Showing papers in "Computational Mathematics and Modeling in 2014"
TL;DR: In this paper, a modified homotopy perturbation (NHPM) method is applied to solve a special kind of nonlinear Volterra integral equations in two-dimensional space.
Abstract: In this work, a new modified homotopy perturbation (NHPM) is applied to solve a special kind of nonlinear Volterra integral equations in two-dimensional space. The two most important steps in the application of the new Homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. In the present paper, convergence of the new approach is proved. Comparison of our solution with the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM) shows that the NHPM is effective and accurate in solving these kind of problems.
17 citations
TL;DR: In this paper, a weakly coupled discrete system of parabolic quasi-variational inequalities (PQVs) is proposed to solve the theta-scheme with respect to the t -variable combined with a finite-element spatial approximation of the evolutionary Hamilton-Jacobi-Bellman equations (HJB equation).
Abstract: This paper is an extension and generalization of the previous results, cf. [2---4]. It is devoted to the theta-scheme with respect to the t -variable combined with a finite-element spatial approximation of the evolutionary Hamilton---Jacobi---Bellman equations (HJB equation) and involves a weakly coupled discrete system of parabolic quasi-variational inequalities (PQVs). Its relation to time energy behavior is proved. In addition, the PQVs are transformed into a coercive discrete system of elliptic quasi-variational inequalities. A new iterative discrete algorithm is also proposed to show the existence and uniqueness of the discrete solution. Moreover, its convergence is established. Then a simple proof to an asymptotic behavior in uniform norm is given. Furthermore the proposed approach is based on a discrete L ? -stability property with respect to the right-hand side and the boundary conditions.
16 citations
TL;DR: In this article, the peristaltic flow of a viscous fluid in a rectangular channel with compliant walls was examined and the reduced linear nonhomogeneous partial differential equations were solved by using the eigenfunction expansion method.
Abstract: In the present article, we have examined the peristaltic flow of a viscous fluid in a rectangular channel with compliant walls. The long wavelength and low Reynolds number approximations are employed to simplify the governing equations. The reduced linear nonhomogeneous partial differential equations are solved by using the eigenfunction expansion method. The physical features of pertinent parameters have been discussed by plotting graphs of velocity for both two-dimensional and three-dimensional cases. The trapping phenomenon is also discussed.
16 citations
TL;DR: A model of the image edge is proposed and a complete solution of the edge width determination problem is obtained and an application of the method to assess the quality of an ophthalmological image is reported.
Abstract: A new method is developed for assessing the image edge width based on the unsharp masking approach. A model of the image edge is proposed and a complete solution of the edge width determination problem is obtained. The accuracy of edge determination is analyzed as a function of the length of segments on which profile information is specified and the noise level. An application of the method to assess the quality of an ophthalmological image is reported.
14 citations
TL;DR: In this paper, the authors apply the game-theoretical approach to examine the optimal organization of hierarchical structures that enforce honest behavior of both the audited agents and the auditors.
Abstract: Controllers and auditors often encounter corruption in organizations, which involves mutually profitable collusion between the audited agent and the auditing inspector. Due to such corrupt collusion, the audited agents avoid the required inspection of their behavior. To enforce the desired behavior of agents and prevent corruption, a hierarchical inspection structure is organized. In the proposed model we apply the game-theoretical approach to examine the optimal organization of hierarchical structures that enforce honest behavior of both the audited agents and the auditors. Inspections are carried out by honest inspectors, who always perform honest audits, and by so-called rational inspectors, who take bribes when they find it advantageous. The inspection superintendent has information on the proportion of honest inspectors at each level of audit and uses this information to reduce the cost of enforcing honest behavior.
11 citations
TL;DR: In this article, an analytic solution of the Klein-Gordon equation is obtained by using a new modification of the homotopy perturbation method (NHPM) and theoretical considerations are discussed.
Abstract: The Klein-Gordon equation is used to model many nonlinear phenomena. In this paper, an analytic solution of the Klein---Gordon equation is obtained by using a new modification of the homotopy perturbation method (NHPM). Theoretical considerations are discussed. The results reveal that the method is explicit, effective, and easy to use.
9 citations
TL;DR: In this paper, the application of the homotopy analysis method (HAM) is presented to obtain analytic solutions of nonlinear systems that often appear in chemical problems and the results show that the HAM is very effective and convenient and the solutions obtained using this method have high accuracy with respect to variational iteration method (VIM) and HPM.
Abstract: In this paper, the application of the homotopy analysis method (HAM) is presented to obtain analytic solutions of nonlinear systems that often appear in chemical problems. Previously, D. D. Ganji et al. in ["Application of He's methods to nonlinear chemistry problems," Comput. Math. Appl., 54 (2007) 1122---1132] used the variational iteration method (VIM) and the homotopy perturbation method (HPM) to obtain a solution of the above problem, but the paper contained some evident mistakes that we could easily identify. The results show that the HAM is very effective and convenient and the solutions obtained using this method have high accuracy with respect to VIM and HPM.
