Authors:Shouguo Qian; Yu Liu; Gang Li; Li Yuan Pages: 23 - 37 Abstract: Publication date: 15 July 2018 Source:Applied Mathematics and Computation, Volume 329 Author(s): Shouguo Qian, Yu Liu, Gang Li, Li Yuan Euler equations under gravitational fields often appear in some interesting astrophysical and atmospheric applications. The Euler equations are coupled with gravitational source term due to the gravity and admit hydrostatic equilibrium state where the flux produced by the pressure gradient is exactly balanced by the gravitational source term. In this paper, we construct high order discontinuous Galerkin methods for the Euler equations under gravitational fields, which are well-balanced for the isentropic type hydrostatic equilibrium state. To maintain the well-balanced property, we first reformulate the governing equations in an equivalent form. Then we propose a novel source term approximation based on a splitting algorithm as well as well-balanced numerical fluxes. Rigorous theoretical analysis and extensive numerical examples all suggest that the proposed methods maintain the hydrostatic equilibrium state up to the machine precision. Moreover, one- and two-dimensional simulations are performed to test the ability of the current methods to capture small perturbation of such equilibrium state, and the genuine high order accuracy in smooth regions.

Authors:Kai-Ning Wu; Han-Xiao Sun; Baoqing Yang; Cheng-Chew Lim Pages: 52 - 63 Abstract: Publication date: 15 July 2018 Source:Applied Mathematics and Computation, Volume 329 Author(s): Kai-Ning Wu, Han-Xiao Sun, Baoqing Yang, Cheng-Chew Lim This paper considers finite-time stabilization and H ∞ performance for delay reaction–diffusion systems by boundary control. First, a full-domain controller is designed and sufficient conditions are obtained to achieve finite-time stability using finite-time stability lemma and Wirtinger’s inequality method. Then a boundary controller furnished with sufficient conditions to achieve finite-time stability is presented. When taking into consideration external noise on a delay reaction–diffusion system, finite horizon H ∞ boundary control with a criterion that guarantees the H ∞ performance of delay reaction–diffusion systems is proposed. How to handle Neumann boundary conditions and mixed boundary conditions are discussed. Numerical simulations are carried out to verify the effectiveness of our theoretical results.

Authors:Hannelore Lisei; Csaba Varga; Orsolya Vas Pages: 64 - 83 Abstract: Publication date: 15 July 2018 Source:Applied Mathematics and Computation, Volume 329 Author(s): Hannelore Lisei, Csaba Varga, Orsolya Vas In this paper, we prove versions of the general minimax theorem of Willem and of the Mountain Pass Theorem of Ambrosetti and Rabinowitz on a wedge intersected with a ball in a reflexive locally uniformly convex smooth Banach space. We apply these results to localize two nontrivial solutions for Dirichlet problems involving nonhomogeneous operators in the context of Orlicz–Sobolev spaces. As a special case, we obtain also the existence of two nontrivial positive solutions located on a certain ball for p-Laplacian boundary value problems.

Authors:Jianwen Chen; Zhi-Min Chen; Bo-Qing Dong Pages: 84 - 91 Abstract: Publication date: 15 July 2018 Source:Applied Mathematics and Computation, Volume 329 Author(s): Jianwen Chen, Zhi-Min Chen, Bo-Qing Dong A new commutator estimate with respect to a nonlinear convection upper bounded by a single partial derivative component in Hilbert spaces is obtained. As an application, regularity criteria on the supercritical quasi-geostrophic equation are obtained provided that solution growth conditions are assumed to involve a single partial derivative component.

Authors:Xiangfeng Yang Pages: 92 - 104 Abstract: Publication date: 15 July 2018 Source:Applied Mathematics and Computation, Volume 329 Author(s): Xiangfeng Yang Uncertain heat equation is a type of uncertain partial differential equations driven by Liu processes. This paper proposes a concept of α-path for uncertain heat equation, and shows that the solution of an uncertain heat equation can be represented by a family of solutions of ordinary heat equations. And, a formula is derived to calculate expected value of solution of uncertain heat equation. Moreover, a numerical method is designed to solve uncertain heat equation. Several examples are given to illustrate the efficiency of the numerical method.

Authors:Baiju Zhang; Minfu Feng Pages: 1 - 25 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Baiju Zhang, Minfu Feng We propose and analyze a virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation, that is to say, stresses are not require to be symmetric, but only to satisfy a weaker condition based on Lagrange multipliers. The proposed method is well-posed, and the error bounds are shown to be uniform with the incompressibility parameter λ. Numerical tests confirm the convergence rate that is expected from the theory.

