Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Zhengwen Tu, Yongxiang Zhao, Nan Ding, Yuming Feng, Wei Zhang The existence, uniqueness and stability of the equilibrium of quaternion-valued neural networks (QVNNs) with both discrete and distributed delays are investigated in this paper. The considered model is managed as a single entirety without decomposition. Based on homeomorphic mapping theorem and linear matrix inequality, several sufficient criteria are derived to ascertain the aforementioned QVNNs to be globally asymptotically stable and exponentially stable. Moreover, provided criteria can be verified by the linear matrix inequality (LMI) toolbox in MATLAB. Finally, one simulation example is demonstrated to verify the effectiveness of obtained results.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Mingkang Long, Housheng Su, Bo Liu This paper addresses the controllability for an interconnected two-time-scale second-order multi-agent system. Firstly, to eliminate the singular perturbation parameter, we separate the multi-agent system into slow subsystem and fast subsystem by using singular perturbation methods. Then, based on matrix theory, some necessary and/or sufficient criteria are derived for second-order controllability of two-time-scale multi-agent systems with multiple leaders. Moreover, we propose some easy-to-use second-order controllability criteria determined only by eigenvalues of system matrices. Lastly, the effectiveness of the proposed theoretical results is illustrated by a simulation example.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Yu Ping Wang, Chung Tsun Shieh The inverse spectral problem for the interior transmission eigenvalue problem with the unit time is studied by given spectral data. The authors show that the refractive index on the whole interval can be uniquely determined by parts of its transmission eigenvalues together with the partial information on the refractive index. In particular, we pose and solve a new type of inverse spectral problems involving the interior transmission eigenvalue problem with complex transmission eigenvalues except for at most finite real eigenvalues.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Burak Şahiner In this paper, we define some new associated curves as integral curves of a vector field generated by Frenet vectors of tangent indicatrix of a curve in Euclidean 3-space. We give some relationships between curvatures of these curves. By using these associated curves, we give some methods to construct helices and slant helices from some special spherical curves such as circles on unit sphere, spherical helices, and spherical slant helices. Finally, we give some related examples.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Saeid Gholami, Esmail Babolian, Mohammad Javidi In this paper, we present a new pseudospectral integration matrix which can be used to compute n−fold integrals of function f for any n∈R+. Also, it can be used to calculate the derivatives of f for any non-integer order α

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Chao Zhang, Tian-jun Wang In this paper, we develop a new mixed pseudospectral method for heat transfer by using generalized Hermite functions and Legendre polynomials in unbounded domains. Fundamental to spectral methods for various unbounded-domain problems, we establish some basic results on the mixed generalized Hermite-Legendre interpolation. As an example, a new mixed generalized Hermite-Legendre pseudospectral scheme is provided for non-isotropic heat transfer. Its convergence is proved. Numerical results demonstrate the spectral accuracy of this approach.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Yuede Ma, Shujuan Cao, Yongtang Shi, Matthias Dehmer, Chengyi Xia A graph whose vertices have the same degree is called regular. Otherwise, the graph is irregular. In fact, various measures of irregularity have been proposed and examined. For a given graph G=(V,E) with V={v1,v2,…,vn} and edge set E(G), di is the vertex degree where 1 ≤ i ≤ n. The irregularity of G is defined by irr(G)=∑vivj∈E(G) di−dj . A similar measure can be defined by irr2(G)=∑vivj∈E(G)(di−dj)2. The total irregularity of G is defined by irrt(G)=12∑vi,vj∈V(G) di−dj . The variance of the vertex degrees is defined var(G)=1n∑i=1ndi2−(2mn)2. In this paper, we present some Nordhaus–Gaddum type results for these measures and draw conclusions.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Qian Li, Xinzhi Liu, Qingxin Zhu, Shouming Zhong, Dian Zhang This paper investigates the distributed state estimation problem for a class of sensor networks described by discrete-time stochastic systems with stochastic switching topologies. In the sensor network, the redundant channel and the randomly varying nonlinearities are considered. The stochastic Brownian motions affect both the dynamical plant and the sensor measurement outputs. Through available output measurements from each individual sensor, the distributed state estimators are designed to approximate the states of the networked dynamic system. Sufficient conditions are established to guarantee the convergence of the estimation error systems for all admissible stochastic disturbances and randomly varying nonlinearities. Then, the distributed state estimator gain matrices are derived using the linear matrix inequality method. Moreover, a numerical example is given to verify the effectiveness of the theoretical results.