9 citations
TL;DR: In this paper, an electro-magneto-thermo-elastic coupled problem for a homogeneous, isotropic, thermally and electrically conducting two-dimensional half-space solid whose surface is subjected to a thermal shock is considered.
Abstract: The present paper is concerned with an electro-magneto-thermoelastic coupled problem for a homogeneous, isotropic, thermally and electrically conducting two-dimensional half-space solid whose surface is subjected to a thermal shock. The modified Ohm's law, including the temperature gradient and charge density effect, to the equations of the theory of generalized electromagneto-thermo-elasticity under the coupled (CD), Lord-Shulman (LS), and Green-Lindsay (GL) model of generalized thermoelasticity, has been introduced. An initial magnetic field acts parallel to the plane boundary of the half-space. The normal mode analysis together with eigenvalue approach techniques are used to solve the resulting nondimensional coupled equations for the three theories. Numerical results for the temperature, displacements, thermal stress, and induced magnetic field distributions are presented graphically for three cases and discussed.
8 citations
TL;DR: In this paper, the authors investigated the reconstruction of the discontinuity line of a piecewise-constant coefficient in the two-dimensional internal initial-boundary value problem for the one-dimensional heat equation.
Abstract: We investigate the reconstruction of the discontinuity line of a piecewise-constant coefficient in the two-dimension internal initial---boundary value problem for the one-dimensional heat equation. Supplementary data include the direct problem solution, which is known for finitely many boundary points at all times. The results of computer experiments reported in the article show that the inverse problem is well-conditioned in this setting. The direct problem has been reduced to the boundary-value problem for the Helmholtz equation and its solution was expressed in terms of potentials.
7 citations
TL;DR: In this article, the authors dealt with a system of parabolic quasi-variational inequalities related to the management of energy production with mixed boundary condition and established a quasi-optimal L? -error estimate using a new discrete algorithm based on a theta time scheme combined with a finite element spatial approximation.
Abstract: This paper deals with a system of parabolic quasi-variational inequalities related to the management of energy production with mixed boundary condition A quasi-optimal L ? -error estimate is established using a new discrete algorithm based on a theta time scheme combined with a finite element spatial approximation Our approach stands on a discrete L ? -stability property with respect to the right-hand side
6 citations
TL;DR: In this article, a novel technique for numerical solution of the nonlinear differential equations arising in nanotechnology and engineering phenomena is presented, which is based on the application of the Laplace transform via the homotopy method to solve non-linear differential-difference models.
Abstract: A novel technique for numerical solution of the nonlinear differential equations arising in nanotechnology and engineering phenomena is presented in this paper. The technique is based on the application of the Laplace transform via the homotopy method to solve nonlinear differential-difference models. This method gives more reliable results as compared to other existing methods available in the literature. The numerical results demonstrate the validity and applicability of the method.
TL;DR: In this paper, a new approach for the numerical solution of linear and nonlinear reaction-diffusion equations in two spatial dimensions with Bitsadze-Samarskii type nonlocal boundary conditions is proposed.
Abstract: This paper is concerned with the development of a new approach for the numerical solution of linear and nonlinear reaction-diffusion equations in two spatial dimensions with Bitsadze-Samarskii type nonlocal boundary conditions. Proper finite-difference approximations are utilized to discretize the time variable. Then, the weak equations of resultant elliptic type PDEs are constructed on local subdomains. These local weak equations are discretized by using the multiquadric (MQ) radial basis function (RBF) approximation where an iterative procedure is proposed to treat the nonlinear terms in each time step. Numerical test problems are given to verify the accuracy of the obtained numerical approximations and stability of the proposed method versus the parameters of the nonlocal boundary conditions.
TL;DR: In this article, a new compact finite-difference discretization of O(k 2 + k 2 h 2 + h 4) using unequal mesh sizes h > 0 and k > 0 in x-and y-coordinate directions, respectively, for the solution of two-dimensional quasi-linear elliptic partial differential equations subject to the appropriate Dirichlet boundary conditions was proposed.
Abstract: We propose a new compact finite-difference discretization of O(k 2 + k 2 h 2 + h 4) using unequal mesh sizes h > 0 and k > 0 in x- and y- coordinate directions, respectively, for the solution of the system of two-dimensional quasi-linear elliptic partial differential equations subject to the appropriate Dirichlet boundary conditions. We use only three function evaluations in comparison to the five function O(k 2 + k 2 h 2 + h 4) convergence of the proposed finite difference scheme. Some numerical examples are given to illustrate the effectiveness of the proposed methods.
