of that is convergent for all . The convergent series is a sum of the Taylor series of and a complementary series that cancels the divergence of the Taylor series for . The method is general and can be applied to other functions known to have finite radius of convergence, such as . A straightforward application of this method is to solve analytically nonlinear differential equations, which we also illustrate here. The method provides also a robust and very efficient numerical algorithm for solving nonlinear differential equations numerically. A detailed comparison with the fourth-order Runge-Kutta method and extensive analysis of the behavior of the error and CPU time are performed. PubDate: Tue, 13 Feb 2018 00:00:00 +000

Abstract: We propose a generalized virus dynamics model with distributed delays and both modes of transmission, one by virus-to-cell infection and the other by cell-to-cell transfer. In the proposed model, the distributed delays describe (i) the time needed for infected cells to produce new virions and (ii) the time necessary for the newly produced virions to become mature and infectious. In addition, the infection transmission process is modeled by general incidence functions for both modes. Furthermore, the qualitative analysis of the model is rigorously established and many known viral infection models with discrete and distributed delays are extended and improved. PubDate: Thu, 01 Feb 2018 00:00:00 +000

Abstract: The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies. In this stage, the growth of the healthy hepatocyte cells is logistic while the growth of the infected ones is linear. To investigate the role of the treatment at this stage, we also consider two types of treatment: interferon- (IFN) and nucleoside analogues (NAs). To find the best strategy to use this treatment, an optimal control approach is developed to find the possibility of having a functional cure to HBV. PubDate: Thu, 01 Feb 2018 00:00:00 +000

Abstract: We discuss the existence of global solutions to the magnetohydrodynamics (MHD) equations, where the effects of finite Larmor radius corrections are taken into account. Unlike the usual MHD, the pressure is a tensor and it depends on not only the density but also the magnetic field. We show the existence of global solutions by the energy methods. Our techniques of proof are based on the existence of local solution by semigroups theory and a priori estimate. PubDate: Sun, 28 Jan 2018 00:00:00 +000

Abstract: In this article, the linearization problem of fifth-order ordinary differential equation is presented by using the generalized Sundman transformation. The necessary and sufficient conditions which allow the nonlinear fifth-order ordinary differential equation to be transformed to the simplest linear equation are found. There is only one case in the part of sufficient conditions which is surprisingly less than the number of cases in the same part for order 2, 3, and 4. Moreover, the derivations of the explicit forms for the linearizing transformation are exhibited. Examples for the main results are included. PubDate: Tue, 02 Jan 2018 00:00:00 +000

Abstract: We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator, and top predator populations. These fish populations are exploited by two fishermen. We study the existence and the stability of the equilibrium points by using eigenvalues analysis and Routh-Hurwitz criterion. We determine the equilibrium point that maximizes the profit of each fisherman by solving the Nash equilibrium problem. Finally, following some numerical simulations, we observe that if the price varies, then the profit behavior of each fisherman will be changed; also, we conclude that the price change mechanism improves the fishing effort of the fishermen. PubDate: Mon, 01 Jan 2018 08:54:26 +000