Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Ricardo Castillo, Miguel Loayza We are concerned with the parabolic equation u t − Δ u = f ( t ) u p ( x ) in Ω × ( 0 , T ) with homogeneous Dirichlet boundary condition, p ∈ C ( Ω ) , f ∈ C ( [ 0 , ∞ ) ) and Ω is either a bounded or an unbounded domain. The initial data is considered in the space { u 0 ∈ C 0 ( Ω ) ; u 0 ≥ 0 } . We find conditions that guarantee the global existence and the blow up in finite time of nonnegative solutions. These conditions are given in terms of the asymptotic behavior of the solution of the homogeneous linear problem u t − Δ u = 0 .

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Gusheng Tang In this paper, we consider the following reaction diffusion systems with gradient nonlinearity under nonlinear boundary condition { u t = △ u + u p v q − ∣ ∇ u ∣ α , ( x , t ) ∈ Ω × ( 0 , t ∗ ) ; v t = △ v + v r u s − ∣ ∇ v ∣ α , ( x , t ) ∈ Ω × ( 0 , t ∗ ) ; ∂ u ∂ ν = g ( u ) , ∂ v ∂ ν = h ( v ) , ( x , t ) ∈ ∂ Ω × ( 0 , t ∗ ) ; u ( x , 0 ) = u 0 ( x ) , v ( x , 0 ) = v 0 ( x ) , x ∈ Ω where Ω ⊂ R N ( N ≥ 1 ) is a bounded region with smooth boundary ∂ Ω , p , q , r , s ≥ 0 , α > 1 , t ∗ is a possible blow-up time when blow-up occurs. By constructing an appropriate auxiliary functions, and by means of Payne–Weinberger or Scott’s method, a lower bound on blow-up time when blow-up occurs is derived.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Hongwei Jin, Minru Bai, Julio Benítez, Xiaoji Liu In this paper, we recall and extend some tensor operations. Then, the generalized inverse of tensors is established by using tensor equations. Moreover, we investigate the least-squares solutions of tensor equations. An algorithm to compute the Moore–Penrose inverse of an arbitrary tensor is constructed. Finally, we apply the obtained results to higher order Gauss–Markov theorem.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Gil Ho Yoon This study considers failure theories for brittle and ductile materials in the stress-based topology optimization method (STOM) for steady state fluid–structure interactions (FSI). In some relevant studies, the subject of the stress-based topology optimization to minimize volumes with local von Mises stress constraints has been researched. However, the various failure theories for ductile and brittle materials, such as the maximum shear stress theory, the brittle and ductile Mohr–Coulomb theory, and the Drucker–Prager theory, have not been considered. For successful STOM for FSI, in addition to alleviating physics interpolation issues between structure and fluid and some numerical issues related to STOM, the mathematical characteristics of the various failure theories should be properly formulated and constrained. To resolve all the involved computational issues, the present study applies the monolithic analysis method, the qp-relaxation method, and the p -norm approach to the failure constraints. The present topology optimization method can create optimal layouts while minimizing volume constraining local failure constraints for ductile and brittle materials for steady state fluid and structural interaction system.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Romit Maulik, Omer San This paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models. The approximate deconvolution (AD) procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the Smagorinsky and Leith models. The novel idea here is to estimate the modeling parameters using the AD method rather than the traditionally used test filtering approach. First, a-priori and a-posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem. The proposed model is then applied to a wind-driven quasigeostrophic four-gyre ocean circulation problem, which is a standard prototype of more realistic ocean dynamics. Results show that the proposed model captures the quasi-stationary ocean dynamics and provides the time averaged four-gyre circulation patterns. Taking locally resolved flow characteristics into account, the model dynamically provides higher eddy viscosity values for lower resolutions.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Sitong Chen, Xianhua Tang This paper is dedicated to studying the following Schrödinger–Poisson system { − △ u + V ( x ) u + ϕ u = K ( x ) f ( u ) , x ∈ R 3 , − △ ϕ = u 2 , x ∈ R 3 , where V , K ∈ C ( R 3 , R ) and f ∈ C ( R , R ) . Under mild assumptions on the decay rate of V ( x ) , we establish the existence of one ground state sign-changing solution with precisely two nodal domains, by using a weaker growth condition lim ∣ t ∣ → ∞ ∫ 0 t f ( s ) d s ∣ t ∣ 3 = ∞ , instead of the usual super-cubic condition lim ∣ t ∣ → ∞ ∫ 0 t f ( s ) d s ∣ t ∣ 4 = ∞ . Our result unifies both asymptotically cubic and super-cubic cases, which generalizes and improves the corresponding ones in the literatures.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Jishan Fan, Ahmed Alsaedi, Tasawar Hayat, Yong Zhou In this paper, we consider an epitaxial growth model with slope selection and a generalized model. First, we establish some regularity criteria of strong solutions for the epitaxial growth model with slope selection. Then, we prove the global-in-time existence of smooth solutions for a generalized model.