Authors:Monika J. Piotrowska; Agnieszka Bartłomiejczyk; Marek Bodnar Pages: 26 - 44 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Monika J. Piotrowska, Agnieszka Bartłomiejczyk, Marek Bodnar We propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate the stability of new born periodic solutions. Theoretical results are illustrated by numerical simulations and interpreted from the biological point of view.

Authors:Shuchao Li; Wei Wei Pages: 45 - 57 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Shuchao Li, Wei Wei Tree-like octagonal systems are cata-condensed systems of octagons, which represent a class of polycyclic conjugated hydrocarbons. An octagonal chain is a cata-condensed octagonal system with no branchings. In this paper, the extremal octagonal chains with n octagons having the minimum and maximum coefficients sum of the permanental polynomial are identified, respectively.

Authors:Baohua Huang; Changfeng Ma Pages: 58 - 74 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Baohua Huang, Changfeng Ma The iterative algorithm of a class of generalized coupled Sylvester-transpose matrix equations is presented. We prove that if the system is consistent, a solution can be obtained within finite iterative steps in the absence of round-off errors for any initial matrices; if the system is inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm least squares solution of the problem. Finally, numerical examples are presented to demonstrate that the algorithm is efficient.

Authors:Vladislav V. Kravchenko Pages: 75 - 81 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Vladislav V. Kravchenko A new representation for solutions of the one-dimensional Schrödinger equation − u ″ + q ( x ) u = ω 2 u is obtained in the form of a series possessing the following attractive feature. The truncation error is ω-independent for all ω ∈ R . For the coefficients of the series simple recurrent integration formulas are obtained which make the new representation applicable for computation.

Authors:J. Enrique Vázquez-Lozano; Alicia Cordero; Juan R. Torregrosa Pages: 82 - 99 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): J. Enrique Vázquez-Lozano, Alicia Cordero, Juan R. Torregrosa In this paper, the performance of a parametric family including Newton’s and Traub’s schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well as the dynamical behavior in terms of the damping parameter on cubic polynomials with multiple roots. The fixed and critical points, and the associated parameter plane are some of the characteristic dynamical features of the family which are obtained in this work. From the analysis of these elements we identify members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots, and also other ones with very unstable behavior.

Authors:Hongbo Chen; Tianliang Hou Pages: 100 - 112 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Hongbo Chen, Tianliang Hou In this paper, we investigate a priori and a posteriori error estimates of H 1-Galerkin mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equations. The state variables and co-state variables are approximated by the lowest order Raviart–Thomas mixed finite element and linear finite element, and the control variable is approximated by piecewise constant functions. Based on two new elliptic projections, we derive a priori error estimates both for the control variable, the state variable and the co-state variable. The related a priori error estimates for the new projections error are also established. Moreover, a posteriori error estimates for all variables are derived via energy method. Such a posteriori error estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

Authors:Yaser Alizadeh; Sandi Klavžar Pages: 113 - 118 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Yaser Alizadeh, Sandi Klavžar If u is a vertex of a graph G, then the transmission of u is the sum of distances from u to all the other vertices of G. The Wiener complexity CW (G) of G is the number of different complexities of its vertices. G is transmission irregular if C W ( G ) = n ( G ) . It is proved that almost no graphs are transmission irregular. Let T n 1 , n 2 , n 3 be the tree obtained from paths of respective lengths n 1, n 2, and n 3, by identifying an end-vertex of each of them. It is proved that T 1 , n 2 , n 3 is transmission irregular if and only if n 3 = n 2 + 1 and n 2 ∉ { ( k 2 − 1 ) / 2 , ( k 2 − 2 ) / 2 } for some k ≥ 3. It is also proved that if T is an asymmetric tree of order n, then the Wiener index of T is bounded by ( n 3 − 13 n + 48 ) / 6 with equality if and only if T = T 1 , 2 , n − 4 . A parallel result is deduced for asymmetric uni-cyclic graphs.

Authors:Cui Li; Chengjian Zhang Pages: 119 - 124 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Cui Li, Chengjian Zhang This paper is concerned with the exponential stability for nonlinear second-order functional differential equations (FDEs) with time-variable delays. An exponential stability relationship between the FDEs and the corresponding ordinary differential equations (ODEs) is derived. It is proved under some appropriate conditions that the second-order FDEs can preserve the exponential stability of the corresponding ODEs. This stability result is also illustrated with a numerical approach.

