Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): J.E. Macías-Díaz, A.S. Hendy, R.H. De Staelen In this work, we investigate numerically a nonlinear hyperbolic partial differential equation with space fractional derivatives of the Riesz type. The model under consideration generalizes various nonlinear wave equations, including the sine-Gordon and the nonlinear Klein–Gordon models. The system considered in this work is conservative when homogeneous Dirichlet boundary conditions are imposed. Motivated by this fact, we propose a finite-difference method based on fractional centered differences that is capable of preserving the discrete energy of the system. The method under consideration is a nonlinear implicit scheme which has various numerical properties. Among the most interesting numerical features, we show that the methodology is consistent of second order in time and fourth order in space. Moreover, we show that the technique is stable and convergent. Some numerical simulations show that the method is capable of preserving the energy of the discrete system. This characteristic of the technique is in obvious agreement with the properties of its continuous counterpart.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Sherry H.F. Yan Set partitions avoiding k-crossing and k-nesting have been extensively studied from the aspects of both combinatorics and mathematical biology. By using the generating tree technique, the obstinate kernel method and Zeilberger’s algorithm, Lin confirmed a conjecture due independently to the author and Martinez–Savage that asserts inversion sequences with no weakly decreasing subsequence of length 3 and enhanced 3-nonnesting partitions have the same cardinality. In this paper, we provide a bijective proof of this conjecture. Our bijection also enables us to provide a new bijective proof of a conjecture posed by Duncan and Steingrímsson, which was proved by the author via an intermediate structure of growth diagrams for 01-fillings of Ferrers shapes.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Zhiguo Yan, Ju H. Park, Weihai Zhang This paper is concerned with a unified framework for asymptotic and transient behavior of stochastic systems. In order to explain this problem explicitly, a concept of mean square (γ, α)-stability is first introduced and two stability criteria are derived. By utilizing an auxiliary definition of mean square (γ, T)-stability, the relations among mean square (γ, α)-stability, mean square (γ, T)-stability and finite-time stochastic stability are established. Subsequently, two new sufficient conditions for the existence of state and output feedback mean square (γ, α)-stabilization controllers are presented in terms of matrix inequalities. A numerical algorithm is given to obtain the relation between γ min and α. Finally, an example is given to illustrate our results.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Jianping Zhou, Chengyan Sang, Xiao Li, Muyun Fang, Zhen Wang This paper is concerned with the problem of H ∞ consensus for nonlinear stochastic multi-agent systems with time-delay. The objective is to design a dynamic output feedback protocol such that the multi-agent system reaches consensus in mean square and has a prescribed H ∞ performance level. First, by transforming models, the H ∞ consensus problem is converted to a standard H ∞ control problem. Then, by using the Lyapunov–Krasovskii functional method and the generalized Itô’s formula, both delay-independent and delay-dependent stochastic bounded real lemmas are developed. Based on these, sufficient conditions on the existence of the desired dynamic output feedback protocol are presented in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Changhui Yao, Yuzhen Zhou, Shanghui Jia ‘In this paper, a finite element method is presented to approximate Maxwell–Polynomial Chaos(PC) Debye model in two spatial dimensions. The existence and uniqueness of the weak solutions are presented firstly according with the differential equations by using the Laplace transform. Then the property of energy decay with respect to the time is derived. Next, the lowest Nédélec–Raviart–Thomas element is chosen in spatial discrete scheme and the Crank–Nicolson scheme is employed in time discrete scheme. The stability of full-discrete scheme is explored before an error estimate of accuracy O ( Δ t 2 + h ) is proved under the L 2 − norm. Numerical experiment is demonstrated for showing the correctness of the results.