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Akhlaq Husain, Arbaz Khan In this paper, we propose preconditioners for the system of linear equations that arise from a discretization of fourth order elliptic problems in two and three dimensions ( d = 2 , 3 ) using spectral element methods. These preconditioners are constructed using separation of variables and can be diagonalized and hence easy to invert. For second order elliptic problems this technique has proven to be successful and performs better than other preconditioners in the framework of least-squares methods. We show that these preconditioners are spectrally equivalent to the quadratic forms by which we approximate them. Numerical results for the condition number reflects the effectiveness of the preconditioners.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Bang-Qing Li, Yu-Lan Ma, Li-Po Mo, Ying-Ying Fu A ( 2 + 1 ) -dimensional Vakhnenko equation is investigated, which describes high-frequent wave propagations in relaxing medium. The N-loop soliton solutions for the equation are calculated by applying the improved Hirota method and the variable transformations. The N-loop soliton solutions can be expressed explicitly. Furthermore, the interaction patterns are graphically observed for the N-loop soliton solutions. The dynamical interactions among the N -solitons ( N ≥ 2 ) are elastic.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Manassés de Souza, Uberlandio B. Severo, Gilberto F. Vieira This paper establishes sufficient conditions for the existence and multiplicity of solutions for nonhomogeneous and singular quasilinear equations of the form − Δ u + V ( x ) u − Δ ( u 2 ) u = g ( x , u ) x a + h ( x ) in R 2 , where a ∈ [ 0 , 2 ) , V ( x ) is a continuous positive potential bounded away from zero and which can be “large” at infinity, the nonlinearity g ( x , s ) is allowed to enjoy the critical exponential growth with respect to the Trudinger–Moser inequality and the nonhomogeneous term h belongs to L q ( R 2 ) for some q ∈ ( 1 , 2 ] . By combining variational arguments in a nonstandard Orlicz space context with a singular version of the Trudinger–Moser inequality, we obtain the existence of two distinct solutions when ‖ h ‖ q is sufficiently small. Schrödinger equations of this type have been studied as models of several physical phenomena.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Bao-Hua Huang, Chang-Feng Ma In this paper, we discuss the finite iterative algorithm to solve a class of generalized coupled Sylvester-conjugate matrix equations. We prove that if the system is consistent, an exact generalized Hamiltonian 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 generalized Hamiltonian 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 minimum norm least squares generalized Hamiltonian solution of the system. Finally, numerical examples are presented to demonstrate the algorithm is efficient.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Xiu-Bin Wang, Shou-Fu Tian, Hui Yan, Tian Tian Zhang Under investigation in this work is a generalized ( 3 + 1 )-dimensional Kadomtsev–Petviashvili (GKP) equation, which can describe many nonlinear phenomena in fluid dynamics. By virtue of the Bell’s polynomials, an effective and straightforward way is presented to explicitly construct its bilinear form and soliton solution. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the kinky breather wave solutions and rational breather wave solutions of the equation are well constructed. It is hoped that our results can be used to enrich the dynamical behavior of the ( 3 + 1 )-dimensional nonlinear wave fields.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Gerardo González, Ville Kolehmainen, Aku Seppänen This paper focuses on studying the effects of isotropic and anisotropic total variation (TV) regularization in electrical impedance tomography (EIT). A characteristic difference between these two widely used TV regularization methods is that the isotropic TV is rotationally invariant and the anisotropic TV is not. The rotational variance of the anisotropic TV is known to cause geometric distortions by favoring edge orientations that are aligned with co-ordinate axes. In many applications, such as transmission tomography problems, these distortions often play only a minor role in the overall accuracy of reconstructed images, because the measurement data is sensitive to the shapes of the edges in the imaged domain. In EIT and other diffusive image modalities, however, the data is severely less sensitive to the fine details of edges, and it is an open question how large impact the selection of the TV regularization variant has on the reconstructed images. In this work, this effect is investigated based on a set of experiments. The results demonstrate that the choice between isotropic and anisotropic TV regularization indeed has a significant impact on the properties of EIT reconstructions; especially, the tendency of the anisotropic TV to favor edges aligned with co-ordinate axes is shown to yield large geometric distortions in EIT reconstructions.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Salim Bettahar, Patrick Lambert, Amine Boudghene Stambouli We are interested in the restoration of blurred colour images corrupted by additive noise. We present a new model for colour image enhancement based on coupling diffusion to shock filter without creating colour artefacts. The suggested model is based on using single vectors of the gradient magnitude and the second derivatives in order to relate different colour components of the image.