Authors:Iria C.S. Cosme; Isaac F. Fernandes; João L. de Carvalho; Samuel Xavier-de-Souza Pages: 125 - 136 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Iria C.S. Cosme, Isaac F. Fernandes, João L. de Carvalho, Samuel Xavier-de-Souza The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider exchanging less memory usage for more processing time in order to enable the computation of the inverse which otherwise would be prohibitive. We propose a new algorithm to compute the inverse of block partitioned matrices with a reduced memory footprint. The algorithm works recursively to invert one block of a k × k block matrix M, with k ≥ 2, based on the successive splitting of M. It computes one block of the inverse at a time, in order to limit memory usage during the entire processing. Experimental results show that, despite increasing computational complexity, matrices that otherwise would exceed the memory-usage limit can be inverted using this technique.

Authors:Jie Xue; Shuting Liu; Jinlong Shu Pages: 137 - 143 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Jie Xue, Shuting Liu, Jinlong Shu Let G be a connected graph with vertex set V(G) and edge set E(G). Let T(G) be the diagonal matrix of vertex transmissions of G and D(G) be the distance matrix of G. The distance Laplacian matrix of G is defined as L ( G ) = T ( G ) − D ( G ) . The distance signless Laplacian matrix of G is defined as Q ( G ) = T ( G ) + D ( G ) . In this paper, we show that the complements of path and cycle are determined by their distance (signless) Laplacian spectra.

Authors:Yali Gao; Liquan Mei; Rui Li Pages: 144 - 161 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Yali Gao, Liquan Mei, Rui Li In this paper, we propose two Galerkin methods to investigate the evolution of the Davey–Stewartson equations. The extrapolated Crank–Nicolson scheme and decoupled semi-implicit multistep scheme are employed to increase the order of the time discrete accuracy, which only requires the solutions of a linear system at each time step. Four numerical experiments are presented to illustrate the features of the proposed numerical methods, such as the optimal convergence order, the conservation variable and the application in rogue waves.

Authors:Qiang Wang; Nanrong He; Xiaojie Chen Pages: 162 - 170 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Qiang Wang, Nanrong He, Xiaojie Chen Costly punishment can promote human cooperation, but the effectiveness of punishment is reduced because of the existence of second-order free-rider problem. How to solve the problem remains a challenge for the emergence of costly punishment. Motivated by the regimes of resource allocation in human society, in this work we consider the resource allocation with threshold for the common pool in the public goods game with an additional strategy of peer punishment, and aim to explore whether such proposed resource allocation can solve the problem of second-order free-riders by using replicator equations in infinite well-mixed populations. We assume that if contributing resources in the common pool exceed the threshold, the contributing resources will be divided into two parts: the first part will be equally allocated by all the players, and the second part will be allocated by all the players based on their strategy choices. Otherwise all the contributing resources are equally allocated by all the players. We find that the second-order free-rider problem can be effectively solved by this regime of resource allocation even when most of contributing resources are equally allocated among individuals. In addition, we find that punishment is the dominant strategy in a broad region of allocation parameters. Our work may thus suggest an effective approach about resource allocation for resisting second-order free-riders in the public goods dilemma.

Authors:N. Rohaninasab; K. Maleknejad; R. Ezzati Pages: 171 - 188 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): N. Rohaninasab, K. Maleknejad, R. Ezzati The main purpose of this paper is to use the Legendre collocation spectral method for solving the high-order linear Volterra–Fredholm integro-differential equations under the mixed conditions. Avoiding integration of both sides of the equation, we expressed mixed conditions as equivalent integral equations, by adding the neutral term to the equation. Error analysis for approximate solution and approximate derivatives up to order k of the solution is obtained in both L 2 norm and L ∞ norm. To illustrate the accuracy of the spectral method, some numerical examples are presented.

Authors:Xiaolin Qin; Lu Yang; Yong Feng; Bernhard Bachmann; Peter Fritzson Pages: 189 - 202 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Xiaolin Qin, Lu Yang, Yong Feng, Bernhard Bachmann, Peter Fritzson High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize the idea of differential elimination with Dixon resultant to polynomially nonlinear DAEs. We propose a new algorithm for index reduction of DAEs and establish the notion of differential Dixon resultant, which can provide the differential resultant of the enlarged system of original equations. To make use of structure of DAEs, variable pencil technique is given to determine the termination of differentiation. Moreover, we also provide a heuristic method for removing the extraneous factors from differential resultant. The experimentation shows that the proposed algorithm outperforms existing ones for many examples taken from the literature.

