Abstract: Publication date: Available online 18 September 2017 Source:Computers & Mathematics with Applications Author(s): Salim A. Messaoudi, Ala A. Talahmeh, Jamal H. Al-Smail In this paper, we consider the following nonlinear wave equation with variable exponents: u t t − Δ u + a u t u t m ( ⋅ ) − 2 = b u u p ( ⋅ ) − 2 , where a , b are positive constants. By using the Faedo–Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p . We also prove the finite time blow-up of solutions and give a two-dimension numerical example to illustrate the blow up result.

Abstract: Publication date: Available online 15 September 2017 Source:Computers & Mathematics with Applications Author(s): Jia Tang, Chang-Feng Ma In this paper, a generalized conjugate direction (GCD) method for finding the generalized Hamiltonian solutions of a class of generalized coupled Sylvester-conjugate transpose matrix equations is proposed. Furthermore, it is proved that the algorithm can compute the least Frobenius norm generalized Hamiltonian solution group of the problem by choosing a special initial matrix group within a finite number of iterations in the absence of round-off errors. Numerical examples are also presented to illustrate the efficiency of the algorithm.

Abstract: Publication date: Available online 13 September 2017 Source:Computers & Mathematics with Applications Author(s): Chang-Qing Lv, Chang-Feng Ma This paper introduces another version of biconjugate residual method (BCR) for solving the generalized coupled Sylvester matrix equations over centrosymmetric or anti-centrosymmetric matrix. We prove this version of BCR algorithm can find the centrosymmetric solution group of the generalized coupled matrix equations for any initial matrix group within finite steps in the absence of round-off errors. Furthermore, a method is provided for choosing the initial matrices to obtain the least norm solution of the problem. At last, some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed.

Abstract: Publication date: Available online 12 September 2017 Source:Computers & Mathematics with Applications Author(s): Rui Ding, Quan Shen, Zhengcheng Zhu This paper is presented for the convergence analysis of the element-free Galerkin method for a class of parabolic evolutionary variational inequalities arising from the heat-servo control problem. The error estimates illustrate that the convergence order depends not only on the number of basis functions in the moving least-squares approximation but also the relationship with the time step and the spatial step. Numerical examples verify the convergence analysis and the error estimates.

Abstract: Publication date: Available online 12 September 2017 Source:Computers & Mathematics with Applications Author(s): A. Mardani, M.R. Hooshmandasl, M.H. Heydari, C. Cattani In this paper, an efficient and accurate meshless method is proposed for solving the time fractional advection–diffusion equation with variable coefficients which is based on the moving least square (MLS) approximation. In the proposed method, firstly the time fractional derivative is approximated by a finite difference scheme of order O ( ( δ t ) 2 − α ) , 0 < α ≤ 1 and then the MLS approach is employed to approximate the spatial derivative where time fractional derivative is expressed in the Caputo sense. Also, the validity of the proposed method is investigated in error analysis discussion. The main aim is to show that the meshless method based on the MLS shape functions is highly appropriate for solving fractional partial differential equations (FPDEs) with variable coefficients. The efficiency and accuracy of the proposed method are verified by solving several examples.

Abstract: Publication date: Available online 11 September 2017 Source:Computers & Mathematics with Applications Author(s): Hyung Jun Choi, Woocheol Choi, Youngwoo Koh In this paper, we study a finite element method overcoming corner singularities for elliptic optimal control problem posed on a polygon. Based on a corner singularity decomposition of singular solution for the associated elliptic system, we derive an extraction formula for coefficients of singular parts, called stress intensity factors, and introduce a finite element discretization for regular parts of the solution pair. Furthermore, we analyze the finite element solutions in L 2 and H 1 norms. By numerical experiments, we confirm the efficiency and reliability of the proposed method.

Abstract: Publication date: Available online 11 September 2017 Source:Computers & Mathematics with Applications Author(s): L. Taddei, N. Lebaal, S. Roth This paper presents the development of a cylindrical SPH formulation based on previous study of the literature (Petschek et al) with an explicit formulation for the artificial viscosity. The entire development is explained to propose a formulation adapted to solve Euler equations in the case of a Riemann problem with axis-symmetric conditions. Thus, the artificial viscosity is constructed to find smooth solutions of well-known Riemann problems such as Sod, Noh and Sedov problems. Numerical results are compared to exact solutions and observations are made on numerical parameters influence. This study contributes to validate the axis-symmetrical formulation for pure hydrodynamics tests.