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Wanping Liu, Xiao Wu, Wu Yang, Xiaofei Zhu, Shouming Zhong By incorporating the spreading characteristics of cyber rumors over mobile social networks, we newly develop a dynamic system to model rumor spreading dynamics by the compartment method. Specifically, a couple of a user and an attached device is viewed as a node, and all network nodes are separated into four compartments: Rumor-Neutral, Rumor-Received, Rumor-Believed and Rumor-Denied. Some transition parameters among these groups are introduced. Additionally, the role of memory, user’s ability to distinguish the rumors and rumor-denier’s behavior of refuting rumors are also incorporated. The stability of the equilibria of the model system is addressed, and the influence of model parameters upon the threshold is analyzed. Finally, numerical simulations illustrate the theoretical results, and also motivate us to propose suitable measures to control cyber rumor spreading by properly adjusting the parameter values.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Marcelo Caniato Renhe, Marcelo Bernardes Vieira, Claudio Esperança The association between fluids and tensors can be observed in some practical situations, such as diffusion tensor imaging and permeable flow. For simulation purposes, tensors may be used to constrain the fluid flow along specific directions. This requires a customized mathematical model for describing fluid motion influenced by tensor. In this work, we propose a formulation for fluid dynamics to locally change momentum, deflecting the fluid along intended paths. Building upon classical computer graphics approaches for fluid simulation, the numerical method is altered to accommodate the new formulation. Gaining control over fluid diffusion can also aid on visualization of tensor fields, where the detection and highlighting of paths of interest is often desired. Experiments show that the fluid adequately follows meaningful paths induced by the underlying tensor field, resulting in a method that is numerically stable and suitable for visualization and animation purposes.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Lucia Valentina Gambuzza, Mattia Frasca, Ernesto Estrada The Laplacian of a graph mathematically formalizes the interactions occurring between nodes/agents connected by a link. Its extension to account for the indirect peer influence through longer paths, weighted as a function of their length, is represented by the notion of transformed d-path Laplacians. In this paper, we propose a second-order consensus protocol based on these matrices and derive criteria for the stability of the error dynamics, which also consider the presence of a communication delay. We show that the new consensus protocol is stable in a wider region of the control gains, but admits a smaller maximum delay than the protocol based on the classical Laplacian. We show numerical examples to illustrate our theoretical results.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Ekin Uğurlu In this paper, we consider some boundary value problems generated by third-order formally symmetric (self-adjoint) regular differential expression and separated, real-coupled and complex-coupled boundary conditions. It is shown that these problems generate self-adjoint operators. Moreover, the dependence of eigenvalues of these problems on the data are studied and some derivatives of the eigenvalues with respect to some elements of data are introduced.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): C. Balbuena, X. Marcote Given a connected graph G and an integer 1 ≤ p ≤ ⌊ V(G) /2⌋, a p-restricted edge-cut of G is any set of edges S ⊂ E(G), if any, such that G−S is not connected and each component of G−S has at least p vertices; and the p-restricted edge-connectivity of G, denoted λp(G), is the minimum cardinality of such a p-restricted edge-cut. When p-restricted edge-cuts exist, G is said to be super-λp if the deletion from G of any p-restricted edge-cut S of cardinality λp(G) yields a graph G−S that has at least one component with exactly p vertices. In this work, we prove that Kneser graphs K(n, k) are λp-connected for a wide range of values of p. Moreover, we obtain the values of λp(G) for all possible p and all n ≥ 5 when G=K(n,2). Also, we discuss in which cases λp(G) attains its maximum possible value, and determine for which values of p graph G=K(n,2) is super-λp.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Muhammad Zeeshan Khalid, Muhammad Zubair, Majid Ali Two phase Stefan problem was solved using analytical method in cylindrical domain. To solve governing equations Eigen conditions were formulated by using separation of variable technique. Eigenvalues of the eigencondition were obtained by applying corresponding boundary conditions for liquid and solid phase. Eigenvalues are graphically validated by using window size method in Mathematica. It is noted radial eigenvalues are free from imaginary values. Interface equation obtained from this method were solved and analyzed by varying the Stefan number and introducing the forced and natural convection. Conduction and convection heat transfer mechanism was studied and results obtained by varying thermal diffusivity, thermal conductivity and Stefan number were discussed. Natural convection effects were studied by introducing Rayleigh number and results showed Stefan number has significant effect than Rayleigh number during Phase transition process. Furthermore, eigen function expansion Method was compared with exact solution of Exponential Integral function method and results showed good agreement for Q = 1.