Authors:Carolina Gómez-Tostón; Manuel Barrena; Álvaro Cortés Pages: 203 - 223 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Carolina Gómez-Tostón, Manuel Barrena, Álvaro Cortés Pivot-based retrieval algorithms are commonly used to solve similarity queries in a number of application domains, such as multimedia retrieval, biomedical databases, time series and computer vision. The query performances of pivot-based index algorithms can be significantly improved by properly choosing the set of pivots that is able to narrow down the database elements to only those relevant to a query. While many other approaches in the literature rely on empirical studies or intuitive observations and assumptions to achieve effective pivot strategies, this paper addresses the problem by using a formal mathematical approach. We conclude in our study that the optimal set of pivots in vector databases with Lp metrics is a set of uniformly distributed points on the surface of an n-sphere defined by these metrics. To make the study mathematically tractable, a uniform distribution of data in the database is assumed, allowing us to outline the problem from a purely geometrical point of view. Then, we present experimental results demonstrating the usefulness of our characterization when applied to real databases in the ( R n , L p ) metric space. Our technique is shown to outperform comparable techniques in the literature. However, we do not propose a new pivot-selection technique but rather experiments that are designed exclusively to show the usefulness of such a characterization.

Authors:Fei Long; Chuan-Ke Zhang; Yong He; Lin Jiang; Qing-Guo Wang; Min Wu Pages: 224 - 242 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Fei Long, Chuan-Ke Zhang, Yong He, Lin Jiang, Qing-Guo Wang, Min Wu This paper is concerned with the stability analysis of Lur’e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov–Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.

Authors:Ivan D. Remizov Pages: 243 - 246 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Ivan D. Remizov We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The method is based on the Chernoff approximation procedure applied to a specially constructed shift operator. It is proven that approximations converge uniformly to the exact solution.

Authors:Jing Wang; Kun Liang; Xia Huang; Zhen Wang; Hao Shen Pages: 247 - 262 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Jing Wang, Kun Liang, Xia Huang, Zhen Wang, Hao Shen This paper focuses on the analysis and design of dissipativity-based fault-tolerant controller for discrete-time nonlinear Markov jump singularly perturbed systems (MJSPSs) which are based on Takagi–Sugeno fuzzy model. A novel strategy is proposed to improve the upper bound of singular perturbation parameter (SPP) ϵ, and the fault-tolerant design is also introduced, namely the susceptible property of systems is made full consideration, to ensure the specified performance of a system. The aim is to design an optimized slow state feedback controller such that the stability of MJSPSs is guaranteed even in faulty case, and the upper bound of the SPP ϵ is improved simultaneously. Utilizing Lyapunov functional technique, a sufficient condition for the existence of controller is shown. Last but not least, the control issue of a series DC motor model as an illustrated example is given to explain the availability of the presented design scheme.

Authors:Lingyu Wang; Tingwen Huang; Qiang Xiao Pages: 263 - 275 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Lingyu Wang, Tingwen Huang, Qiang Xiao This paper is concerned on the global exponential synchronization in timescale sense for a class of nonautonomous recurrent neural networks (NRNNs) with discrete-time delays on time scales. Firstly, a timescale-type comparison result is given based on the induction principle of time scales. Then by the constructed comparison lemma, the theory of time scales and analytical techniques, several synchronization criteria for the driven and response NRNNs are obtained. Moreover, several examples are given to show the effectiveness and validity of the main results. The obtained synchronization criteria improve or extend some existing ones in the literature.

Authors:Nikolai Dokuchaev Pages: 276 - 286 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Nikolai Dokuchaev The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for forecasting. This lead to a forecasting method for more general sequences without this feature based on minimization of the mean square error between the observed path and a predicable sequence. These procedure involves calculation of this predictable path; the procedure can be interpreted as causal smoothing. The corresponding smoothed sequences allow unique extrapolations to future times that can be interpreted as optimal forecasts.

Authors:Frederic Hecht; Temur Jangveladze; Zurab Kiguradze; Olivier Pironneau Pages: 287 - 300 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Frederic Hecht, Temur Jangveladze, Zurab Kiguradze, Olivier Pironneau System of Maxwell equations is considered. Reduction to the integro-differential form is given. Existence, uniqueness and large time behavior of solutions of the initial-boundary value problem for integro-differential model with two-component and one-dimensional case are studied. Finite difference scheme is investigated. Wider class of nonlinearity is studied than one has been investigated before. FreeFem++ realization code and results of numerical experiments are given.