Abstract: Publication date: 1 August 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 3 Author(s): Jian-bing Zhang, Wen-Xiu Ma By using the Hirota bilinear form of the (2+1)-dimensional BKP equation, ten classes of interaction solutions between lumps and kinks are constructed through Maple symbolic computations beginning with a linear combination ansatz. The resulting lump-kink solutions are reduced to lumps and kinks when the exponential function and the quadratic function disappears, respectively. Analyticity is naturally guaranteed for the presented lump-kink solution if the constant term is chosen to be positive.

Abstract: Publication date: Available online 8 July 2017 Source:Computers & Mathematics with Applications Author(s): Zhihan Wei, Chuan Li, Shan Zhao A new matched alternating direction implicit (ADI) method is proposed in this paper for solving three-dimensional (3D) parabolic interface problems with discontinuous jumps and complex interfaces. This scheme inherits the merits of its ancestor for two-dimensional problems, while possesses several novel features, such as a non-orthogonal local coordinate system for decoupling the jump conditions, two-side estimation of tangential derivatives at an interface point, and a new Douglas–Rachford ADI formulation that minimizes the number of perturbation terms, to attack more challenging 3D problems. In time discretization, this new ADI method is found to be of first order and stable in various experiments. In space discretization, the matched ADI method achieves the second order accuracy based on simple Cartesian grids for various irregularly-shaped surfaces and spatial–temporal dependent jumps. Computationally, the matched ADI method is as efficient as the fastest implicit scheme based on the geometrical multigrid for solving 3D parabolic equations, in the sense that its complexity in each time step scales linearly with respect to the spatial degree of freedom N , i.e., O ( N ) . Furthermore, unlike iterative methods, the ADI method is an exact or non-iterative algebraic solver which guarantees to stop after a certain number of computations for a fixed N . Therefore, the proposed matched ADI method provides a very promising tool for solving 3D parabolic interface problems.

Abstract: Publication date: Available online 8 July 2017 Source:Computers & Mathematics with Applications Author(s): Shangyou Zhang On triangular grids, the continuous P k plus discontinuous P k − 1 mixed finite element is stable for polynomial degree k ≥ 4 . When k = 3 , the inf–sup condition fails and the mixed finite element converges at an order that is two orders lower than the optimal order. We enrich the continuous P 3 by adding some P 4 divergence-free bubble functions, to be exact, one P 4 divergence-free bubble function each component each edge. We show that such an enriched P 3 – P 2 mixed element is inf–sup stable, and converges at the optimal order. Numerical tests are presented, comparing the new element with the P 4 – P 3 element and the unstable P 3 – P 2 element.