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): R.M. Gregório, P.R. Oliveira, C.D.S. Alves This paper improves a decomposition-like proximal point algorithm, developed for computing minima of nonsmooth convex functions within a framework of symmetric positive semidefinite matrices, and extends it to domains of positivity of reducible type, in a nonlinear sense and in a Riemannian setting. Several computational experiments with weighted Lp (p=1,2) centers of mass are performed to demonstrate the practical feasibility of the method.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Tserendorj Batbold, Laith E. Azar, Mario Krnić In the present paper we establish a unified treatment of Hilbert–Pachpatte-type inequalities for a class of non-homogeneous kernels. Our results are derived in both discrete and integral versions. A particular emphasis is devoted to constants and weight functions appearing on the right-hand sides of the established inequalities. As an application, we obtain inequalities with constants and weight functions expressed in terms of generalized harmonic numbers, the incomplete Beta and Gamma function, and the logarithmic integral function.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Ziqiang Lu, Yuanguo Zhu Uncertain fractional differential equation (UFDE) is of importance tool for the description of uncertain dynamic systems. Generally we may not obtain its analytic solutions in most cases. This paper focuses on proposing a numerical method for solving UFDE involving Caputo derivative. First, the concept of α-path to an UFDE with initial value conditions is introduced, which is a solution of the corresponding fractional differential equation (FDE) involving with the same initial value conditions. Then the relations between its solution and associate α-path are investigated. Besides, a formula is derived for calculating expected value of a monotonic function with respect to solutions of UFDEs. Based on the established relations, numerical algorithms are designed. Finally, some numerical experiments of nonlinear UFDEs are given to demonstrate the effectiveness of the numerical algorithms.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Gang Wang, Min-Yao Niu, Fang-Wei Fu Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that a sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a main problem in compressed sensing theory. In this paper, the deterministic compressed sensing matrices are provided using optimal codebooks and codes. Using specific linear and nonlinear codes, we present deterministic constructions of compressed sensing matrices, which are generalizations of DeVore′s construction and Li et al.′s construction. Compared with DeVore′s matrices and Li et al.′s matrices, by using appropriate optimal codebooks and specific codes, the compressed sensing matrices we construct are superior to DeVore′s matrices and Li et al.′s matrices.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Ying Guo, Wei Zhao, Xiaohua Ding In this paper, the input-to-state stability (ISS) for a general class of stochastic multi-group models with multi-dispersal and time-varying delay is investigated. By means of graph theory and Lyapunov method as well as stochastic analysis techniques, sufficient criteria including a Lyapunov-type theorem and a coefficient-type theorem are obtained to guarantee that the proposed model is input-to-state stable. In addition, to show the applicability of our findings, the coefficient-type theorem is employed to study the ISS of stochastic coupled oscillators with time-varying delay and control input. Finally, a numerical example is offered to illustrate the effectiveness of the theoretical results.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Bingquan Ji, Luming Zhang In this article, several exponential wave integrator Fourier pseudospectra methods are developed for solving the nonlinear Schrödinger equation in two dimensions. These numerical methods are based on the Fourier pseudospectral discretization for spatial derivative first and then utilizing four types of numerical integration formulas, including the Gautschi-type, trapezoidal, middle rectangle and Simpson rules, to approximate the time integral in phase space. The resulting numerical methods cover two explicit and an implicit schemes and can be implemented effectively thanks to the fast discrete Fourier transform. Additionally, the error estimates of two explicit schemes are established by virtue of the mathematical induction and standard energy method. Finally, extensive numerical results are reported to show the efficiency and accuracy of the proposed new methods and confirm our theoretical analysis.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Zhangqing Yu, Liying Kang, Lele Liu, Erfang Shan Let G be a graph of order n with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For any real α ∈ [0, 1], write Aα(G) for the matrixAα(G)=αD(G)+(1−α)A(G).This paper shows some extremal results on the spectral radius ρα(G) of Aα(G). We determine the upper bound on ρα(G) if α ∈ (0, 1) and G is a graph with no K2, t (t ≥ 3) minor. We also show that the unique outerplanar graph of order n with maximum ρα(G) is the join of a vertex and a path Pn−1. Moreover, we prove that the unique planar graph of order n with maximum signless Laplacian spectral radius is the join of an edge and a path Pn−2.