Authors:S.S. Askar Pages: 301 - 311 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): S.S. Askar This paper is devoted to introduce and study a Stackelberg game consisting of three competed firms. The three firms are classified as a leader which is the first firm and the other two firms are called the followers. A linear inverse demand function is used. In addition a quadratic cost based on an actual and announced quantities is adopted. Based on bounded rationality, a three-dimensional discrete dynamical system is constructed. For the system, the backward induction is used to solve the system and to get Nash equilibrium. The obtained results are shown that Nash equilibrium is unique and its stability is affected by the system’s parameters by which the system behaves chaotically due to bifurcation and chaos appeared. Some numerical experiments are performed to portrays such chaotic behavior. A control scheme is used to return the system back to its stability state and is supported by some simulations.

Authors:D.C. Lo; C-P Lee; I-F Lin Pages: 312 - 337 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): D.C. Lo, C-P Lee, I-F Lin An efficient immersed boundary (IB) method is presented for the direct numerical simulation of fluid flow past a pair of circular cylinders and rigid particulate flows. The cylinders are settled in either a tandem or side-by-side arrangement. The grid applied in this paper involves an uneven Cartesian grid, and local differential quadrature (LDQ) is employed to discretize the governing equations. Specifically, a solid in a target region is embedded into the Cartesian grid, and linear interpolation is adopted to calculate the IB and the virtual force on the cell center. The virtual force is substituted into the governing equations to determine the effect of the solid in the IB. The parameters for numerical calculation are the Reynolds number (10–200) and the Prandtl number of air (0.7). The spacing intervals of the tandem arrangement and side-by-side arrangement are g* = 1.5–4 and s* = 1.5–4, respectively. According to the aforementioned conditions, the local Nusselt number and average Nusselt number of the cylinder surface in each arrangement are calculated to investigate how dissimilar flow conditions and spacing intervals between the cylinders influence the effect of heat transfer enhancement. In addition, the present model is applied to simulate the sedimentation of one particle and two particles in a box. Related changes in the flow field of fluid-particles interaction are also discussed.

Authors:Vaishali Sharma; Amit Setia; Ravi P. Agarwal Pages: 338 - 352 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Vaishali Sharma, Amit Setia, Ravi P. Agarwal In this paper, the problem of finding numerical solution for a system of Cauchy type singular integral equations of first kind with index zero is considered. The analytic solution of such system is known. But it is of limited use as it is a nontrivial task to use it practically due to the presence of singularity in the known solution itself. Therefore, a residual based Galerkin method is proposed with Legendre polynomials as basis functions to find its numerical solution. The proposed method converts the system of Cauchy type singular integral equations into a system of linear algebraic equations which can be solved easily. Further, Hadamard conditions of well-posedness are established for system of Cauchy singular integral equations as well as for system of linear algebraic equations which is obtained as a result of approximation of system of singular integral equations with Cauchy kernel. The theoretical error bound is derived which can be used to obtain any desired accuracy in the approximate solution of system of Cauchy singular integral equations. The derived theoretical error bound is also validated with the help of numerical examples.

Authors:Bijaya Laxmi Panigrahi Pages: 353 - 364 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Bijaya Laxmi Panigrahi In this paper, we consider the hybrid collocation methods to solve the eigenvalue problem of a compact integral operator with weakly singular kernels of algebraic and logarithmic type. We obtain the global convergence rates for eigenvalues, the gap between the spectral subspaces and iterated eigenvectors. The numerical examples are presented to verify the theoretical estimates and also shown that this method is computationally useful in comparison to other methods.

Authors:Zhousheng Ruan; Wen Zhang; Zewen Wang Pages: 365 - 379 Abstract: Publication date: 1 July 2018 Source:Applied Mathematics and Computation, Volume 328 Author(s): Zhousheng Ruan, Wen Zhang, Zewen Wang In this paper, a simultaneous identification problem of the spacewise source term and the fractional order for a time-fractional diffusion equation is considered. Firstly, under some assumption and with two different kinds of observation data for one-dimensional and two-dimensional time-fractional diffusion equation, the unique results of the inverse problem are proven by the Laplace transformation method and analytic continuation technique. Then the inverse problems are transformed into Tikhonov type optimization problems, the existence of optimal solutions to the Tikhonov functional is proven. Finally, we adopt an alternating minimization algorithm to solve the optimization problems. The efficiency and stability of the inversion algorithm are tested by several one- and two-dimensional examples.