Abstract: Publication date: Available online 8 July 2017 Source:Computers & Mathematics with Applications 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: Available online 8 July 2017 Source:Computers & Mathematics with Applications 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: Available online 8 July 2017 Source:Computers & Mathematics with Applications Author(s): Jinhu Xu, Yan Geng, Jiangyong Hou A non-standard finite difference scheme is proposed to solve a delayed and diffusive viral infection model with general nonlinear incidence rate. The results show that the discrete model preserves the positivity and boundedness of solutions in order to ensure the well-posedness of the problem. Moreover, this method preserves all equilibria of the original continuous model. By constructing Lyapunov functionals, we show that the global stability of equilibria is completely determined by the basic reproduction number ℜ 0 , which implies that the proposed discrete model can efficiently blue preserve the global stability of equilibria of the corresponding continuous model. Numerical experiments are carried out to support the theoretical results.

Abstract: Publication date: Available online 8 July 2017 Source:Computers & Mathematics with Applications 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: Available online 8 July 2017 Source:Computers & Mathematics with Applications 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: Available online 6 July 2017 Source:Computers & Mathematics with Applications 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 July 2017 Source:Computers & Mathematics with Applications 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: Available online 6 July 2017 Source:Computers & Mathematics with Applications Author(s): Jan Petsche, Andreas Schröder In this paper, mixed and mixed-hybrid methods for h - and h p -adaptive finite elements on quadrilateral meshes are discussed for variational equations and, in particular, for variational inequalities. The main result is the derivation of reliable error estimates for mixed methods for the obstacle problem. The estimates rely on the use of a post-processing of the potential in H 1 and on the introduction of a certain Lagrange multiplier which is associated with the obstacle constraints. The error estimates consist of the dual norm of the residual, which is defined by an appropriate approximation of the Lagrange multiplier, plus some computable remainder terms. In numerical experiments, the applicability of the post-processing procedure on quadrilateral meshes with multilevel hanging-nodes is verified and the use of the estimates in h - and h p -adaptive schemes is demonstrated by means of convergence rates and effectivity indices.

Abstract: Publication date: Available online 6 July 2017 Source:Computers & Mathematics with Applications Author(s): Cheng-Cheng Zhu, Jiang Zhu To understand the impact of tax policy on the persistence of a drinking behavior, a reaction–diffusion alcohol model with the impact of tax policy is studied, with the focus on the positivity and boundedness of solutions and particularly the asymptotic profile of the equilibria. The basic reproduction number R 0 is calculated, and existence of a drinking-free equilibrium and a unique drinking-present equilibrium is established for R 0 above the threshold value 1. For both of ODE system and reaction–diffusion model, it is shown that the drinking-free equilibrium is globally asymptotically stable if R 0 ≤ 1 , and if R 0 > 1 , we obtain a sufficient condition for global asymptotically stability of the drinking-present equilibrium. Numerical simulations are also provided to illustrate our analytical results.

Abstract: Publication date: Available online 6 July 2017 Source:Computers & Mathematics with Applications 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: Available online 6 July 2017 Source:Computers & Mathematics with Applications 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: Available online 5 July 2017 Source:Computers & Mathematics with Applications 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: Available online 5 July 2017 Source:Computers & Mathematics with Applications Author(s): Tom Gustafsson, Harri Hakula, Matti Leinonen We consider the approximation of the Reynolds equation with an uncertain film thickness. The resulting stochastic partial differential equation is solved numerically by the stochastic Galerkin finite element method with high-order discretizations both in spatial and stochastic domains. We compute the pressure field of a journal bearing in various numerical examples that demonstrate the effectiveness and versatility of the approach. The results suggest that the stochastic Galerkin method is capable of supporting design when manufacturing imperfections are the main sources of uncertainty.