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Marcin Anholcer, Sylwia Cichacz, Jakub Przybyło We investigate the group irregularity strength, sg(G), of a graph, i.e., the least integer k such that taking any Abelian group G of order k, there exists a function f:E(G)→G so that the sums of edge labels incident with every vertex are distinct. So far the best upper bound on sg(G) for a general graph G was exponential in n−c, where n is the order of G and c denotes the number of its components. In this note we prove that sg(G) is linear in n, namely not greater than 2n. In fact, we prove a stronger result, as we additionally forbid the identity element of a group to be an edge label or the sum of labels around a vertex. We consider also locally irregular labelings where we require only sums of adjacent vertices to be distinct. For the corresponding graph invariant we prove the general upper bound: Δ(G)+col(G)−1 (where col(G) is the coloring number of G) in the case when we do not use the identity element as an edge label, and a slightly worse one if we additionally forbid it as the sum of labels around a vertex. In the both cases we also provide a sharp upper bound for trees and a constant upper bound for the family of planar graphs.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Irina V. Stepanova The paper presents symmetry analysis of three-dimensional equations of heat and mass transfer in a binary liquid. The system contains three unknown functions related to physical properties of liquid. Supposing thermal diffusivity to be depended on temperature with respect to power law, diffusion and thermal diffusion coefficients are found using of classical Lie symmetry approach. It is shown that the solution of the group classification problem consists of two parts. We obtain different results if we take into account that diffusion coefficient either has the same form as the thermal diffusivity coefficient or it depends on temperature and concentration essentially. Some reductions of the governing equations are constructed with the help of the obtained transformations of dependent and independent variables. New exact solutions of the reduced equations have been found in several cases.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Lifen Jia, Yuhong Sheng As a type of differential equation, uncertain delay differential equation is driven by Liu process. Stability in measure, stability in mean and stability in moment for uncertain delay differential equation have been proposed. This paper mainly gives a concept of stability in distribution, and proves a sufficient condition for uncertain delay differential equation being stable in distribution as a supplement. Moreover, this paper further discusses their relationships among stability in distribution, stability in measure, stability in mean and stability in moment.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Tianjun Wang, Yujian Jiao, Wenjie Liu In this paper, we develop a mixed Jacobi–Fourier pseudospectral method for solving the Fisher equation in a disc. Fisher’s equation always plays a large role in many fields, such as logistic population growth models, tissue engineering, nuclear reactions, and neurophysiology, etc.. It is very important to study how to solve these equations numerically. In this work, we employ the generalized Jacobi approximation to simulate the singularity of solutions at the regional center. Some mixed Jacobi–Fourier interpolation approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. As an application, the mixed Jacobi–Fourier pseudospectral scheme is provided for the Fisher equation in a disk. The generalized stability and convergence of the proposed scheme are proved. Some numerical results are presented to demonstrate the efficiency of this new algorithm.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Emil Cătinaş Twenty years after the classical book of Ortega and Rheinboldt was published, five definitions for the Q-convergence orders of sequences were independently and rigorously studied (i.e., some orders characterized in terms of others), by Potra (1989), resp. Beyer, Ebanks and Qualls (1990). The relationship between all the five definitions (only partially analyzed in each of the two papers) was not subsequently followed and, moreover, the second paper slept from the readers attention.The main aim of this paper is to provide a rigorous, selfcontained, and, as much as possible, a comprehensive picture of the theoretical aspects of this topic, as the current literature has taken away the credit from authors who obtained important results long ago.Moreover, this paper provides rigorous support for the numerical examples recently presented in an increasing number of papers, where the authors check the convergence orders of different iterative methods for solving nonlinear (systems of) equations. Tight connections between some asymptotic quantities defined by theoretical and computational elements are shown to hold.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Mirosław Lachowicz, Henryk Leszczyński, Krzysztof A. Topolski We study a kinetic equation which describes self-organization of various complex systems, assuming the interacting rate with small support. This corresponds to interactions between an agent with a given internal state and agents having short distance states only. We identify all possible stationary (equilibrium) solutions and describe the possibility of creating of bipolar (bimodal) distribution that is able to capture interesting behavior in modeling systems, e.g. in political sciences.