Abstract: Publication date: Available online 9 September 2017 Source:Computers & Mathematics with Applications Author(s): R.E. Bird, W.M. Coombs, S. Giani When written in MATLAB the finite element method (FEM) can be implemented quickly and with significantly fewer lines, when compared to compiled code. MATLAB is also an attractive environment for generating bespoke routines for scientific computation as it contains a library of easily accessible inbuilt functions, effective debugging tools and a simple syntax for generating scripts. However, there is a general view that MATLAB is too inefficient for the analysis of large problems. Here this preconception is challenged by detailing a vectorised and blocked algorithm for the global stiffness matrix computation of the symmetric interior penalty discontinuous Galerkin (SIPG) FEM. The major difference between the computation of the global stiffness matrix for SIPG and conventional continuous Galerkin approximations is the requirement to evaluate inter-element face terms, this significantly increases the computational effort. This paper focuses on the face integrals as they dominate the computation time and have not been addressed in the existing literature. Unlike existing optimised finite element algorithms available in the literature the paper makes use of only native MATLAB functionality and is compatible with GNU Octave. The algorithm is primarily described for 2D analysis for meshes with homogeneous element type and polynomial order. The same structure is also applied to, and results presented for, a 3D analysis. For problem sizes of 1 0 6 degrees of freedom (DOF), 2D computations of the local stiffness matrices were at least ≈ 24 times faster, with 13.7 times improvement from vectorisation and a further 1.8 times improvement from blocking. The speed up from blocking and vectorisation is dependent on the computer architecture, with the range of potential improvements shown for two architectures in this paper.

Abstract: Publication date: Available online 8 September 2017 Source:Computers & Mathematics with Applications Author(s): Shanlin Qin, Fawang Liu, Ian W. Turner, Qianqian Yang, Qiang Yu Diffusion-weighted imaging is an in vivo, non-invasive medical diagnosis technique that uses the Brownian motion of water molecules to generate contrast in the image and therefore reveals exquisite details about the complex structures and adjunctive information of its surrounding biological environment. Recent work highlights that the diffusion-induced magnetic resonance imaging signal loss deviates from the classic monoexponential decay. To investigate the underlying mechanism of this deviated signal decay, diffusion is re-examined through the Bloch–Torrey equation by using fractional calculus with respect to both time and space. In this study, we explore the influence of the complex geometrical structure on the diffusion process. An effective implicit alternating direction method implemented on approximate irregular domains is proposed to solve the two-dimensional time–space Riesz fractional partial differential equation with Dirichlet boundary conditions. This scheme is proved to be unconditionally stable and convergent. Numerical examples are given to support our analysis. We then applied the proposed numerical scheme with some decoupling techniques to investigate the magnetisation evolution governed by the time–space fractional Bloch–Torrey equations on irregular domains.

Abstract: Publication date: Available online 8 September 2017 Source:Computers & Mathematics with Applications Author(s): Matthew W. Scroggs, Timo Betcke, Erik Burman, Wojciech Śmigaj, Elwin van ’t Wout In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairings of discretisation spaces have been developed that allow robust formulations of the preconditioned electric field, magnetic field and combined field integral equations. Within the BEM++ boundary element library we have developed implementations of these frameworks that allow an intuitive formulation of the typical Maxwell boundary integral formulations within a few lines of code. The basis for these developments is an efficient and robust implementation of Calderón identities together with a product algebra that hides and automates most technicalities involved in assembling Galerkin boundary integral equations. In this paper we demonstrate this framework and use it to derive very simple and robust software formulations of the standard preconditioned electric field, magnetic field and regularised combined field integral equations for Maxwell.