Abstract: Publication date: Available online 19 June 2017 Source:Computers & Mathematics with Applications Author(s): Jingtang Ma, Zhiqiang Zhou, Zhenyu Cui In this paper, we propose a hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump–diffusion (HEJD), Markov regime switching models, and the finite moment log stable (FMLS) models. We first apply Laplace transforms to free boundary partial differential equations (PDEs) or fractional partial differential equations (FPDEs) governing the American option prices with respect to time, and obtain second order ordinary differential equations (ODEs) or fractional differential equations (FDEs) with free boundary, which is named as the early exercise boundary in the American option pricing. Then, we develop an iterative algorithm based on finite difference methods to solve the ODEs or FDEs together with the unknown free boundary values in the Laplace space. Both the early exercise boundary and the prices of American options are recovered through inverse Laplace transforms. Numerical examples demonstrate the accuracy and efficiency of the method in CEV, HEJD, Markov regime switching models and the FMLS models.

Abstract: Publication date: 15 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 2 Author(s): Ola Ragb, L.F. Seddek, M.S. Matbuly A numerical scheme based on differential quadrature methods, is introduced for solving Bratu problem. The problem is firstly reduced to an iterative one. Then, both of differential quadrature method (DQM) and moving least squares differential quadrature method (MLSDQM) are applied to solve iteratively the nonlinear problem. The proposed scheme successfully computes multiple solutions to Bratu’s problem. The obtained results agree with the 1D and 2D closed forms. Further a parametric study is introduced to investigate the computational characteristics of the proposed scheme.

Abstract: Publication date: 15 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 2 Author(s): Jianping Yu, Yongli Sun In this paper, we study the Gaussian solitary waves for some nonlinear evolution equations with logarithmic nonlinearities. These studied logarithmic evolution equations are the generalized logarithmic BBM equations, the logarithmic ( 2 + 1 ) -dimensional KP-like equations, the logarithmic ( 3 + 1 ) -dimensional KP-like equations, the generalized logarithmic ( 2 + 1 ) -dimensional Klein-Gordon equations and the generalized logarithmic ( 3 + 1 ) -dimensional Klein-Gordon equations. We not only prove that they possess Gaussons: solitary wave solutions of Gaussian shape but also derive the relationships among the parameters.

Abstract: Publication date: 15 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 2 Author(s): Hongyu Ye In this paper, we study the existence and the concentration behavior of critical points for the following functional derived from the Schrödinger–Poisson system: E ( u ) = 1 2 ∫ R 3 ∇ u 2 + 1 4 ∫ R 3 ( x − 1 ∗ u 2 ) u 2 − 3 10 ∫ R 3 u 10 3 constrained on the L 2 -spheres S ( c ) = { u ∈ H 1 ( R 3 ) u 2 = c } when c > c ∗ = Q 2 , where Q is up to translations, the unique positive of − Δ Q + 2 3 Q = Q 4 3 Q in R 3 . As such constrained problem is L 2 -critical, E ( u ) is unbounded from below on S ( c ) when c > c ∗ and the existence of critical points constrained on S ( c ) is obtained by a mountain pass argument on S ( c ) . We show that there exists c 1 > ( 9 7 ) 3 4 c ∗ such that E ( u ) has at least one positive critical point restricted to S ( c ) for c ∗ < c ≤ c 1 . As c approaches c PubDate: 2017-06-06T16:30:40Z

Abstract: Publication date: 15 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 2 Author(s): Imtiaz Ahmad, Siraj-ul-Islam, Abdul Q.M. Khaliq In this paper, a local meshless differential quadrature collocation method is utilized to solve multi-dimensional reaction–convection–diffusion PDEs numerically. In some cases, global version of the meshless method is considered as well. The meshless methods approximate solution on scattered and uniform nodes in both local and global sense. In the case of convection-dominated PDEs, the local meshless method is coupled with an upwind technique to avoid spurious oscillations. For this purpose, a physically motivated local domain is utilized in the flow direction. Both regular and irregular geometries are taken into consideration. Numerical experiments are performed to demonstrate effective applications and accuracy of the meshless method on regular and irregular domains.