Abstract: Publication date: 15 February 2019Source: Applied Mathematics and Computation, Volume 343Author(s): Jinde Cao, Luca Guerrini, Zunshui Cheng This paper considers Hopf bifurcation of complex network with two independent delays. By analyzing the eigenvalue equations, the local stability of the system is studied. Taking delay as parameter, the change of system stability with time is studied and the emergence of inherent bifurcation is given. By changing the value of the delay, the bifurcation of a given system can be controlled. Numerical simulation results confirm the validity of the results found.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Sean Breckling, Sidney Shields Herein we present a study on the long-time stability of finite element discretizations of a generalized class of semi-implicit second-order time-stepping schemes for the 2D incompressible Navier–Stokes equations. These remarkably efficient schemes require only a single linear solve per time-step through the use of a linearly-extrapolated advective term. Our result develops a class of sufficient conditions such that if external forcing is uniformly bounded in time, velocity solutions are uniformly bounded in time in both the L2 and H1 norms. We provide numerical verification of these results. We also demonstrate that divergence-free finite elements are critical for long-time H1 stability.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Chen Liu, Li Li, Zhen Wang, Ruiwu Wang Regular pattern is a typical feature of vegetation distribution which can be recognized as early warnings of desertification. In this work, a vegetation system with cross diffusion is presented based on reaction-diffusion equations. By means of mathematical analysis, we obtain the appropriate parameter space which can ensure the emergence of stationary patterns. Moreover, it is unveiled that cross diffusion not only induces the pattern transitions, yet promotes the density of the vegetation. These obtained results suggest that cross diffusion is an important mechanism in vegetation dynamics.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Chen Liu, Juan Shi, Tong Li, Jinzhuo Liu In realistic world, the role or influence of each individual is heterogeneous and usually varies according to surroundings. Inspired by this fact, here we study the emergence of cooperative behavior in weighted networks under the coevolution of game strategy and node weight, where the node weight is used to mimic the role or influence of subjects. In the prisoner's dilemma, if an individual's fitness exceeds the aspiration level, its weight becomes larger; otherwise weight decreases. While such an adjustment of weight is defined by the intensity parameter δ, it is interesting that there is an optimal range for δ guaranteeing the best evolution of cooperation. The facilitation of cooperative behavior mainly depends on the weight distribution of players, which is based on the formation of a cooperative cluster controlled by high-weight cooperators. These cooperators are able to prevail against defectors even when there is a large temptation to defect. Our research provides a viable route to resolve social dilemma and will inspire further applications.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Mohammed Al-Smadi, Omar Abu Arqub Numerical modeling of partial integrodifferential equations of fractional order shows interesting properties in various aspects of science, which means increased attention to fractional calculus. This paper is concerned with a feasible and accurate technique for obtaining numerical solutions for a class of partial integrodifferential equations of fractional order in Hilbert space within appropriate kernel functions. The algorithm relies on the reproducing kernel Hilbert space method that provides the solutions in rapidly convergent series representations for the reproducing kernel based upon the Fourier coefficients of orthogonalization process. The Caputo fractional derivatives are introduced to address these issues. Moreover, the error estimate of the generated solutions is established as well as the convergence of the iterative method is investigated under some theoretical assumptions. The superiority and applicability of the present technique is illustrated by handling linear and nonlinear numerical examples. The outcomes obtained are compared with exact solutions and existing methods to confirm the effectiveness of the reproducing kernel method.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Fahimeh Saberi Zafarghandi, Maryam Mohammadi, Esmail Babolian, Shahnam Javadi Fractional order diffusion equations are generalizations of classical diffusion equations, treating super-diffusive flow processes. The paper presents a meshless method based on spatial trial spaces spanned by the radial basis functions (RBFs) for the numerical solution of a class of initial-boundary value fractional diffusion equations with variable coefficients on a finite domain. The space fractional derivatives are defined by using Riemann–Liouville fractional derivative. We first provide Riemann–Liouville fractional derivatives for the five kinds of RBFs, including the Powers, Gaussian, Multiquadric, Matérn and Thin-plate splines, in one dimension. The time-dependent fractional diffusion equation is discretized in space with the RBF collocation method and the remaining system of ordinary differential equations (ODEs) is advanced in time with an ODE method using a method of lines approach. Some numerical results are given in order to demonstrate the efficiency and accuracy of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method. The stability of the linear systems arising from discretizing Riemann–Liouville fractional differential operator with RBFs is also analysed.