Abstract: Publication date: Available online 2 August 2017 Source:Computers & Mathematics with Applications Author(s): Shimin Guo, Liquan Mei, Ying Li The aim of this paper is to develop an efficient numerical treatment for the two-dimensional fractional nonlinear reaction–diffusion-wave equation with the time-fractional derivative of order α ( 1 < α < 2 ). For this purpose, we employ the alternating direction implicit (ADI) method based on the Crank–Nicolson scheme for the time stepping, while we apply the Legendre–Galerkin spectral method for the space discretization. The stability and convergence analysis are rigorously set up. In addition, the proposed method is extended to solve the time-fractional Klein–Gordon and sine-Gordon models. Numerical experiments are included, which verifies the theoretical predictions.

Abstract: Publication date: Available online 1 August 2017 Source:Computers & Mathematics with Applications Author(s): Xiaoen Zhang, Yong Chen, Yong Zhang Breather, lump and X soliton solutions are presented via the Hirota bilinear method, to the nonlocal (2+1)-dimensional KP equation, derived from the Alice–Bob system. The resulting breather contains two cases, one is the line breather and another is the normal breather, both of which are different from the solutions of the classical (2+1)-dimensional KP equation; the X soliton is found with the long wave limit by some constraints to the parameters; the lump solution is obtained in virtue of two methods, one is as the long wave limit of breather theoretically, the other is with the quadratic function method, which can be guaranteed rationally localized in all directions in the space under some constraints of the parameters. By choosing specific values of the involved parameters, the dynamic properties of some breather, lump solutions to nonlocal KP equation are plotted, as illustrative examples.

Abstract: Publication date: Available online 1 August 2017 Source:Computers & Mathematics with Applications Author(s): Juan Carlos Araujo-Cabarcas, Christian Engström In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when the computational domain is truncated with a perfectly matched layer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is based on the Lippmann–Schwinger equation and we use computations of the pseudospectrum to show that this is a suitable choice. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases.

Abstract: Publication date: Available online 31 July 2017 Source:Computers & Mathematics with Applications Author(s): Na Huang, Chang-Feng Ma By using the Galerkin finite element method, the distributed control problems can be discretized into a saddle point problem with a coefficient matrix of block three-by-three, which can be reduced to a linear system with lower order. We first introduce a class of inexact block diagonal preconditioners and estimate the lower and upper bounds of positive and negative eigenvalues of the preconditioned matrices, respectively. Based on the Cholesky decomposition of the known matrices, we also analyze a lower triangular preconditioner to accelerate the minimal residual method for the reduced linear system and discuss its real and complex eigenvalues respectively. Moreover, these bounds do not rely on the regularization parameter and the eigenvalues of the matrices in the discrete system. Numerical experiments are also presented to demonstrate the effectiveness and robustness of the two new preconditioners.

Abstract: Publication date: Available online 31 July 2017 Source:Computers & Mathematics with Applications Author(s): W. Li, Z.X. Gong, Y.B. Chai, C. Cheng, T.Y. Li, Q.F. Zhang, M.S. Wang In order to enhance the performance of the discrete shear gap technique (DSG) for shell structures, the coupling of hybrid gradient smoothing technique (H-GST) with DSG using triangular elements (HS-DSG3) is presented to solve the governing partial differential equations of shell structures. In the formulation HS-DSG3, we firstly employ the node-based gradient smoothing technique (N-GST) to obtain the node-based smoothed strain field, then a scale factor α ∈ [ 0 , 1 ] is used to reconstruct a new strain field which includes both the strain components from standard DGS3 and the strain components from node-based smoothed DSG3 (NS-DSG3). The HS-DSG3 takes advantage of the “overly-soft” NS-DSG3 model and the “overly-stiff” DSG3 model, and has a relatively appropriate stiffness of the continuous system. Therefore, the degree of the solution accuracy can be improved significantly. Several typical benchmark numerical examples have been investigated and it is demonstrated that the present HS-DSG3 can provide better numerical solutions than the original DSG3 for shell structures.