Abstract: Publication date: Available online 8 September 2017 Source:Computers & Mathematics with Applications Author(s): M.S. Osman In this work, we construct multi-soliton solutions of the ( 2 + 1 ) -dimensional breaking soliton equation with variable coefficients by using the generalized unified method. We employ this method to obtain double- and triple-soliton solutions. Furthermore, we study the nonlinear interactions between these solutions in a graded-index waveguide. The physical insight and the movement role of the waves are discussed and analyzed graphically for different choices of the arbitrary functions in the obtained solutions. The interactions between the solitons are elastic whether the coefficients of the equation are constants or variables.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Yan-Fang Xue, Jiu Liu, Chun-Lei Tang This article is concerned with the existence of positive ground state solutions for an asymptotically periodic quasilinear Schrödinger equation. By using a change of variables, the quasilinear problem is transformed into a semilinear one. Then, we use a Nehari-type constraint to get the existence result.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): S. Saha Ray In this paper, using the Lie group analysis method, the infinitesimal generators for (2+1)-dimensional Bogoyavlensky–Konopelchenko equation are obtained. The new concept of nonlinear self-adjointness of differential equations is used for construction of nonlocal conservation laws. The conservation laws for the (2+1)-dimensional Bogoyavlensky–Konopelchenko equation are obtained by using the new conservation theorem method and the formal Lagrangian approach. Transforming this equation into a system of equations involving with two dependent variables, it has been shown that the resultant system of equations is quasi self-adjoint and finally the new nonlocal conservation laws are constructed by using the Lie symmetry operators.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Sheng-Wei Zhou, Ai-Li Yang, Yu-Jiang Wu For the generalized saddle-point problems, firstly, we introduce a modified generalized relaxed splitting (MGRS) preconditioner to accelerate the convergence rate of the Krylov subspace methods. Based on a block-triangular splitting of the saddle-point matrix, secondly, we propose a modified block-triangular splitting (MBTS). This new preconditioner is easily implemented since it has simple block structure. The spectral properties and the degrees of the minimal polynomials of the preconditioned matrices are discussed, respectively. Moreover, we apply the MGRS and the MBTS preconditioners to three-dimensional linearized Navier–Stokes equations. Then we derive the quasi-optimal parameters of the MGRS and the MBTS preconditioners for two and three-dimensional Navier–Stokes equations, respectively. Finally, numerical experiments are illustrated to show the preconditioning effects of the two new preconditioners.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Eric T. Chung, Jie Du, Chi Yeung Lam In this paper, we will develop a new staggered hybridization technique for discontinuous Galerkin methods to discretize linear elastodynamic equations. The idea of hybridization is used extensively in many discontinuous Galerkin methods, but the idea of staggered hybridization is new. Our new approach offers several advantages, namely energy conservation, high-order optimal convergence, preservation of symmetry for the stress tensor, block diagonal mass matrices as well as low dispersion error. The key idea is to use two staggered hybrid variables to enforce the continuity of the velocity and the continuity of the normal component of the stress tensor on a staggered mesh. We prove the stability and the convergence of the proposed scheme in both the semi-discrete and the fully-discrete settings. Numerical results confirm the optimal rate of convergence and show that the method has a superconvergent property for dispersion. Furthermore, an application of this method to Rayleigh wave propagation is presented.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Cai-Rong Chen, Chang-Feng Ma In this paper, we apply Kronecker product and vectorization operator to extend the conjugate residual squared (CRS) method for solving a class of coupled Sylvester-transpose matrix equations. Some numerical examples are given to compare the accuracy and efficiency of the new matrix iterative method with other methods presented in the literature. Numerical results validate that the proposed method can be much more efficient than some existing methods.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Won-Kwang Park This paper concerns a mathematical formulation of the well-known MUltiple SIgnal Classification (MUSIC)-type imaging functional in the inverse scattering problem by an open sound-hard arc. Based on the physical factorization of the so-called Multi-Static Response (MSR) matrix and the structure of left-singular vectors linked to the non-zero singular values of the MSR matrix, we construct a relationship between the imaging functional and the Bessel functions of order 0 , 1 , and 2 of the first kind. We then expound certain properties of MUSIC and present numerical results for several differently chosen smooth arcs.