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Dian Zhang, Jun Cheng, Choon Ki Ahn, Hongjie Ni This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ(t) is assumed to satisfy τ1 ≤ τ(t) ≤ τ2. Based on the flexible terminal approach, the time-varying delay τ(t) is first transformed such that τ1(t) ≤ τ(t) ≤ τ2(t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Alexander Blokhin, Boris Semisalov We propose and describe in detail an effective numerical algorithm for finding the stationary solution of charge transport problem in a DG-MOSFET. Hydrodynamical models describing the process of charge transport in semiconductors are sets of nonlinear PDE's with small parameters and specific conditions on the boundary of transistor that essentially complicates the process of numerical simulations. We construct a new algorithm based on the stabilization method and ideas of approximation without saturation and pseudo-spectral methods that enables one to overcome all of the mentioned difficulties. The proposed algorithm enables us to obtain the solution for different geometrical characteristics of DG-MOSFET and boundary conditions (including the non-symmetric cases) with extremely small values of dimensionless doping density and dielectric constant that are used in practice.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Changbum Chun, Beny Neta Two families of order six for the solution of systems of nonlinear equations are developed and compared to existing schemes of order up to six. We have found that one of the methods in the literature has been rediscovered. The comparison is based on the total cost of an iteration and the performance on 14 examples of systems of dimensions 2–9.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Xiaodi Li, Xueyan Yang, Tingwen Huang In this paper, the problem of impulsive control for persistence of N-species cooperative models with time-varying delays are studied. A method on impulsive control is introduced to delayed cooperative models and some sufficient conditions for the persistence of the addressed models are derived, which are easy to check in real problems. The results show that proper impulsive control strategy may contribute to the persistence of cooperative populations and maintain the balance of an ecosystem. Conversely, the undesired impulsive control such as impulsive harvesting too frequently or impulsive harvesting too drastically may destroy the persistence of populations and leads to the extinction of some species. In addition, some discussions and comparisons with the recent works in the literature are given. Finally, the proposed method is applied to two numerical examples to show the effectiveness and advantages of our results.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Maohua Ran, Taibai Luo, Li Zhang This paper is concerned with numerical methods for solving a class of fourth-order diffusion equations. Combining the compact difference operator in space discretization and the linear θ method in time, the compact theta scheme for the linear problem is first proposed. By virtue of the Fourier method, the suggested scheme is shown to be unconditionally stable and convergent in the discrete L2-norm for any θ ∈ [1/2, 1]. And then this idea is generalized to the semi-linear case, the corresponding compact theta scheme is constructed and analyzed in detail. Numerical experiments corresponding to the linear and semi-linear situations are carried out to support our theoretical statements.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Hamza Chehabi, Omar Chakrone, Mohammed Chehabi This work deals with the antimaximum principle for the discrete Neumann and Dirichlet problem−Δφp(Δu(k−1))=λm(k) u(k) p−2u(k)+h(k)in[1,n].We prove the existence of three real numbers 0 ≤ a

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Xiaoli Li, Hongxing Rui In this paper, we establish the LBB condition and stability for both velocity and pressure of characteristic MAC scheme for the Oseen equations on non-uniform grids. We obtain the second order convergence in discrete L2 norm for both velocity and pressure and the first order convergence in discrete H1 norm for velocity. Moreover, we construct the post-processing characteristic MAC scheme to obtain second order accuracy in discrete H1 norm for the velocity. Finally, some numerical experiments are presented to show the correctness and accuracy of the MAC scheme.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): J.P. Chaudhary, L.P. Singh The present paper concerns with the study of the Riemann problem for a quasi-linear hyperbolic system of partial differential equations governing the one dimensional isentropic dusty gas flow. The shock and rarefaction waves and their properties for the problem are investigated. We also examine how some of the properties of shock and rarefaction waves in a dusty gas flow differ from isentropic ideal gas flow. The solution of Riemann problem of dusty gas flow for different initial data is discussed. Under certain conditions, the uniqueness and existence of the solution of the Riemann problem has been analyzed. Finally, all possible interactions of elementary waves are discussed.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Jesús Martín-Vaquero, Svajūnas Sajavičius In this paper, the two-level finite difference schemes for the one-dimensional heat equation with a nonlocal initial condition are analyzed. As the main result, we obtain conditions for the numerical stability of the schemes. In addition, we revise the stability conditions obtained in [21] for the Crank–Nicolson scheme. We present several numerical examples that confirm the theoretical results within linear, as well as nonlinear problems. In some particular cases, it is shown that for small regions of the time step size values, the explicit FTCS scheme is stable while certain implicit methods, such as Crank–Nicolson scheme, are not.