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Huiru Wang, Chengjian Zhang, Yongtao Zhou This paper deals with a class of compact boundary value methods (CBVMs) for solving semi-linear reaction–diffusion equations (SLREs). The presented CBVMs are constructed by combining a fourth-order compact difference method (CDM) with the p-order boundary value methods (BVMs), where the former is for the spatial discretization and the latter for temporal discretization. It is proven under some suitable conditions that the CBVMs are locally stable and uniquely solvable and have fourth-order accuracy in space and p-order accuracy in time. The computational effectiveness and accuracy of CBVMs are further testified by applying the methods to the Fisher equation. Besides these research, we also extend the CBVMs to solve the two-component coupled system of SLREs. The numerical experiment shows that the extended CBVMs are effective and can arrive at the high-precision.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Elyas Shivanian, Ahmad Jafarabadi This study proposes a kind of spectral meshless radial point interpolation (SMRPI) for solving two and three-dimensional parabolic inverse problems on regular and irregular domains. The SMRPI is developed for identifying the control parameter which satisfies the semilinear time-dependent two and three-dimensional diffusion equation with both integral overspecialization and overspecialization at a point in the spatial domain. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions are used to construct shape functions which act as basis functions in the frame of SMRPI. It is proved that the scheme is stable with respect to the time variable in H 1 and convergent by the order of convergence O(δt). The results of numerical experiments are compared to analytical solutions to confirm the accuracy and efficiency of the presented scheme.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Gerasim V. Krivovichev In the paper, a system of hyperbolic linear Bhatnagar–Gross–Krook equations with single relaxation time for simulation of linear diffusion is presented. The lattices based on orthogonal, antitropic and null velocities are considered. Cases of parametric and non-parametric coefficients are considered. The Chapman–Enskog method is applied to the derivation of the linear diffusion equation from the proposed system. The expression for the diffusion coefficient with dependency on relaxation time is obtained. The structure of the solution of the proposed system is analyzed. Lattice Boltzmann equations and finite-difference-based lattice Boltzmann schemes are considered as discrete approximations for the proposed system. The existence of the fictitious numerical diffusion is demonstrated. Stability with respect to initial conditions is analyzed by investigation of wave modes. The necessary stability condition is written as a physical consistent condition of positivity of relaxation time. The sufficiency of this condition is demonstrated analytically and numerically for all considered lattices in parametric and nonparametric cases. It is demonstrated, that the dispersion of the solutions takes place at some values of relaxation time and parameter. The dispersion exists due to hyperbolicity of the proposed system. The presence of the dispersion may lead to effects, which are not typical for the solution of linear diffusion equation. But it is demonstrated, that the effect of the dispersion may take place only in the cases, when image parts of the frequencies of wave modes are equal to null. In the case of positive image parts this effect is damped and solutions decrease at the same manner, as a solution of the diffusion equation. Presented system may be considered as a basis for the construction of lattice Boltzmann equations and lattice Boltzmann schemes of various accuracy orders.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Qiao Wang, Wei Zhou, Yonggang Cheng, Gang Ma, Xiaolin Chang, Yu Miao, E Chen The moving least-square (MLS) method has been popular applied in surface construction and meshless methods. However, the moment matrix in MLS method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult. To overcome this problem, a regularized moving least-square method with nonsingular moment matrix is proposed. The shape functions obtained from the regularized MLS method still do not have the delta function property and may result in difficulty for imposing boundary conditions in regularized MLS based meshless method. To overcome this problem, a regularized improved interpolating moving least-square (IIMLS) method based on the IIMLS method is also proposed. Compared with the regularized MLS method, the regularized IIMLS not only has nonsingular moment matrices, but also obtains shape functions with delta function property. Shape functions of the proposed methods are compared in 1D and 2D cases, and the methods have been applied in curve fitting, surface fitting and meshless method in numerical examples.