Organizational Design of Post Corporation Structure Using Fuzzy Multicriteria Decision Making

A model for organizational design of post corporation structure is developed in this paper. Alternative organization solutions have been designed taking into account the post environment characterized by private operators' competition and development of new message transmission technologies. Criteria for organizational design have been considered as numerical and uncertain linguistic variables describes by fuzzy sets. The model has been tested on a numerical example.     

SUPERCONVERGENCE AND NONSUPERCONVERGENCE OF THE SHORTLEY-WELLER APPROXIMATIONS FOR DIRICHLET PROBLEMS

We are concerned with the numerical solutions of Dirichlet problems of elliptic equations. The convergence behavior of numerical solutions by using Shortley-Weller approximation is considered. We give three examples and prove that they have properties of nonsuperconvergence near any boundary point, superconvergence near a side and superconvergence near a corner, respectively.     

Regularized state-constrained boundary optimal control of the Navier-Stokes equations

The numerical solution of the Dirichlet boundary optimal control problem of the Navier-Stokes equations in presence of pointwise state constraints is investigated. Two different regularization techniques are considered. First, a Moreau-Yosida regularization of the problem is studied. Optimality conditions are derived and the convergence of the regularized solutions towards the original one is proved. A source representation of the control combined with a Lavrentiev type regularization strategy is also presented. The analysis concerning optimality conditions and convergence of the regularized solutions is carried out. In the last part of the paper numerical experiments are presented. For the numerical solution of each regularized problem a semi-smooth Newton method is applied.     

Convergence of numerical solutions to stochastic age-dependent population equations with Markovian switching

In this paper, a class of stochastic age-dependent population equations with Markovian switching is considered. The main aim of this paper is to investigate the convergence of the numerical approximation of stochastic age-dependent population equations with Markovian switching. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions. An example is given for illustration.     

Case of a Boltzmann gas leading to the Smoluchowski coagulation equation

A special model of a rarefied hard-sphere gas is considered. The hard-sphere particles undergo absolutely elastic collisions. It is assumed that particles can collide only if their nonzero velocities are orthogonal to each other. The model makes it possible to proceed from the Boltzmann equation to the Smoluchowski coagulation equation, where coagulation means that the kinetic energies of the colliding particles are added. A Monte Carlo scheme for simulation of the phenomenon is described, and the convergence of the simulation algorithm is proved. The convergence of numerical results to exact solutions of the Smoluchowski equation and to finite-difference solutions is tested.     

Numerical analysis for stochastic age-dependent population equations with Poisson jumps

In this paper, stochastic age-dependent population equations with Poisson jumps are considered. In general, most of stochastic age-dependent population equations with jumps do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical Euler scheme and show the convergence of the numerical approximation solution to the true solution.     

Bifurcations in a diffusive predator–prey model with predator saturation and competition response

A diffusive predator–prey model with predator saturation and competition response subject to homogeneous Neumann boundary conditions is considered in this paper. We find that the spatially homogeneous and non‐homogeneous periodic solutions through all parameters of the system are spatially homogeneous. To verify our theoretical results, some numerical simulations are also carried out. Copyright © 2014 John Wiley & Sons, Ltd.     

A new consistent discrete‐velocity model for the Boltzmann equation

This paper discusses the convergence of a new discrete‐velocity model to the Boltzmann equation. First the consistency of the collision integral approximation is proved. Based on this we prove the convergence of solutions for a modified model to renormalized solutions of the Boltzmann equation. In a numerical example, the solutions to the discrete problems are compared with the exact solution of the Boltzmann equation in the space‐homogeneous case. Copyright © 2002 John Wiley & Sons, Ltd.     

Finite difference discretization of the Rosenau-RLW equation

In this paper, numerical solutions of the Rosenau-RLW equation are considered using Crank–Nicolson type finite difference method. Existence of the numerical solutions is derived by Brouwer fixed point theorem. A priori bound and the error estimates as well as conservation of discrete mass and discrete energy for the finite difference solutions are discussed. Unconditional stability, second-order convergence and uniqueness of the scheme are proved using discrete energy method. Some numerical experiments have been conducted in order to verify the theoretical results.     

On constructing generally periodic solutions of a complicated structure of a non-autonomous system of differential equations

In this paper, a numerical scheme of constructing approximate generally periodical solutions of a complicated structure of a non-autonomous system of ordinary differential equations with periodical right-hand sides on the surface of a torus is considered. The existence of such solutions, as well as convergence of the method of successive approximations, is demonstrated. Results of a computational experiment are presented.     