Abstract: Publication date: Available online 31 July 2017 Source:Computers & Mathematics with Applications Author(s): Zohar Yosibash, Ernst Rank, Alexander Düster, Alessandro Reali

Abstract: Publication date: Available online 29 July 2017 Source:Computers & Mathematics with Applications Author(s): Socratis Petrides, Leszek F. Demkowicz The Discontinuous Petrov–Galerkin (DPG) method for high frequency wave propagation problems is discussed. The DPG method, with its attractive uniform (mesh and wavenumber independent) pre-asymptotic stability property, allows for a fully automatic adaptive h p -algorithm that can be initiated from very coarse meshes. Moreover, DPG always delivers a Hermitian positive definite system, suggesting the use of the Conjugate Gradient algorithm for its solution. We present a new iterative solution scheme which capitalizes on these attractive properties of DPG. This novel solver is integrated within the adaptive procedure by constructing a two-grid-like preconditioner for the Conjugate Gradient method that exploits information from previous meshes. The construction of our preconditioner is discussed, and its efficacy is illustrated with an example of a 2D acoustics problem. Our results show that the proposed iterative algorithm converges at a rate independent of the mesh and the wavenumber.

Abstract: Publication date: Available online 29 July 2017 Source:Computers & Mathematics with Applications Author(s): Asma Rouatbi, Moeiz Rouis, Khaled Omrani A nonlinear difference scheme is considered for the two-dimensional Rosenau–Burgers equation. Some priori estimates, existence and uniqueness of the difference solution have been shown. A second-order convergence in the uniform norm and stability are proved. Also a convergent iterative algorithm is presented. All results are obtained without any restrictions on the meshsizes. At last numerical experiments are carried out to support the theoretical claims.

Abstract: Publication date: Available online 29 July 2017 Source:Computers & Mathematics with Applications Author(s): David Kamensky, John A. Evans, Ming-Chen Hsu, Yuri Bazilevs This paper discusses a method of stabilizing Lagrange multiplier fields used to couple thin immersed shell structures and surrounding fluids. The method retains essential conservation properties by stabilizing only the portion of the constraint orthogonal to a coarse multiplier space. This stabilization can easily be applied within iterative methods or semi-implicit time integrators that avoid directly solving a saddle point problem for the Lagrange multiplier field. Heart valve simulations demonstrate applicability of the proposed method to 3D unsteady simulations. An appendix sketches the relation between the proposed method and a high-order-accurate approach for simpler model problems.

Abstract: Publication date: Available online 27 July 2017 Source:Computers & Mathematics with Applications Author(s): Chuan-Long Wang, Chao Li, Jin Wang In this paper, we propose two modified augmented Lagrange multiplier algorithms by mean-value for Toeplitz matrix compressive recovery. In the algorithms, the mean-value modification makes the iteration matrices keep the Toeplitz structure which contributes to reduce the SVD time and CPU time. Numerical experiments show that the proposed algorithms achieve better precision than the augmented Lagrange multiplier method, especially when the matrix E is less sparse. Convergence analysis of the proposed algorithms is also given in detail.

Abstract: Publication date: Available online 26 July 2017 Source:Computers & Mathematics with Applications Author(s): Keunsoo Park, Maria Fernandino, Carlos A. Dorao, Marc Gerritsma The phase-field approach has been regarded as a powerful method in numerically handling the interface dynamics in multiphase flow in several scientific and engineering applications. For an isothermal fluid mixture, the Navier–Stokes–Korteweg equation and the Navier–Stokes–Cahn–Hilliard equation have represented two major branches of the phase-field methods. We present a general discretization formulation for these two equations and conduct a comparison study of them. The formulation using a least-squares spectral element method is implemented by adopting a time-stepping procedure, a high-order continuity approximation and an element-by-element solver technique. To describe the same fluid mixtures by the isothermal Navier–Stokes–Korteweg and the Navier–Stokes–Cahn–Hilliard equations, we suggest a non-dimensionalization with the same dimensionless quantities. Numerical experiments are conducted to verify the spectral/hp least-squares formulation for the isothermal Navier–Stokes–Korteweg model. Besides, the equilibrium state of the van der Waals fluid model is calculated both analytically and numerically. Through spontaneous decomposition example, the isothermal Navier–Stokes–Korteweg system and the Navier–Stokes–Cahn–Hilliard system are compared in terms of the equilibrium pressure and the energy minimizing process. As a general example, the coalescence of two liquid droplets is studied with our solver for the isothermal Navier–Stokes–Korteweg system. The minimum discretization levels for space and time are investigated and a parametric study on Weber number is carried out.