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Hongfei Fu, Hui Guo, Jian Hou, Jiansong Zhang We propose a stabilized mixed finite element approximation for optimal control problems governed by bilinear state equations. It is proved that the resulting mixed bilinear formulation is coercive and also continuous, which avoids the difficulty in choosing the mixed finite element spaces, i.e., the Ladyzhenkaya–Babuska–Brezzi matching condition for the mixed finite element spaces is unnecessary. Under pointwise bilateral constraint on the control variable, we deduce the optimality conditions at both continuous and discrete levels for the optimal control problems under consideration. Then an a priori error analysis in a weighted norm is discussed, with relatively low regularity requirements for the solutions to the optimal control problems. Finally, numerical experiments are given to confirm the efficiency and reliability of the proposed stabilized mixed finite element method.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Shougui Zhang We propose two new projection methods for solving the Signorini problem and study the relationship between them. Since the Signorini boundary condition is equivalent to a projection fixed point problem, the methods formulate the Signorini boundary condition into a sequence of Robin boundary conditions and only require solving a variational problem with simple boundary conditions at each iterative step. The convergence speed of the first method depends on the parameter ρ heavily, and it is difficult to choose a proper ρ for individual problems. To improve the efficiency of the method, we propose an adaptive projection method which adjusts the parameter ρ automatically per iteration. We establish the convergence analysis of the methods. Because the Signorini boundary condition is given in an iterative form by the potential and its derivative on the boundary of the domain, we can easily provide the boundary element approximation of the problem. Finally, we present some numerical simulations which illustrate the performance of the methods.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Mohammed O. Al-Amr, Shoukry El-Ganaini In this paper, two distinct methods are applied to look for exact traveling wave solutions of the (4+1)-dimensional nonlinear Fokas equation, namely the modified simple equation method (MSEM) and the extended simplest equation method (ESEM). Some new exact traveling wave solutions involving some parameters are obtained. The solitary wave solutions can be extracted by assigning special values of these parameters. The obtained solutions show the simplicity and efficiency of the used approaches that can be applied for nonlinear equations as well as linear ones.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Raimund Bürger, Sudarshan Kumar Kenettinkara, David Zorío The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and efficient than RKDG methods of comparable order of accuracy, the formulation of LWDG methods involves the successive computation of exact flux derivatives. This procedure allows one to construct schemes of arbitrary formal order of accuracy in space and time. A new approximation procedure avoids the computation of exact flux derivatives. The resulting approximate LWDG schemes, addressed as ALWDG schemes, are easier to implement than their original LWDG versions. In particular, the formulation of the time discretization of the ALWDG approach does not depend on the flux being used. Numerical results for the scalar and system cases in one and two space dimensions indicate that ALWDG methods are more efficient in terms of error reduction per CPU time than LWDG methods of the same order of accuracy. Moreover, increasing the order of accuracy leads to substantial reductions of numerical error and gains in efficiency for solutions that vary smoothly.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Xiao-Yan Tang, Xia-Zhi Hao, Zu-feng Liang Modulational unstable regions of the Davey–Stewartson (DS) III system have been determined from the generalized dispersion relation associating the frequency and wavenumber of the modulating perturbations. By means of the multilinear variable separation approach, the variable separation solution for the DS III equation is obtained with two arbitrary functions of ( x , t ) and two arbitrary functions of ( y , t ) , which can be utilized to generate various ( 2 + 1 ) -dimensional localized excitations. Particular attention is paid on the interacting waves between periodic multivalued foldons and single-valued dromions, which can be viewed as periodic extensions of single foldon–dromion excitations.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Wen Zhang, Jian Zhang, Heilong Mi In this paper, we study the following fractional Schrödinger equation ( − Δ ) s u + V ( x ) u = f ( x , u ) , x ∈ R N , where ( − Δ ) s ( s ∈ ( 0 , 1 ) ) denotes the fractional Laplacian. Under some weaker conditions on the nonlinearity, we obtain the existence of solutions for the above problem in periodic case and asymptotically periodic case via variational methods, respectively.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Nguyen Huy Tuan, Mokhtar Kirane, Bandar Bin-Mohsin, Pham Thi Minh Tam In this paper, we consider an inverse problem for a time fractional diffusion equation with inhomogeneous source to determine the initial data from the observation data provided at a later time. In general, this problem is ill-posed, therefore we construct a regularized solution using the filter regularization method in both cases: the deterministic case and random noise case. First, we propose both parameter choice rule methods, the a-priori and the a-posteriori methods. Then, we obtain the convergence rates and provide examples of filters. We also provide a numerical example to illustrate our results.