Authors:Lily Chen; Yingbin Ma; Yongtang Shi; Yan Zhao Pages: 1 - 7 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Lily Chen, Yingbin Ma, Yongtang Shi, Yan Zhao A dominating set in a graph G = ( V , E ) is a subset S of V such that N [ S ] = V , that is, each vertex of G either belongs to S or is adjacent to at least one vertex in S. The minimum cardinality of a dominating set in G is called the domination number, denoted by γ(G). A subset S of V is a [1,2]-set if, for every vertex v ∈ V∖S, v is adjacent to at least one but no more than two vertices in S. The [1,2]-domination number of a graph G, denoted by γ [1, 2](G), is the minimum cardinality of a [1, 2]-set of Chellali et al. gave some bounds for γ [1, 2](G) and proposed the following problem: which graphs satisfy γ ( G ) = γ [ 1 , 2 ] ( G ) . Ebrahimi et al. determined the exact value of the domination number for generalized Petersen graphs P(n, k) when k ∈ {1, 2, 3}. In this paper, we determine the exact values of γ [1, 2](P(n, k)) for k ∈ {1, 2, 3}. We also show that γ [ 1 , 2 ] ( P ( n , k ) ) = γ ( P ( n , k ) ) for k = 1 and k = 3 , respectively, while for k = 2 , γ [1, 2](P(n, k)) ≠ γ(P(n, k)) except for n = 6 , 7 , 9 , 12 .

Authors:Gopal Priyadarshi; B.V. Rathish Kumar Pages: 8 - 21 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Gopal Priyadarshi, B.V. Rathish Kumar In this paper, we propose a wavelet Galerkin method for fourth order linear and nonlinear differential equations using compactly supported Daubechies wavelets. 2-term connection coefficients have been effectively used for a computationally economical evaluation of higher order derivatives. The orthogonality and compact support properties of basis functions lead to highly sparse linear systems. The quasilinearization strategy is effectively employed in dealing with wavelet coefficients of nonlinear problems. The stability and the convergence analysis, in the form of error analysis, have been carried out. An efficient compression algorithm is proposed to reduce the computational cost of the method. Finally, the method is tested on several examples and found to be in good agreement with exact solution.

Authors:Jinming Cai; Zhaowen Zheng Pages: 22 - 34 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Jinming Cai, Zhaowen Zheng We investigate inverse spectral problems for discontinuous Sturm–Liouville problems of Atkinson type whose spectrum consists of a finite set of eigenvalues. For given two finite sets of interlacing real numbers, there exists a class of Sturm–Liouville equations such that the two sets of numbers are exactly the eigenvalues of their associated Sturm–Liouville problems with two different separated boundary conditions. The main approach is to give an equivalent relation between Sturm–Liouville problems of Atkinson type and matrix eigenvalue problems, and the theory of inverse matrix eigenvalue problems.

Authors:P. Favati; G. Lotti; O. Menchi; F. Romani Pages: 35 - 45 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): P. Favati, G. Lotti, O. Menchi, F. Romani In the image reconstruction context the nonnegativity of the computed solution is often required. Conjugate Gradient (CG), used as a reliable regularization tool, may give solutions with negative entries, particularly when large nearly zero plateaus are present. The active constraints set, detected by projection onto the nonnegative orthant, turns out to be largely incomplete leading to poor effects on the accuracy of the reconstructed image. In this paper an inner-outer method based on CG is proposed to compute nonnegative reconstructed images with a strategy which enlarges subsequently the active constraints set. This method appears to be especially suitable for the reconstruction of images having large nearly zero backgrounds. The numerical experimentation validates the effectiveness of the proposed method when compared to other strategies for nonnegative reconstruction.

Authors:Meiling Chi; Fuyi Xu; Yonghong Wu Pages: 46 - 54 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Meiling Chi, Fuyi Xu, Yonghong Wu In this paper, we prove a logarithmic improvement of regularity criterion only in terms of the pressure in Morrey–Campanato spaces for the Cauchy problem to the incompressible MHD equations.

Authors:Shuangshuang Chen; Hongxing Rui Pages: 55 - 69 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Shuangshuang Chen, Hongxing Rui In this paper, a node-centered finite volume method based on triangulations for a fracture model is presented, in which we restrict the pressure to the linear finite element space while the velocity can be approximated by constant vectors element by element. The numerical scheme is established just associated with the pressure to avoid the saddle-point problem. Error estimates of O(h) accuracy for the discrete H 1 semi-norm and the discrete L 2 norm of pressure p and the (L 2)2 norm of velocity u are developed on general triangulations. Under an additional assumption about essentially symmetric control volumes, the error estimates for the pressure p can be improved to O(h 3/2). Finally, numerical experiments are carried out to verify the accuracy and convergence rates for the proposed finite volume scheme.