TL;DR: In this article, the steady two-dimensional laminar incompressible electrically conducting viscous fluid on a moving flat plate in the presence of a transverse magnetic field is studied.
Abstract: The steady two-dimensional laminar incompressible electrically conducting viscous fluid on a moving flat plate in the presence of a transverse magnetic field is studied. Taking suitable similarity variables, we transform the governing boundary layer equations into ordinary differential equations and solve them numerically by standard techniques. The effects of moving and magnetic parameters, Prandtl number, and Eckert number on the velocity and temperature as well as on the skin-friction coefficient and Nusselt number are studied.
TL;DR: In this paper, a method for the construction of conservative flow difference schemes that compute compressible viscous gas flows in curvilinear coordinates based on an arbitrary Cartesian Godunov-type scheme is proposed.
Abstract: A method is proposed for the construction of conservative flow difference schemes that compute compressible viscous gas flows in curvilinear coordinates based on an arbitrary Cartesian Godunov-type scheme. The method is designed for easy use in the sense that the implementation of the scheme in curvilinear coordinates requires only minimal additions to the program code of the basic Cartesian scheme. The scheme construction procedure is illustrated for the case of cylindrical coordinates. A cylindrical scheme is constructed to second order approximation in space. Results of test calculations are reported.
TL;DR: In this article, the authors present simulation results for oscillatory modes in supersonic flow past an aircraft with a hypersonic jet engine using a quasi-gas dynamic (QGD) system of equations.
Abstract: We present simulation results for oscillatory modes in supersonic flow past an aircraft with a hypersonic jet engine. The flow of viscous compressible gas is modeled by a quasi-gas dynamic (QGD) system of equations. A coordinate transformation is applied to adapt the computational region to the configuration of the compression shock in supersonic flow past an object. An original method is proposed for the introduction of additional dissipation that smooths the instability in the neighborhood of the compression shock. The spectral characteristics of the oscillatory flow in the turbulence region follow the Kolmogorov law of oscillation energy decrease with increasing oscillation frequency.
TL;DR: In this paper, an iterative method was proposed to find soliton solutions of the two-dimensional Gross-Pitaevskii equation, which can be efficiently implemented on parallel computer systems.
Abstract: The article proposes an iterative method to find soliton solutions of the two-dimensional Gross-Pitaevskii equation. The method also finds soliton solutions of other nonlinear evolution equations. The method can be efficiently implemented on parallel computer systems, producing high-accuracy soliton solutions.
TL;DR: In this article, an iterative method was proposed to find soliton solutions of the Gross-Pitaevskii equation that describes the interaction of a Bose-Einstein condensate with an external potential (a magnetic trap, an obstacle, etc.).
Abstract: The article proposes an iterative method to find soliton solutions of the three-dimensional Gross---Pitaevskii equation that describes the interaction of a Bose---Einstein condensate with an external potential (a magnetic trap, an obstacle, etc.). The method finds both primary and reflected soliton solutions. It can also be applied to find soliton solutions of other nonlinear differential evolution equations. The method can be efficiently implemented on parallel computer systems, producing high-accuracy soliton solutions.
TL;DR: In this paper, the authors consider a linear differential game of N players described by a linear equation and establish a sufficient condition of the general form for the differential game guaranteeing the existence of at least one equilibrium point in Nash's sense.
Abstract: We consider a linear differential game of N players described by a linear equation and establish a sufficient condition of the general form for the differential game guaranteeing the existence of at least one equilibrium point in Nash's sense.
TL;DR: In this article, a new numerical algorithm is proposed for gas-dynamic Euler equations in three spatial dimensions, based on piecewise-linear reconstruction and quasi-acoustic representation of the solution inside a grid cell.
Abstract: A new numerical algorithm is proposed for gas-dynamic Euler equations in three spatial dimensions. The algorithm is based on piecewise-linear reconstruction and quasi-acoustic representation of the solution inside a grid cell. As an application of the numerical scheme, we consider the problem of interaction of gas jets from aircraft engines with a reflecting baffle screen.
TL;DR: In this article, conditions on the parameters under which the optimal control and optimal trajectory can be found explicitly are proposed for a class of affine controlled systems with integral quality functional on infinite time interval.
Abstract: For a class of affine controlled systems with integral quality functional on infinite time interval, we propose conditions on the parameters under which the optimal control and optimal trajectory can be found explicitly. An example of controlled system satisfying all conditions imposed on the parameters is considered.
TL;DR: The article presents the main mathematical methods developed during the design of the BARD software package for multilayer thin film reflectometry and it is shown that the application of these methods broadens the possibilities of analyzing thin-film structure.
Abstract: The article presents the main mathematical methods developed during the design of the BARD software package for multilayer thin film reflectometry. It is shown that the application of these methods broadens the possibilities of analyzing thin-film structure. The mutually complementary algorithms of the BARD package facilitate the development of a unified approach to analysis and simplify the solutionseeking process. The potential of the proposed package is demonstrated with specific examples.