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Mojtaba Hajipour, Amin Jajarmi, Alaeddin Malek, Dumitru Baleanu This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscillations close to non-smooth points. In order to admit large time steps, a class of implicit Runge–Kutta methods is used for the temporal discretization. The implicit parts of these methods are linearized in time by using the local Taylor expansion of the flux. The stability analysis of the semi-implicit WENO scheme with 3-stages form is provided. Finally, some comparative results for one-, two- and three-dimensional PDEs are included to illustrate the effectiveness of the proposed approach.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Mai Duc Thanh We consider the Riemann problem for the system of shallow water equations with horizontal temperature gradients (the Ripa system). The model under investigation has the form of a nonconservative system, and it is hyperbolic, but is not strictly hyperbolic. We construct all solutions of the Riemann problem. It turns out that there may be up to three distinct solutions. A resonant phenomenon which causes the colliding shock waves is observed, where multiple waves associated with different characteristic fields propagate with the same shock speed.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): A. San Antolín, R.A. Zalik Let d ≥ 1. For any A ∈ Z d × d such that det A = 2 , we construct two families of Parseval wavelet frames with two generators. These generators have compact support, any desired number of vanishing moments, and any given degree of regularity. The first family is real valued while the second family is complex valued. To construct these families we use Daubechies low pass filters to obtain refinable functions, and adapt methods employed by Chui and He and Petukhov for dyadic dilations to this more general case. We also construct several families of Parseval wavelet frames with three generators having various symmetry properties. Our constructions are based on the same refinable functions and on techniques developed by Han and Mo and by Dong and Shen for the univariate case with dyadic dilations.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Murad Banaji Some results are presented on how oscillation is inherited by chemical reaction networks (CRNs) when they are built in natural ways from smaller oscillatory networks. The main results describe four important ways in which a CRN can be enlarged while preserving its capacity for oscillation. The results are for general CRNs, not necessarily fully open, but lead to an important corollary for fully open networks: if a fully open CRN R with mass action kinetics admits a nondegenerate (resp., linearly stable) periodic orbit, then so do all such CRNs which include R as an induced subnetwork. This claim holds for other classes of kinetics, but fails, in general, for CRNs which are not fully open. Where analogous results for multistationarity can be proved using the implicit function theorem alone, the results here call on regular and singular perturbation theory. Equipped with these results and with the help of some analysis and numerical simulation, lower bounds are put on the proportion of small fully open CRNs capable of stable oscillation under various assumptions on the kinetics. This exploration suggests that small oscillatory motifs are an important source of oscillation in CRNs.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Joshua L. Padgett, Qin Sheng The numerical solution of a highly nonlinear two-dimensional degenerate stochastic Kawarada equation is investigated. A semi-discretized approximation in space is comprised on arbitrary nonuniform grids. Exponential splitting strategies are then applied to advance solutions of the semi-discretized scheme over adaptive grids in time. It is shown that key quenching solution features including the positivity and monotonicity are well preserved under modest restrictions. The numerical stability of the underlying splitting method is also maintained without any additional restriction. Computational experiments are provided to not only illustrate our results, but also provide further insights into the global nonlinear convergence of the numerical solution.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Ivan Gutman A graph is stepwise irregular (SI) if the degrees of any two of its adjacent vertices differ by exactly one. Among graphs with non-zero edge imbalance, SI graphs are least irregular. Some basic properties of SI graphs are established.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): Jing Jian Li, Bo Ling, Guodong Liu Let Γ be a finite simple undirected graph and G ≤ Aut(Γ). If G is transitive on the set of s-arcs but not on the set of ( s + 1 ) -arcs of Γ, then Γ is called (G, s)-transitive. For a connected (G, s)-transitive graph Γ of prime valency, the vertex-stabilizer Gα with α ∈ V(Γ) has been determined when Gα is solvable. In this paper, we give a characterization of the vertex-stabilizers of (G, s)-transitive graphs of prime valency when Gα is unsolvable.