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Yuan-Ming Wang, Lei Ren A high-order compact finite difference method is proposed for solving a class of time-fractional sub-diffusion equations. The diffusion coefficient of the equation may be spatially variable and the time-fractional derivative is in the Caputo sense with the order α ∈ (0, 1). The Caputo time-fractional derivative is discretized by a (3−α) th-order numerical formula (called the L2 formula here) which is constructed by piecewise quadratic interpolating polynomials but does not require any sub-stepping scheme for the approximation at the first-time level. The variable coefficient spatial differential operator is approximated by a fourth-order compact finite difference operator. By developing a technique of discrete energy analysis, a full theoretical analysis of the stability and convergence of the method is carried out for the general case of variable coefficient and for all α ∈ (0, 1). The optimal error estimate is obtained in the L2 norm and shows that the proposed method has the temporal (3−α) th-order accuracy and the spatial fourth-order accuracy. Further approximations are also considered for enlarging the applicability of the method while preserving its high-order accuracy. Applications are given to three model problems, and numerical results are presented to demonstrate the theoretical analysis results.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Guodong Ren, Yuxiong Xue, Yuwei Li, Jun Ma Some evidences have confirmed that field coupling is much effective to realize signal propagation between neurons, and the biological function of synapse connection has also been modulated when field coupling is activated. These theoretical prediction and confirmation are approached on neuron model with electromagnetic induction and magnetic flux coupling is used to describe the effect of field coupling. Neuron is treated as a smart signal processor and neuronal activities can be reproduced in electric circuit by setting appropriate parameters. When time-varying current flows along the inductorium, magnetic flux across the coil is changed and induced electromotive force of the inductor is triggered. Indeed, exchange of magnetic flux between inductoriums (induction coils) can trigger modulation on magnetic field. Therefore, two nonlinear circuits can be connected to reach possible consensus of outputs by using this kind of field coupling. In this paper, two identical Colpitts oscillators are coupled by transformer which is introduced from partial inductance equivalent circuit (PEEC), and the potential differences between circuit nodes are analysed to find synchronization approach under field coupling. An unit matrix is used to derive the Master Stability Functions of the coupled systems, and the synchronization manifold of the system describes the effect of the parasitic elements on dynamical behaviour. It is also found that both of the gain of the oscillators and the coupling coefficient of transformer are important bifurcation parameters for synchronization manifold of the system. Similar investigation is as well practiced on printed circuit board (PCB) and the synchronization approach is confirmed under field coupling. This kind of field coupling provides another effective way to synchronization modulation via continuous exchange of field energy in the coupling device.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Bao-Xuan Zhu, Yun Chen An independent set in a graph G is a set of pairwise non-adjacent vertices. Let ik(G) denote the number of independent sets of cardinality k in G. Then, its generating functionI(G;x)=∑k=0α(G)ik(G)xkis called the independence polynomial of G (Gutman and Harary, 1983).Alavi et al. (1987) conjectured that the independence polynomial of any tree or forest is unimodal. This conjecture is still open. In this paper, after obtaining recurrence relations and giving factorizations of independence polynomials for certain classes of trees, we prove the log-concavity of their independence polynomials. Thus, our results confirm the conjecture of Alavi et al. for some special cases.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Juan Monsalve, Juan Rada, Yongtang Shi Graph energy can be extended to digraphs via the trace norm. The trace norm of a digraph is the trace norm of its adjacency matrix, i.e. the sum of its singular values. In this work we find the oriented graphs that attain minimal and maximal trace norm over the set of oriented bicyclic graphs.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Xiaofeng Wang, Weizhong Dai, Shuangbing Guo In the present work, a three-level in time linear and conservative implicit finite difference scheme for solving the 2D regularized long-wave equation is proposed. The existence, uniqueness, and conservations for mass and energy of the numerical solution are proved by the discrete energy method. The new scheme is shown to be second-order convergent and unconditionally stable. Numerical examples are provided to show the present scheme to be efficient and reliable.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Hossein Lakzian, B.E. Rhoades In the present paper we prove some new fixed point theorems for self-mappings defined on a complete metric space with a w-distance. These results extend some previous fixed point theorems in this field to more general contractive conditions in the setting of w-distances for selfmappings which satisfy certain weaker Meir–Keeler conditions.