Abstract: Publication date: Available online 26 July 2017 Source:Computers & Mathematics with Applications Author(s): Duong Thanh Pham, Tung Le We prove a posteriori upper and lower bounds for the error estimates when solving the Laplace–Beltrami equation on the unit sphere by using the Galerkin method with spherical splines. Adaptive mesh refinements based on these a posteriori error estimates are used to reduce complexity and computational cost of the corresponding discrete problems. The theoretical results are corroborated by numerical experiments.

Abstract: Publication date: Available online 26 July 2017 Source:Computers & Mathematics with Applications Author(s): Avary Kolasinski, Weizhang Huang A new functional is presented for variational mesh generation and adaptation. It is formulated based on combining the equidistribution and alignment conditions into a single condition with only one dimensionless parameter. The functional is shown to be coercive but not convex. A solution procedure using a discrete moving mesh partial differential equation is employed. It is shown that the element volumes and altitudes of a mesh trajectory of the mesh equation associated with the new functional are bounded away from zero and the mesh trajectory stays nonsingular if it is so initially. Numerical examples demonstrate that the new functional performs comparably as an existing one that is also based on the equidistribution and alignment conditions and known to work well but contains an additional parameter.

Abstract: Publication date: Available online 26 July 2017 Source:Computers & Mathematics with Applications Author(s): Zhimin Hou, Baochang Shi, Zhenhua Chai Suppression of spiral wave attracts more and more attention in nonlinear systems. In this paper, a spiral wave local feedback control approach based on the FitzHugh–Nagumo (FHN) model is studied with lattice Boltzmann method. Numerical simulations are performed to investigate the effects of initial conditions for the spiral wave formation, model parameters, size and position of the feedback control region, and feedback control parameters on the behavior of spiral wave. The results show that there are three characteristics of spiral wave elimination. The first is that initial conditions of the spiral wave formation have little influence on feedback control of spiral wave. Secondly, the model parameters are related to the time needed for the elimination of spiral wave, for example, the larger the mutual time scales, the faster the elimination of spiral wave. Finally, through selecting the size and position of the feedback region, spiral wave can be effectively removed with weak feedback signal.

Abstract: Publication date: Available online 24 July 2017 Source:Computers & Mathematics with Applications Author(s): J.A. Ferreira, P. de Oliveira, G. Pena The use of enhancers to increase the drug molecules penetration into target tissues is a usual technique in drug delivery. In transdermal drug delivery, electric fields are often used to increase the drug transport through the skin. In this paper we study a drug delivery mechanism from a reservoir which is in contact with the skin. We assume that the drug transport in the coupled system is enhanced by a small electric field that induces a convective field. We establish energy estimates for the coupled system and we propose a semi-analytical discrete coupled model that mimics the continuous model. The qualitative behaviour of the system is illustrated.

Abstract: Publication date: Available online 22 July 2017 Source:Computers & Mathematics with Applications Author(s): Z.G. Shi, Y.M. Zhao, F. Liu, Y.F. Tang, F.L. Wang, Y.H. Shi In this paper, an H 1 -Galerkin mixed finite element approximate scheme is established for a class of two-dimensional time fractional diffusion equations by using the bilinear element, Raviart–Thomas element and L 1 time stepping method, which is unconditionally stable and free of LBB condition. And then, without the classical Ritz projection, superclose results for the original variable u in H 1 -norm and the flux p → = ∇ u in H ( d i v , Ω ) -norm are derived by means of properties of the elements and L 1 approximation. Furthermore, with the help of the interpolation postprocessing operator, the global superconvergence results for the original variable u in H 1 -norm are obtained. Finally, numerical simulations verify that the theoretical results are true on both regular meshes and anisotropic meshes.