Abstract: Publication date: 15 May 2018 Source:Applied Mathematics and Computation, Volume 325 Author(s): M.S. Bruzón, R. de la Rosa, R. Tracinà In this paper, a family of variable-coefficient fifth-order KdV equations has been considered. By using an infinitesimal method based on the determination of the equivalence group, differential invariants and invariant equations are obtained. Invariants provide an alternative way to find equations from the family which may be equivalent to a specific subclass of the same family and the invertible transformation which maps both equivalent equations. Here, differential invariants are applied to obtain exact solutions.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): E. Ramya, M. Muthtamilselvan, Deog Hee Doh A mathematical model is developed to examine the effects of radiation and slanted magnetic on boundary layer flow of a micropolar fluid containing gyrostatic microorganisms through a vertical fixed or continuous moving porous plate. The governing boundary layer equations are cast into a matrix form and solved analytically by utilizing the state space approach and the inversion of the Laplace transform is carried out, utilizing numerical approach. Numerical outcomes for the momentum, microrotation, density of motile microorganism and temperature distributions are given and illustrated graphically for the problem. Excellent agreement is found when present solutions are compared with the numerical solutions by utilizing the Crank–Nicolson implicit finite difference method. It is found that the density of the motile microorganisms is increasing functions of the bioconvection Lewis number in both cases moving and fixed plate.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Zaheer-ud-DinSiraj-ul-Islam In this paper, efficient and simple algorithms based on Levin’s quadrature theory and our earlier work involving local radial basis function (RBF) and Chebyshev differentiation matrices, are adopted for numerical solution of one-dimensional highly oscillatory Fredholm integral equations. This work is focused on the comparative performance of local RBF meshless and pseudospectral procedures. We have tested the proposed methods on phase functions with and without stationary phase point(s), both on uniform and Chebyshev grid points. The proposed procedures are shown accurate and efficient, and therefore provide a reliable platform for the numerical solution of integral equations. From the numerical results, we draw some conclusions about accuracy, efficiency and robustness of the proposed approaches.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Rida T. Farouki A reduced difference polynomial f ( u , v ) = ( p ( u ) − p ( v ) ) / ( u − v ) may be associated with any given univariate polynomial p(t), t ∈ [ 0, 1 ] such that the locus f ( u , v ) = 0 identifies the pairs of distinct values u and v satisfying p ( u ) = p ( v ) . The Bernstein coefficients of f(u, v) on [ 0, 1 ]2 can be determined from those of p(t) through a simple algorithm, and can be restricted to any subdomain of [ 0, 1 ]2 by standard subdivision methods. By constructing the reduced difference polynomials f(u, v) and g(u, v) associated with the coordinate components of a polynomial curve r ( t ) = ( x ( t ) , y ( t ) ) , a quadtree decomposition of [ 0, 1 ]2 guided by the variation-diminishing property yields a numerically stable scheme for isolating real solutions of the system f ( u , v ) = g ( u , v ) = 0 , which identify self-intersections of the curve r(t). Through the Kantorovich theorem for guaranteed convergence of Newton–Raphson iterations to a unique solution, the self-intersections can be efficiently computed to machine precision. By generalizing the reduced difference polynomial to encompass products of univariate polynomials, the method can be readily extended to compute the self-intersections of rational curves, and of the rational offsets to Pythagorean–hodograph curves.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Muhuo Liu, Kinkar Ch. Das Let d(u, v) be the distance between u and v of graph G, and let Wf (G) be the sum of f(d(u, v)) over all unordered pairs {u, v} of vertices of G, where f(x) is a function of x. In some literatures, Wf (G) is also called the Q-index of G. In this paper, some unified properties to Q-indices are given, and the majorization theorem is illustrated to be a good tool to deal with the ordering problem of Q-index among trees with n vertices. With the application of our new results, we determine the four largest and three smallest (resp. four smallest and three largest) Q-indices of trees with n vertices for strictly decreasing (resp. increasing) nonnegative function f(x), and we also identify the twelve largest (resp. eighteen smallest) Harary indices of trees of order n ≥ 22 (resp. n ≥ 38) and the ten smallest hyper-Wiener indices of trees of order n ≥ 18, which improve the corresponding main results of Xu (2012) and Liu and Liu (2010), respectively. Furthermore, we obtain some new relations involving Wiener index, hyper-Wiener index and Harary index, which gives partial answers to some problems raised in Xu (2012).