Abstract: Publication date: 15 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 2 Author(s): Shaolei Ru, Jiecheng Chen In this paper, we first prove the local well-posedness of the fractional Burgers equations in N Dimensions. Combining the local well-posedness and the method of modulus of continuity, we show the global well-posedness of the N-D critical Burgers equation in critical Besov spaces B ̇ p , 1 N p ( R N ) with p ∈ [ N , ∞ ) .

Abstract: Publication date: 15 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 2 Author(s): Andrzej Karafiat A classical mixed boundary-value problem of linear elasticity in two dimensions in the Galerkin boundary integral formulation is considered. We prove a-priori error estimates of the solution to this problem by the isogeometric adaptive method using NURBS. The estimates include approximation of the boundary of the domain.

Abstract: Publication date: 1 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 1 Author(s): D. Fishelov We present a high-order finite difference scheme for Navier–Stokes equations in irregular domains. The scheme is an extension of a fourth-order scheme for Navier–Stokes equations in streamfunction formulation on a rectangular domain (Ben-Artzi et al., 2010). The discretization offered here contains two types of interior points. The first is regular interior points, where all eight neighboring points of a grid point are inside the domain and not too close to the boundary. The second is interior points where at least one of the closest eight neighbors is outside the computational domain or too close to the boundary. In the second case we design discrete operators which approximate spatial derivatives of the streamfunction on irregular meshes, using discretizations of pure derivatives in the x , y and along the diagonals of the element.

Abstract: Publication date: 1 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 1 Author(s): Mayken Espinoza-Andaluz, Martin Andersson, Bengt Sundén The purpose of this study is to investigate the computational time required to describe the fluid flow behavior through a porous medium and its relation to the corresponding domain size. The fluid flow behavior is recovered using the lattice Boltzmann method (LBM). The selected methodology has been applied because of its feasibility for mimicking the fluid flow behavior in complex geometries and moving boundaries. In this study, three different porosities are selected to calculate, for several sizes domain, the required computational time to reach the steady state. Two different cases are implemented: (1) increasing the transversal area, but keeping the layer thickness as a constant, and (2) increasing the total volume of the pore domain by increasing all the dimensions of the volume equally. The porous media are digitally generated by placing the solid obstacles randomly, but uniformly distributed in the whole domain. Several relationships relating the computational time, domain size and porosity are proposed. Additionally, an expression that relates the hydraulic tortuosity to the porosity is proposed.

Abstract: Publication date: 1 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 1 Author(s): Moritz Braun, Kingsley O. Obodo In this contribution a multi domain finite element density functional code for molecules is presented. The method makes use of higher order elements to enforce the continuity of the orbitals between the spherical domains and the interstitial domain. The salient computational details of the algorithm are described in some detail. Results of calculations for the orbital energies of methane, ethane, water, ammonia and benzene are given and compared with those obtained using GPAW.

Abstract: Publication date: 1 July 2017 Source:Computers & Mathematics with Applications, Volume 74, Issue 1 Author(s): Vít Dolejší, Georg May, Filip Roskovec, Pavel Solin We develop a new mesh adaptive technique for the numerical solution of partial differential equations (PDEs) using the h p -version of the finite element method ( h p -FEM). The technique uses a combination of approximation and interpolation error estimates to generate anisotropic triangular elements as well as appropriate polynomial approximation degrees. We present a h p -version of the continuous mesh model as well as the continuous error model which are used for the formulation of a mesh optimization problem. Solving the optimization problem leads to h p -mesh with the smallest number of degrees of freedom, under the constraint that the approximate solution has an error estimate below a given tolerance. Further, we propose an iterative algorithm to find a suitable anisotropic h p -mesh in the sense of the mesh optimization problem. Several numerical examples demonstrating the efficiency and applicability of the new method are presented.

Abstract: Publication date: Available online 12 May 2017 Source:Computers & Mathematics with Applications Author(s): José L. Galán-García, Gabriel Aguilera-Venegas