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Gholamreza Imani In the present paper, for the first time, the lattice Boltzmann (LB) simulation of the three-dimensional steady and transient natural convection problem in a differentially heated cubical enclosure with a conducting fin on its hot wall is performed. As such, two main variants associated with the thermal lattice Boltzmann simulation of the finned natural convection problems namely, three popular forcing and two widely used conjugate heat transfer schemes are assessed for the Rayleigh numbers 10 3 , 10 4 , and 10 5 . The results of the different forcing and conjugate heat transfer schemes are compared against each other and against those of the conventional methods to find the most computationally efficient schemes.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Hai-qiong Zhao, Wen-Xiu Ma By using the Hirota bilinear form of the KP equation, twelve classes of lump–kink solutions are presented under the help of symbolic computations with Maple. Analyticity is naturally achieved by taking special choices of the involved parameters to guarantee a positive constant term. A key step in generating lump–kink solutions is to combine quadratic functions and the exponential function in the second-order logarithmic derivative transformation.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Liju Yu We study the blowup for a type of generalized Zakharov system in this paper. It is proved that the solution of such system either blows up in finite time or blows up in infinite time provided that the initial energy is negative.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Swapan K. Pandit, Anirban Chattopadhyay A fourth order compact finite difference scheme is proposed for solving general second order steady partial differential equation (PDE) in two-dimension (2D) on geometries having nonuniform curvilinear grids. In this work, the main efforts are focused not only on nonorthogonal curvilinear grids but also on the presence of mixed derivative term and nonhomogeneous derivative source terms in the governing equation. This is in turn suitable for solving fluid flow and heat transfer problems governed by Navier–Stokes(N–S) equations on geometries having nonuniform and nonorthogonal curvilinear grids. The newly proposed scheme has been applied to solve general second order partial differential equation having analytical solution and some pertinent fluid flow problems, namely, viscous flows in a lid driven cavity such as trapezoidal cavity using nonorthogonal grid, square cavity using distorted grid, complicated enclosures using curvilinear grid, and mixed convection flow in a bottom wavy wall cavity. It is seen to efficiently capture steady-state solutions of the N–S equations with Dirichlet as well as Neumann boundary conditions. Detailed comparison data produced by the proposed scheme for all the test cases are provided and compared with existing analytical as well as established numerical results available in the literature. Excellent comparison is obtained in all the cases.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Haiyong Xu, Gangyi Jiang, Mei Yu, Ting Luo Most of local region-based active contour models in terms of the level set approach are able to segment images with intensity inhomogeneity. However, these models do not utilize global statistical information and are quite sensitive to the initial placement of the contour. This paper presents a new global and local region-based active contour model to segment images with intensity inhomogeneity. First, in order to reduce number of iterations, the global energy functional of the Chan–Vese (C–V) model is used as the global term. Then, the local term is proposed to incorporate both local spatial information and local intensity information to handle intensity inhomogeneity. Moreover, to increase robustness of the initialization of the contour and reduce number of iterations, a convex energy functional and the dual algorithm are designed in the numerical implementation. Experimental results for synthetic and medical images have shown the efficiency and robustness of the proposed method.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Keyan Wang, Yanping Chen In this paper, a combination method of mixed finite element method and two-grid scheme is constructed for solving numerically the two-dimensional nonlinear hyperbolic equations. In this approach, the nonlinear system is solved on a coarse mesh with width H , and the linear system is solved on a fine mesh with width h ≪ H . It is proved that the coarse grid can be much coarser than the fine grid. The two-grid methods achieve asymptotically optimal approximation as long as the mesh sizes H = O ( h 1 2 ) in the first algorithm and H = O ( h 1 4 ) in the second algorithm, respectively. Error estimates are derived in detail. Finally, two numerical examples are carried out to verify the accuracy and efficiency of the presented method.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Jum-Ran Kang, Mi Jin Lee, Sun Hye Park A viscoelastic problem with Balakrishnan–Taylordamping and time-varying delay of the form u t t − ( a + b ‖ ∇ u ‖ 2 + σ ( ∇ u , ∇ u t ) ) Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + μ 1 f 1 ( u t ( x , t ) ) + μ 2 f 2 ( u t ( x , t − τ ( t ) ) ) = 0 is considered. We prove a general stability result for the equation without the condition μ 2 > 0 by establishing some Lyapunov functionals which are equivalent to the energy of the equation instead of multiplier technique and using some properties of convex functions.