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Bingyi Kang, Gyan Chhipi-Shrestha, Yong Deng, Kasun Hewage, Rehan Sadiq Evolutionary games with the fuzzy set are attracting growing interest. While among previous studies, the role of the reliability of knowledge in such an infrastructure is still virgin and may become a fascinating issue. Z-number is combined with “restriction” and “reliability”, which is an efficient framework to simulate the thinking of human. In this paper, the stable strategies analysis based on the utility of Z-number in the evolutionary games is proposed, which can simulate the procedure of human’s competition and cooperation more authentically and more flexibly. Some numerical examples and an application are used to illustrate the effectiveness of the proposed methodology. Results show that total utility of Z-number can be used as an index to extend the classical evolutionary games into ones linguistic-based, which is applicable in the real applications since the payoff matrix is always determined by the knowledge of human using uncertain information, e.g., (outcome of the next year, about fifty thousand dollars, likely).

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): JiHong Zhang, JunSheng Zheng, QinJiao Gao In this paper, a numerical scheme is presented to solve the non-dissipative Degasperis–Procesi equation based on the u-p formulation. The cubic B-spline quasi-interpolation coupled with the finite difference method is applied to approximate the spatial derivatives and an optimal third order TVD Runge–Kutta method to estimate the time derivative of the dependent variable. The accuracy and effectiveness of the proposed method are validated by six classical problems. Numerical results indicate that the proposed scheme is simple, easy to implement with high accuracy.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Kejal Khatri, Vishnu Narayan Mishra The aim of the present paper is to introduce generalized Szász–Mirakyan operators including Brenke type polynomials and investigate their approximation properties. We obtain convergence properties of our operators with the help of Korovkin’s theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre’s K-functional. We also give asymptotic formula and the convergence of the derivatives for these operators. Furthermore, an example of Szász–Mirakyan operators including Gould–Hopper polynomials is presented. In the end, we show graphical representation.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Xin Li, Yubo Chang This paper presents an interpolatory subdivision scheme with non-uniform parametrization for arbitrary polygon meshes with arbitrary manifold topology. This is the first attempt to generalize the non-uniform four point interpolatory curve subdivision to surface with extraordinary points. The scheme is constructed from the inspiration of the relation between the non-uniform four-point interpolatory subdivision scheme and the non-uniform B-spline refinement rule. Numerical examples and comparisons with the uniform interpolatory subdivision schemes indicate that the quality of the limit surface can be improved by using non-uniform parameter values for non-uniform initial data.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Mengmeng Li, JinRong Wang In this paper, we introduce a concept of delayed two parameters Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler matrix function. With the help of the delayed two parameters Mittag-Leffler type matrix function, we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations via the variation of constants method. In addition, we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations. Thereafter, we present finite time stability results of nonlinear fractional delay differential equations under mild conditions on nonlinear term. Finally, an example is presented to illustrate the validity of the main theorems.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Paul Andries Zegeling, Sehar Iqbal In this paper, we consider theoretical and numerical properties of a nonlinear boundary-value problem which is strongly related to the well-known Gelfand–Bratu model with parameter λ. When approximating the nonlinear term in the model via a Taylor expansion, we are able to find new types of solutions and multiplicities, depending on the final index N in the expansion. The number of solutions may vary from 0, 1, 2 to ∞. In the latter case of infinitely many solutions, we find both periodic and semi-periodic solutions. Numerical experiments using a non-standard finite-difference (NSFD) approximation illustrate all these aspects. We also show the difference in accuracy for different denominator functions in NSFD when applied to this model. A full classification is given of all possible cases depending on the parameters N and λ.

Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): R. Gatto This article considers the random walk over R p , with any p ≥ 2, where a particle starts at the origin and progresses stepwise with fixed step lengths and von Mises–Fisher distributed step directions. The total number of steps follows a continuous time counting process. The saddlepoint approximation to the distribution of the distance between the origin and the position of the particle at any time is derived. Despite the p-dimensionality of the random walk, the computation of the proposed saddlepoint approximation is one-dimensional and thus simple. The high accuracy of the saddlepoint approximation is illustrated by a numerical comparison with Monte Carlo simulation.

Authors:Tomoaki Okayama Pages: 1 - 15 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Tomoaki Okayama A Sinc-Nyström method for Volterra integro-differential equations was developed by Zarebnia (2010). The method is quite efficient in the sense that exponential convergence can be obtained even if the given problem has endpoint singularity. However, its exponential convergence has not been proved theoretically. In addition, to implement the method, the regularity of the solution is required, although the solution is an unknown function in practice. This paper reinforces the method by presenting two theoretical results: (1) the regularity of the solution is analyzed, and (2) its convergence rate is rigorously analyzed. Moreover, this paper improves the method so that a much higher convergence rate can be attained, and theoretical results similar to those listed above are provided. Numerical comparisons are also provided.

Authors:Haochen Li; Chaolong Jiang; Zhongquan Lv Pages: 16 - 27 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Haochen Li, Chaolong Jiang, Zhongquan Lv In this paper, a Galerkin energy-preserving scheme is proposed for solving nonlinear Schrödinger equation in two dimensions. The nonlinear Schrödinger equation is first rewritten as an infinite-dimensional Hamiltonian system. Following the method of lines, the spatial derivatives of the nonlinear Schrödinger equation are approximated with the aid of the Galerkin methods. The resulting ordinary differential equations can be cast into a canonical Hamiltonian system. A fully-discretized scheme is then devised by considering an average vector field method in time. Moreover, based on the fast Fourier transform and the matrix diagonalization method, a fast solver is developed to solving the resulting algebraic equations. Finally, the proposed scheme is employed to capture the blow-up phenomena of the nonlinear Schrödinger equation.

Authors:Francisco J. Solis; Luz M. Gonzalez Pages: 28 - 35 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Francisco J. Solis, Luz M. Gonzalez In this paper analytical properties of solutions of a novel human papillomavirus (HPV) infected cells model is investigated. We show existence, uniqueness and stability of solutions by using standard techniques based on the energy method and the method of upper and lower solutions. For the numerical counterpart, we develop and implement one efficient numerical algorithm scheme which satisfies nonnegative conditions and dynamical consistency. Efficiency of this method is shown by its longtime approximations, which are of paramount importance for a slow process like the evolution of HPV infected cells.

Authors:Jiao Wang; Tian-Zhou Xu; Yan-Qiao Wei; Jia-Quan Xie Pages: 36 - 50 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Jiao Wang, Tian-Zhou Xu, Yan-Qiao Wei, Jia-Quan Xie In this paper, a new method for solving coupled systems of nonlinear fractional order integro-differential equations is proposed. The idea is to use Bernoulli wavelets and operational matrix. The main purpose of the technique is to transform the studied systems of fractional order integro-differential equations into systems of algebraic equations which can be solved easily. Illustrative examples and comparisons with Haar wavelets and Legendre wavelets are included to reveal the effectiveness of the method and the accuracy of the convergence analysis.

Authors:Yuan He; Taekyun Kim Pages: 51 - 58 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Yuan He, Taekyun Kim In this paper, we perform a further investigation for the Bernoulli polynomials of the second kind. By making use of the generating function methods and summation transform techniques, we establish a higher-order convolution identity for the Bernoulli polynomials of the second kind. We also present some illustrative special cases as well as immediate consequences of the main result.

Authors:Wenjie Liu; Boying Wu Pages: 59 - 68 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Wenjie Liu, Boying Wu In this paper, we propose Galerkin–Legendre spectral method with implicit Runge-Kutta method for solving the unsteady two-dimensional Schrödinger equation with nonhomogeneous Dirichlet boundary conditions and initial condition. We apply a Galerkin–Legendre spectral method for discretizing spatial derivatives, and then employ the implicit Runge–Kutta method for the time integration of the resulting linear first-order system of ordinary differential equations in complex domain. We derive the spectral rate of convergence for the proposed method in the L 2-norm for the semidiscrete formulation. Numerical experiments show our formulation have high-order accuracy.