Authors:Rafael G. Campos; Adolfo Huet Pages: 70 - 78 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Rafael G. Campos, Adolfo Huet A procedure for computing the inverse Laplace transform of real data is obtained by using a Bessel-type quadrature which is given in terms of Laguerre polynomials L N ( α ) ( x ) and their zeros. This quadrature yields a very simple matrix expression for the Laplace transform g(s) of a function f(t) which can be inverted for real values of s. We show in this paper that the inherent instability of this inversion formula can be controlled by selecting a proper set of the parameters involved in the procedure instead of using standard regularization methods. We demonstrate how this inversion method is particularly well suited to solve problems of the form L − 1 [ s g ( s ) ; t ] = f ′ ( t ) + f ( 0 ) δ ( t ) . As an application of this procedure, numerical solutions of a fractional differential equation modeling subdiffusion are obtained and a mean-square displacement law is numerically found.

Authors:S. Nemati; P.M. Lima Pages: 79 - 92 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): S. Nemati, P.M. Lima In the present paper, a modification of hat functions (MHFs) has been considered for solving a class of nonlinear fractional integro-differential equations with weakly singular kernels, numerically. The fractional order operational matrix of integration is introduced. We provide an error estimation for the approximation of a function by a series of MHFs. To suggest a numerical method, the main problem is converted to an equivalent Volterra integral equation of the second kind and operational matrices of MHFs are used to reduce the problem to the solution of bivariate polynomial equations. Finally, illustrative examples are provided to confirm the accuracy and validity of the proposed method.

Authors:Annie Cuyt; Min-nan Tsai; Marleen Verhoye; Wen-shin Lee Pages: 93 - 103 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Annie Cuyt, Min-nan Tsai, Marleen Verhoye, Wen-shin Lee An important hurdle in multi-exponential analysis is the correct detection of the number of components in a multi-exponential signal and their subsequent identification. This is especially difficult if one or more of these terms are faint and/or covered by noise. We present an approach to tackle this problem and illustrate its usefulness in motor current signature analysis (MCSA), relaxometry (in FLIM and MRI) and magnetic resonance spectroscopy (MRS). The approach is based on viewing the exponential analysis as a Padé approximation problem and makes use of some well-known theorems from Padé approximation theory. We show how to achieve a clear separation of signal and noise by computing sufficiently high order Padé approximants, thus modeling both the signal and the noise, rather than filtering out the noise at an earlier stage and return a low order approximant. We illustrate the usefulness of the approach in different practical situations, where some exponential components are difficult to detect and retrieve because they are either faint compared to the other signal elements or contained in a cluster of similar exponential components.

Authors:Changna Lu; Chen Fu; Hongwei Yang Pages: 104 - 116 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Changna Lu, Chen Fu, Hongwei Yang Construct fractional order model to describe Rossby solitary waves can provide more pronounced effects and deeper insight for comprehending generalization and evolution of Rossby solitary waves in stratified fluid. In the paper, from the quasi-geostrophic vorticity equation with dissipation effect and complete Coriolis force, based on the multi-scale analysis and perturbation method, a classical generalized Boussinesq equation is derived to describe the Rossby solitary waves in stratified fluid. Further, by employing the reduction perturbation method, the semi-inverse method, the Agrawal method, we derive the Euler–lagrangian equation of classical generalized Boussinesq equation and obtain the time-fractional generalized Boussinesq equation. Without dissipation effect, by using Lie group analysis method, the conservation laws of time-fractional Boussinesq equation are given. Finally, with the help of the improved (G′/G) expansion method, the exact solutions of the above equation are generated. Meanwhile, in order to consider the dissipation effect, we have to derive the approximate solutions by adopting the New Iterative Method. We remark that the fractional order model can open up a new window for better understanding the waves in fluid.

Authors:Minhajul; D. Zeidan; T. Raja Sekhar Pages: 117 - 131 Abstract: Publication date: 15 June 2018 Source:Applied Mathematics and Computation, Volume 327 Author(s): Minhajul, D. Zeidan, T. Raja Sekhar In the present work, we investigate the Riemann problem and interaction of weak shocks for the widely used isentropic drift-flux equations of two-phase flows. The complete structure of solution is analyzed and with the help of Rankine–Hugoniot jump condition and Lax entropy conditions we establish the existence and uniqueness condition for elementary waves. The explicit form of the shock waves, contact discontinuities and rarefaction waves are derived analytically. Within this respect, we develop an exact Riemann solver to present the complete solution structure. A necessary and sufficient condition for the existence of solution to the Riemann problem is derived and presented in terms of initial data. Furthermore, we present a necessary and sufficient condition on initial data which provides the information about the existence of a rarefaction wave or a shock wave for one or three family of waves. To validate the performance and the efficiency of the developed exact Riemann solver, a series of test problems selected from the open literature are presented and compared with independent numerical methods. Simulation results demonstrate that the present exact solver is capable of reproducing the complete wave propagation using the current drift-flux equations as the numerical resolution. The provided computations indicate that accurate results be accomplished efficiently and in a satisfactory agreement with the exact solution.