Abstract: Publication date: Available online 22 July 2017 Source:Computers & Mathematics with Applications Author(s): Joo Hyeong Han, Jae Ryong Kweon, Minje Park In this paper we show an interior discontinuity and its piecewise regularity for a stationary compressible Stokes problem with inflow jump datum. The discontinuity is preserved along the interior curve directed by the ambient vector field. The difficulty lies in controlling the gradient of the pressure across the interior curve starting at the jump point that the inflow datum has. We deal with this issue by constructing a vector function K corresponding to the interior jump and splitting the vector K from the velocity vector. Finally the remainder for the velocity vector and pressure function is shown to be in the space H 2 , q × H 1 , q for q ≥ 2 .

Abstract: Publication date: Available online 22 July 2017 Source:Computers & Mathematics with Applications Author(s): Christoph Hofer In this paper we investigate the parallelization of dual–primal isogeometric tearing and interconnecting (IETI-DP) type methods for solving large-scale continuous and discontinuous Galerkin systems of equations arising from Isogeometric analysis of elliptic boundary value problems. These methods are extensions of the finite element tearing and interconnecting methods to isogeometric analysis. The algorithms are implemented by means of energy minimizing primal subspaces. We discuss how these methods can efficiently be parallelized in a distributed memory setting. Weak and strong scaling studies presented for two and three dimensional problems show an excellent parallel efficiency.

Abstract: Publication date: Available online 21 July 2017 Source:Computers & Mathematics with Applications Author(s): Dow Drake, Jay Gopalakrishnan, Ammar Harb This paper shows that the test spaces in discontinuous Petrov Galerkin (DPG) methods can be reduced on rectangular elements without affecting unisolvency or rates of convergences. One reduced case is obtained by decreasing the polynomial degree of a standard test space in both coordinate directions by one. A further reduction of test space by almost another full degree is possible if one is willing to implement a nonstandard test space. The error analysis of such cases is based on an extension of the second Strang lemma and an interpretation of the DPG method as a nonconforming method. The key technical ingredient in obtaining unisolvency is the identification of a discontinuous piecewise polynomial on the element boundary that is orthogonal to all continuous piecewise polynomials of one degree higher.

Abstract: Publication date: Available online 21 July 2017 Source:Computers & Mathematics with Applications Author(s): Huiru Li, Haibin Xiao Traveling wave solution for a class of diffusive predator–prey system with nonlinear density dependence is considered. Using methods of topological shooting, we show the existence of a non-negative traveling wave solution connecting a boundary equilibrium to the co-existence steady state with the help of a Wazewski-like set together with Lyapunov function constructed elaborately. This means that the traveling wave solution established by Huang (2012) can be preserved in the presence of the nonlinear density dependence for the predator and the results of Huang (2012) are generalized.

Abstract: Publication date: Available online 21 July 2017 Source:Computers & Mathematics with Applications Author(s): Abdullahi Rashid Adem A coupled Kadomtsev–Petviashvili equation is investigated by using Lie symmetry analysis. The similarity reductions and new exact solutions are obtained via the extended tanh method with symbolic computation. Exact solutions including solitons are shown. The solutions derived have dissimilar physical structures and depend on the real parameters.

Abstract: Publication date: Available online 21 July 2017 Source:Computers & Mathematics with Applications Author(s): Xiao-Yong Xiao, Xiang Wang, Hong-Wei Yin We propose a single-step preconditioned variant of HSS (SPHSS) and an efficient parameterized SPHSS (PSPHSS) iteration method for solving a class of complex symmetric linear systems. Under suitable conditions, we analyze the convergence properties of the SPHSS and PSPHSS iteration methods. Theoretical analysis shows that the minimal upper bounds for the spectral radius of the SPHSS and PSPHSS iteration matrices are less than those of the SHSS and PSHSS iteration matrices when using the optimal parameters, respectively. Numerical results show that the PSPHSS iteration method has comparable advantage over several other iteration methods whether the experimental optimal parameters are used or not.

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.

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 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.