Authors:Jianxi Li; Ji-Ming Guo; Wai Chee Shiu; Ş. Burcu Bozkurt Altındağ; Durmuş Bozkurt Pages: 82 - 92 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Jianxi Li, Ji-Ming Guo, Wai Chee Shiu, Ş. Burcu Bozkurt Altındağ, Durmuş Bozkurt Let G be a simple connected graph of order n. Its normalized Laplacian eigenvalues are λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n − 1 ≥ λ n = 0 . In this paper, new bounds on S β * ( G ) = ∑ i = 1 n − 1 λ i β (β ≠ 0, 1) are derived.

Authors:Shu-Xin Miao; Yu-Hua Luo; Guang-Bin Wang Pages: 93 - 104 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Shu-Xin Miao, Yu-Hua Luo, Guang-Bin Wang In this paper, the preconditioned generalized accelerated overrelaxation (GAOR) methods for solving weighted linear least squares problems are considered. Two new preconditioners are proposed and the convergence rates of the new preconditioned GAOR methods are studied. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods in the previous literatures whenever these methods are convergent. A numerical example is given to confirm our theoretical results.

Authors:A.F. Cheviakov; J. Heß Pages: 105 - 118 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): A.F. Cheviakov, J. Heß The entropy principle in the formulation of Müller and Liu is a common tool used in constitutive modelling for the development of restrictions on the unknown constitutive functions describing material properties of various physical continua. In the current work, a symbolic software implementation of the Liu algorithm, based on Maple software and the GeM package, is presented. The computational framework is used to algorithmically perform technically demanding symbolic computations related to the entropy principle, to simplify and reduce Liu identities, and ultimately to derive explicit formulas describing classes of constitutive functions that do not violate the entropy principle. Detailed physical examples are presented and discussed.

Authors:Yanhong Yang; Yushun Wang; Yongzhong Song Pages: 119 - 130 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Yanhong Yang, Yushun Wang, Yongzhong Song In this paper, a new local energy-preserving algorithm is proposed based on the temporal and spatial discretizations where the Average Vector Field (AVF) method and the implicit midpoint method are used for the temporal discretization and spatial discretization, respectively. In any local time-space region, the local mass and local energy are conserved by the algorithm. With periodic boundary conditions, it is worth noting that the global mass and global energy conservation law are also admitted. Numerical experiments are performed to support our theoretical analysis and show the conservation properties of the algorithm intuitively.

Authors:Yanan Li; Yuangong Sun; Fanwei Meng; Yazhou Tian Pages: 131 - 140 Abstract: Publication date: 1 May 2018 Source:Applied Mathematics and Computation, Volume 324 Author(s): Yanan Li, Yuangong Sun, Fanwei Meng, Yazhou Tian This paper deals with exponential stabilization for a class of switched time-varying systems. By taking time-varying delays and nonlinear disturbances into consideration, time dependent switching signals have been characterized in terms of Metzler matrices such that the resulting system is globally exponentially stable. Compared with preceding works, we introduce a model transformation and an approach without involving the Lyapunov-Krasovskii functional to derive new exponential stability criteria for switched time-varying systems under the average dwell time switching. Numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results.

Authors:A.M. Portillo Pages: 1 - 16 Abstract: Publication date: 15 April 2018 Source:Applied Mathematics and Computation, Volume 323 Author(s): A.M. Portillo Two-dimensional linear wave equation in anisotropic media, on a rectangular domain with initial conditions and periodic boundary conditions, is considered. The energy of the problem is contemplated. The space discretization is reached by means of finite differences on a uniform grid, paying attention to the mixed derivative of the equation. The discrete energy of the semi-discrete problem is introduced. For the time integration of the system of ordinary differential equations obtained, a fourth order exponential splitting method, which is a geometric integrator, is proposed. This time integrator is efficient and easy to implement. The stability condition for time step and space step ratio is deduced. Numerical experiments displaying the good behavior in the long time integration and the efficiency of the numerical solution are provided.