Abstract: Publication date: 1 February 2019Source: Applied Mathematics and Computation, Volume 342Author(s): Fernanda Paula Barnosa Pola, Ives Renê Venturini Pola Many numerical methods are based in mesh files to represent the computational domain. Also, an efficient storage and retrieval of mesh information can be achieved by data structures. Moreover, the development of topological operators is one of the important goals of the geometric modeling research field. While it loads mesh files more efficiently, it also allocates less main memory, provides persistence and allows consistent query operations. This paper proposes an improving of the computational scheme of high-order WENO schemes by coupling a standard cell centered, unstructured mesh, finite volume method with an topological data structure. The solver module uses the finite volume technique with a formulation that sets the property values to the control volume centroids. The two dimensional Euler equations are considered to represent the flow of interest. Beyond experiments using the improved approach, the computational cost of the data structure was measured by comparing with the traditional representation, and the results showed that our approach provides scalable loading and managing of meshes, having less memory occupation rate when comparing meshes with an increasing number of elements.

Abstract: Publication date: Available online 16 February 2018Source: Applied Mathematics and ComputationAuthor(s): Marcel Ilie Strong (two-way) coupling of fluid and structure presents interest to vary engineering applications, particularly when the flow is turbulent and sensitive to the structure motions. In the present work a CFD based algorithm, using large-eddy simulation, is proposed for the numerical investigation of strong aeroelastic fluid-structure coupling. The present work concerns the highly turbulent flows. The Reynolds number effect on the aeroelastic response of vertical flat plate in cross-flow is subject of investigation. The results of the present work indicate that there is a strong coupling between fluid and structure, and thus the fluid and structure influence each other in a particular manner. Also the results show that the aeroelastic response of the structure depends on the flow Reynolds number. It was observed that the structure's deformations increase with the Reynolds number.

Abstract: Publication date: Available online 1 February 2018Source: Applied Mathematics and ComputationAuthor(s): E. Karimi-Sibaki, A. Kharicha, M. Wu, A. Ludwig, J. Bohacek Electrically resistive CaF2-based slags are extensively used in many metallurgical processes such as electroslag remelting (ESR). Chemical and electrochemical reactions as well as transport of ions in the molten slag (electrolyte) are critical phenomena for those processes. In this paper, an electrochemical system including two parallel, planar electrodes and a completely dissociated electrolyte operating under a DC voltage is modeled. The transport of ions by electro-migration and diffusion is modeled by solving the Poisson–Nernst–Planck (PNP) equations using the Finite Volume Method (FVM). The non-linear Butler–Volmer equations are implemented to describe the boundary condition for the reacting ions at the electrode–electrolyte interface. Firstly, we study a binary symmetrical electrolyte, which was previously addressed by Bazant et al. (2005), to verify the numerical model. Secondly, we employed the model to investigate our target CaF2–FeO system. The electrolyte is consisted of reacting (Fe2+) and non-reacting (Ca+2, O2−, F−) ions. Spatial distributions of concentrations of ions, charge density, and electric potential across the electrolyte at steady state are analyzed. It is found that the Faradaic reaction of the ferrous ion (Fe2+) has negligible impact on the electric potential field at very low current density (