Authors:Hongjie Li; Yinglian Zhu; Liu jing; Wang ying Pages: 1 - 15 Abstract: Publication date: 1 June 2018 Source:Applied Mathematics and Computation, Volume 326 Author(s): Hongjie Li, Yinglian Zhu, Liu jing, Wang ying The paper discusses second-order consensus problem of nonlinear multi-agent systems with time delay and intermittent communications. Basing on local intermittent information among the agents, an effective control protocol is proposed by node-based distributed adaptive intermittent information, which a time-varying coupling weight to each node in the communication, some novel criteria are derived in matrix inequalities form by resorting to the generalized Halanay inequality. It is proved that second-order consensus can be reached if the measure of communication is larger than a threshold value under the strongly connected and balanced topology. Moreover, consensus problem is also considered for second-order non-delayed nonlinear multi-agent systems. Finally, a simulation example is presented to illustrate the theoretical results.

Authors:Yanhui Zhang; Hongjing Liang; Hui Ma; Qi Zhou; Zhandong Yu Pages: 16 - 32 Abstract: Publication date: 1 June 2018 Source:Applied Mathematics and Computation, Volume 326 Author(s): Yanhui Zhang, Hongjing Liang, Hui Ma, Qi Zhou, Zhandong Yu This paper investigates the consensus tracking problem of nonlinear multi-agent systems with state constraints and unknown disturbances. An observer is presented for the case that the states of each follower and its neighbors are unmeasurable. State constraint for multi-agent systems is a challenging problem. Barrier Lyapunov functions are applied in this paper to deal with this difficulty. Then based on adaptive back-stepping control approach and dynamic surface control technique, an adaptive fuzzy distributed controller is proposed to guarantee that the tracking errors between all followers and the leader converge to a small neighborhood of the origin. Moreover, it is proved that all the signals in the multi-agent systems are semi-globally uniformly ultimately bounded (SUUB). Finally, some numerical simulation results are presented to testify the effectiveness of the proposed algorithm.

Authors:Zhiqiang Yang; Ziqiang Wang; Zihao Yang; Yi Sun Pages: 56 - 74 Abstract: Publication date: 1 June 2018 Source:Applied Mathematics and Computation, Volume 326 Author(s): Zhiqiang Yang, Ziqiang Wang, Zihao Yang, Yi Sun This paper discusses the multiscale analysis and numerical algorithms for coupled conduction, convection and radiation heat transfer problem in periodic porous materials. First, the multiscale asymptotic expansion of the solution for the coupled problem is presented, and high-order correctors are constructed. Then, error estimates and their proofs will be given on some regularity hypothesis. Finally, the corresponding finite element algorithms based on multiscale method are introduced and some numerical results are given in detail. The numerical tests demonstrate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper.

Authors:Maharajan Raja; Jinde Cao Rajchakit Zhengwen Ahmed Alsaedi Abstract: Publication date: 1 June 2018 Source:Applied Mathematics and Computation, Volume 326 Author(s): C. Maharajan, R. Raja, Jinde Cao, G. Rajchakit, Zhengwen Tu, Ahmed Alsaedi In this epigrammatic, the problem of exponential stability for BAM-type neural networks (BAMNNs) with non-fragile state estimator is investigated under time-varying delays. The delays in discrete and distributed terms are assumed to be time-varying, which means that the lower and upper bounds can be derived. Without involving the time-delays or the activation functions, the non-fragile estimators are constructed in terms of simple linear formation and also the implementation of state estimators are uncomplicated. In addition, the non-fragile estimators are reduced the possible implementation errors in neural networks. For consequence, reason of energy saving, the non-fragile estimators are designed with neural networks. By fabricating a suitable LKF (Lyapunov–Krasovskii functional) and enroling some analysis techniques, a novel sufficient conditions for exponential stability of the designated neural networks are derived in terms of Linear Matrix Inequalities (LMIs), which can be easily assessed by MATLAB LMI Control toolbox. Accordingly, the research proposed here, is advanced and less conservative than the previous one exists in the literature. Finally, two numerical examples with simulations and comparative studies are performed to substantiate the advantage and validity of our theoretical findings.