Authors:Kai Cheng; Zhenzhou Lu Pages: 17 - 30 Abstract: Publication date: 15 April 2018 Source:Applied Mathematics and Computation, Volume 323 Author(s): Kai Cheng, Zhenzhou Lu Polynomial chaos expansion (PCE) is widely used by engineers and modelers in various engineering fields for uncertainty analysis. The computational cost of full PCE is unaffordable for the “curse of dimensionality” of the expansion coefficients. In this paper, a new method for developing sparse PCE is proposed based on the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) algorithm. D-MORPH is a regression technique, it can construct the full PCE models with model evaluations much less than the unknown coefficients. This technique determines the unknown coefficients by minimizing the least-squared error and an objective function. For the purpose of developing sparse PCE, an iterative reweighted algorithm is proposed to construct the objective function. As a result, the objective in D-MORPH regression is converted to minimize the ℓ1 norm of PCE coefficients, and the sparse PCE is established after the proposed algorithm converges to the optimal value. To validate the performance of the developed methodology, several benchmark examples are investigated. The accuracy and efficiency are compared to the well-established least angle regression (LAR) sparse PCE, and results show that the developed method is superior to the LAR-based sparse PCE in terms of efficiency and accuracy.

Authors:Dongyang Shi; Huaijun Yang Pages: 31 - 42 Abstract: Publication date: 15 April 2018 Source:Applied Mathematics and Computation, Volume 323 Author(s): Dongyang Shi, Huaijun Yang In this paper, the superclose and superconvergence analysis of the nonlinear time-fractional thermistor problem are investigated by bilinear finite element method (FEM) for a fully-discrete scheme, in which the Caputo derivative is approximated by the classical L1 method. By dealing with the error estimates in the spatial direction rigorously, which are one order higher than the traditional FEMs, the superclose estimates in H 1-norm are obtained for the corresponding variables based on the special properties of this element together with mean value technique. Subsequently, the global superconvergence results are derived by employing the interpolation postprocessing approach. Finally, a numerical experiment is carried out to confirm the theoretical analysis.

Authors:Abdolreza Amiri; Alicia Cordero; M. Taghi Darvishi; Juan R. Torregrosa Pages: 43 - 57 Abstract: Publication date: 15 April 2018 Source:Applied Mathematics and Computation, Volume 323 Author(s): Abdolreza Amiri, Alicia Cordero, M. Taghi Darvishi, Juan R. Torregrosa In this paper, a parametric family of seventh-order of iterative method to solve systems of nonlinear equations is presented. Its local convergence is studied and quadratic polynomials are used to investigate its dynamical behavior. The study of the fixed and critical points of the rational function associated to this class allows us to obtain regions of the complex plane where the method is stable. By depicting parameter planes and dynamical planes we obtain complementary information of the analytical results. These results are used to solve some nonlinear problems.

Authors:Yuxuan Yang; Mei Lu Pages: 58 - 63 Abstract: Publication date: 15 April 2018 Source:Applied Mathematics and Computation, Volume 323 Author(s): Yuxuan Yang, Mei Lu Given a graph G = ( V , E ) , a subset S of V is a dominating set of G if every vertex in V∖S is adjacent to a vertex in S. The minimum cardinality of a dominating set in a graph G is called the domination number of G and is denoted by γ(G). A graph G is said to be k-γ-critical if γ ( G ) = k , but γ ( G + e ) < k for each edge e ∈ E ( G ¯ ) , where G ¯ is the complement of G. In this paper, we first provide the structure of k-γ-critical connected graphs with a nontrivial cut edge. Then we establish that each 5-γ-critical leafless connected graph of even order contains a perfect matching.