TL;DR: In this article, a mobile method for marine electromagnetic sounding in which the field source and the field detector are both towed above the sea bottom with the objective of discovering hydrocarbon deposits under the seafloor is presented.
Abstract: The article models a mobile method for marine electromagnetic sounding in which the field source and the field detector are both towed above the sea bottom with the objective of discovering hydrocarbon deposits under the sea bottom. The problem of determining the electromagnetic field in a nonhomogeneous medium is solved by the integral equation method. We show that the highest efficiency is achieved in a symmetrical setup with simultaneous field excitation by a horizontal electrical dipole and a vertical magnetic dipole.
TL;DR: The accuracy of drop edge detection is investigated and accuracy-enhancing methods are proposed, in particular, compensation of systematic errors associated with edge blurring and curvature, which improves the accuracy of determination of the drop parameter.
Abstract: We consider the determination of surface tension from the image of the profile of a sessile or pendant drop The accuracy of drop edge detection is investigated and accuracy-enhancing methods are proposed, in particular, compensation of systematic errors associated with edge blurring and curvature The proposed edge detector is virtually free from systematic error and can be used also in other problems A convenient practical method has been developed for calibrating the camera scale with the aid of calibration objects of simple fixed shape, such as a disk or a rectangle The method is based on overlapping the calibration object with the image We also consider the stability of surface tension reconstruction in the presence of outliers, eg, outliers due to the overlapping of the drop contour by a foreign object An iterative algorithm is proposed for automatic outlier exclusion, which improves the accuracy of determination of the drop parameter
TL;DR: A numerical method for the solution of the problem of speed action with phase restrictions for the model of jumping one-legged robot and sufficient conditions for the convergence of the algorithm as well as the results of numerical simulations are presented.
Abstract: We propose a numerical method for the solution of the problem of speed action with phase restrictions for the model of jumping one-legged robot and present sufficient conditions for the convergence of the algorithm as well as the results of numerical simulations.
Journal Article•
TL;DR: In this article, the authors prove the existence and construct the form of the asymptotic solution for an initial-boundary value problem that describes diffusive filling of thin shells with a real gas.
Abstract: We prove the existence and construct the form of the asymptotic solution for an initial---boundary value problem that describes diffusive filling of thin shells with a real gas. Such problems arise in the manufacturing of laser targets, where a thin spherical shell is filled with hydrogen isotopes to a high pressure [1---3]. In this article we apply the methods of [4], but the nonlinearity of the boundary conditions requires new approaches to the problem.
TL;DR: In this paper, the authors considered the problem of optimal control of the maximization of income for the nonlinear mathematical model of microeconomical system used for the description of production, storage, and selling of consumer goods.
Abstract: We consider the problem of optimal control of the maximization of income for the nonlinear mathematical model of microeconomical system used for the description of production, storage, and selling of consumer goods.
For this model, we formulate the boundary-value problem of the maximum principle giving the necessary conditions of optimality. We consider conditions for the parameters characterizing the original system under which the solution of the boundary-value problem of maximum principle possesses a section of singular mode. It is shown that this section of singular mode neighbors with nonsingular sections containing containing infinitely many switchings on finite periods of time.
For the investigation of this phenomenon, we use the theory developed by M. Zelikin and V. Borisov. It is shown that the solution of the boundary-value problem of maximum principle is locally optimal in the analyzed problem of optimal control. Hence, the corresponding optimal trajectory has three sections. The first part is a nonsingular section in which the original system with infinitely many switchings passes to the singular section for a finite period of time. The second part is the section of singular mode and the last (third) part is a section of the trajectory in which the analyzed system leaves the singular mode with more and more frequent switchings in the inverse time.
TL;DR: In this paper, a numerical method of determining a localized initial excitation for cardiac excitation mathematical models is proposed. But the method is not suitable for the case of the heart.
Abstract: We consider a numerical method of determining a localized initial excitation for cardiac excitation mathematical models. In the direct problem we model the variation of fields in the region corresponding to a heart section. The variation of the potential is described by the Aliev---Panfilov model for regions from R 2. The inverse problem involves determining the coordinates of a localized initial excitation in the heart from potential values at several point on the inner boundary of the ventricles. Results of computer experiments are reported.
TL;DR: The stability of the output parameters of the model under variations in key variables is analyzed and the concepts of global and comparative sensitivity are introduced.
Abstract: The interdisciplinary optimization model MERGE is widely used for studying climate change problems. MERGE is intended primarily for quantitative assessment of the results achieved by various natureconservation strategies. In this article, we analyze the stability of the output parameters of the model under variations in key variables and introduce the concepts of global and comparative sensitivity.