Abstract: Publication date: 15 September 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 6 Author(s): Chun-Yu Lei, Hong-Min Suo In this paper, we study the critical growth Schrödinger–Poisson system with a concave term, and establish the existence of multiple positive solutions via using the variational method.

Abstract: Publication date: Available online 6 September 2017 Source:Computers & Mathematics with Applications Author(s): Zhan-Ping Ma, Yu-Xia Wang In this paper, we consider a reaction–diffusion system describing a three-species Lotka–Volterra food chain model with homogeneous Dirichlet boundary conditions. By regarding the birth rate of prey r 1 as a bifurcation parameter, the global bifurcation of positive steady-state solutions from the semi-trivial solution set is obtained via the bifurcation theory. The results show that if the birth rate of mid-level predator and top predator are located in the regions 0 < r 2 < λ 1 a 23 u 3 r 3 and r 3 > λ 1 , respectively. Then the three species can co-exist provided the birth rate of prey exceeds a critical value. Moreover, an explicit expression of coexistence steady-state solutions is constructed by applying the implicit function theorem. It is demonstrated that the explicit coexistence steady-state solutions is locally asymptotically stable.

Abstract: Publication date: Available online 6 September 2017 Source:Computers & Mathematics with Applications Author(s): Yan Gu, Xiaoqiao He, Wen Chen, Chuanzeng Zhang In this paper, an advanced boundary element method (BEM) is developed for solving three-dimensional (3D) anisotropic heat conduction problems in thin-walled structures. The troublesome nearly singular integrals, which are crucial in the applications of the BEM to thin structures, are calculated efficiently by using a nonlinear coordinate transformation method. For the test problems studied, promising BEM results with only a small number of boundary elements have been obtained when the thickness of the structure is in the orders of micro-scales (10−6), which is sufficient for modeling most thin-walled structures as used in, for example, smart materials and thin layered coating systems. The advantages, disadvantages as well as potential applications of the proposed method, as compared with the finite element method (FEM), are also discussed.

Abstract: Publication date: Available online 6 September 2017 Source:Computers & Mathematics with Applications Author(s): Kamran Ayub, M. Yaqub Khan, Qazi Mahmood-Ul-Hassan In this paper, some proficient techniques, called the exp-function method, modified exp-function method and improved modified exp-function method are implemented to compute generalized solitary and periodic wave solutions of the nonlinear Calogero–Bogoyavlenskii–Schiff equation. It has been attempted to show the compatibility and reliability of these mathematical techniques. The first partial differential equation is converted into an ordinary differential equation by a suitable transformation, then a trial solution is assumed. Results indicate complete consistency and effectiveness of the suggested schemes.

Abstract: Publication date: Available online 5 September 2017 Source:Computers & Mathematics with Applications Author(s): Huamin Zhang, Hongcai Yin By applying the hierarchical identification principle, the gradient-based iterative algorithm is suggested for solving the Sylvester conjugate matrix equation. With the real representation of a complex matrix, a new convergence proof is given. The necessary and sufficient conditions for the convergence factor is determined to guarantee the convergence of the algorithm for any initial iterative matrix. Also a conjecture by Wu et al. (2010) is solved. A numerical example is offered to illustrate the effectiveness of the suggested algorithm and verify some conclusions proposed in this paper.

Abstract: Publication date: Available online 4 September 2017 Source:Computers & Mathematics with Applications Author(s): O. Sepahi, L. Radtke, S.E. Debus, A. Düster A 3D anisotropic hierarchic solid finite element formulation is provided for the passive and active mechanical response of arteries. The artery is modeled as an anisotropic nearly incompressible hyperelastic tube consisting of two layers that correspond to the media and the adventitia. These layers are considered as a fiber-reinforced material consisting of two collagen fiber families that are symmetrically disposed and helically oriented around the tube’s axis. The numerical analysis is based on a 3D anisotropic hierarchic solid finite element formulation, including the possibility of varying the polynomial degree in all local directions as well as for all displacement components. For the purpose of verification, analytical solutions are provided for different benchmarks focusing on the aspects of compressible and incompressible 3D stretch, plane strain and plane stress pure shear, as well as a mono-layer anisotropic incompressible circular cylindrical artery of Holzapfel–Gasser–Ogden material under inflation and extension. The resulting solutions, including stress and strain distribution through the arterial wall, are plotted to point out the passive response and different activation levels. In addition the effect of various compressibility levels, including nearly incompressibility, is studied by numerical examples. The robustness and accuracy of the proposed method is demonstrated by comparing the results of different ansatz spaces.

Abstract: Publication date: Available online 4 September 2017 Source:Computers & Mathematics with Applications Author(s): Chuanjian Wang, Hui Fang In this paper, we study the Bogoyavlenskii–Kadomtsev– Petviashvili (BKP) equation by using the truncated Painlevé method and consistent Riccati expansion (CRE). Through the truncated Painlevé method, its nonlocal symmetry and non-auto Bäcklund transformation are presented. The nonlocal symmetry is localized to a local Lie point group via a prolonged system. Moreover, with the help of the CRE method, we prove that the BKP equation is CRE solvable. Finally, the kink-lump wave interaction solution of BKP equation is explicitly given by using the trilinear form. The interaction between kink wave and lump wave is investigated and exhibited mathematically and graphically.

Abstract: Publication date: Available online 21 July 2017 Source:Computers & Mathematics with Applications Author(s): Tanki Motsepa, Chaudry Masood Khalique In this paper we study a generalized coupled (2+1)-dimensional Burgers system, which is a nonlinear version of a bilinear system under some dependent variable transformations. It was introduced recently in the literature and has attracted a fair amount of interest from physicists. The Lie symmetry analysis together with the Kudryashov approach are utilized to obtain new travelling wave solutions of the system. Furthermore, for the first time, conservation laws of the system are derived using the multiplier method.

Abstract: Publication date: Available online 20 July 2017 Source:Computers & Mathematics with Applications Author(s): S.O. Hussein, D. Lesnic, M. Yamamoto In this paper, nonlinear reconstructions of the space-dependent potential and/or damping coefficients in the wave equation from Cauchy data boundary measurements of the displacement and the flux tension are investigated. This is a very interesting and challenging nonlinear inverse coefficient problem with important applications in wave propagation phenomena. The uniqueness and stability results that are revised and in some cases proved demonstrate an advancement in understanding the stability of the inverse coefficient problems. However, in practice, the inverse coefficient identification problems under investigation are still ill-posed since small random errors in the input data cause large errors in the output solution. In order to stabilize the solution we employ the nonlinear Tikhonov regularization method. Numerical reconstructions performed for the first time are presented and discussed to illustrate the accuracy and stability of the numerical solutions under finite difference mesh refinement and noise in the measured data.

Abstract: Publication date: Available online 19 July 2017 Source:Computers & Mathematics with Applications Author(s): Wei Liu, Zhengjia Sun A block-centered finite difference scheme is given for the approximation of reduced coupled model in the fractured media aquifer system. The fluid flow of aquifer system is governed by Darcy’s law in both fracture and surrounding porous media. The degrees of freedom are given separately on both sides of fracture to capture the discontinuity of pressure and velocity. Optimal error estimates in discrete L 2 norms are obtained. Numerical experiments are provided to verify the second-order accuracy of presented method. It is demonstrated whether the fracture acts as a fast pathway or geological barrier is totally determined by the value of its permeability tensor.