Superconvergence of finite difference approximations for convection–diffusion problems

An Erratum has been published for this article in Numerical Linear Algebra with Applications 8 (4) 2001, iii–iv. We are concerned with numerical solutions of convection–diffusion equations. The convergence behaviour of numerical solutions is considered by using the finite difference approximation with respect to spatial variables and implicit method with respect to time variable. It is shown that superconvergence occurs near a part of the boundary which has Dirichlet's data. Copyright © 2001 John Wiley & Sons, Ltd.     

Global boundedness of the solutions to a Gurtin-MacCamy system

This paper is concerned with the analysis of a generalized Gurtin-MacCamy model describing the evolution of an age-structured population. The problem of global boundedness is studied. Namely we ask whether there are simple general assumptions that one can make on the vital rates in order to have boundedness of the solution. Next a fully implicit finite difference scheme along the characteristic is considered to approximate the solution of the system. Global boundedness of the numerical solutions is investigated. The optimal rate of convergence of the scheme is obtained in the maximum norm. Numerical examples are presented.     

Stability and convergence of difference schemes for boundary value problems for the fractional-order diffusion equation

A family of difference schemes for the fractional-order diffusion equation with variable coefficients is considered. By the method of energetic inequalities, a priori estimates are obtained for solutions of finite-difference problems, which imply the stability and convergence of the difference schemes considered. The validity of the results is confirmed by numerical calculations for test examples.     

Interface problem in holonomic elastoplasticity

The three-dimensional interface problem with the homogeneous Lamé system in an unbounded exterior domain and holonomic material behaviour in a bounded interior Lipschitz domain is considered. Existence and uniqueness of solutions of the interface problem are obtained rewriting the exterior problem in terms of boundary integral operators following the symmetric coupling procedure. The numerical approximation of the solutions consists in coupling of the boundary element method (BEM) and the finite element method (FEM). A Céa-like error estimate is presented for the discrete solutions of the numerical procedure proving its convergence.     

Finite Element Approximation of Eigenvalue Problem for a Coupled Vibration Between Acoustic Field and Plate

1.IntroductionInthispaper,westudyanumericalmethodtocalculateeigen-frequenciesofacoupledvibrationbetweenacousticfieldandplate.Atypicalapplicationofthisresearchistoreduceanoiseinsideacarcausedbyanengineorothersourcesofthesound.OurstudywasmotivatedbytheworkofHagiwaraetal.15].Thebackgroundoftheresearchandsomeapplicationscanbeseenin[5].Werestrictourresearchtotheproblemswhereexactsolutionscanbegiveninaspecialcase.Themainfeatureofourresearchisthemathematicallyrigorousapproachtotheproblem.Weformulat…     

Study on autonomous and nonautonomous version of a food chain model with intraspecific competition in top predator

In this article, a three-species food chain model with intraspecific competition in top predators has been considered. Ecological and mathematical well posedness of the model system has been established by showing that all the solutions of the model are positive and bounded. The extinction scenarios of intermediate and top predator species along with the existence and stability of all equilibrium points have been discussed. The effects of competition and conversion efficiency of top predators in the dynamics of the system have been discussed with great thrust, and it is observed that the conversion efficiency of top predators deteriorates the stability of the system, whereas intraspecific competition in top predators enhances the stable coexistence of all the populations of the system. Further, nonautonomous version of the model system has been taken into consideration to study the impact of seasonal variation in the dynamics of the model system. Sufficient conditions for the existence of a globally attractive positive periodic have been established in a periodic environment. Finally, numerical simulations have been carried out to validate our analytical findings.     

Variational inequalities of multilayer viscoelastic systems with interlayer Tresca friction: Existence and uniqueness of solution and convergence of numerical solution

The mathematical model of multilayer viscoelastic system based on the actual structure of asphalt pavement and the properties of its numerical solutions are studied. Firstly, based on the partial differential equations, the variational inequality model of the multilayer viscoelastic system is derived, and the existence and uniqueness of its solutions are further proved. Then, based on the finite element theory, the convergence property and error analysis of the semi-discrete numerical solutions of the variational inequalities are further studied. Finally, the convergence and error analysis of the fully discrete numerical solutions of the variational inequalities are derived by the forward difference method. The conclusion of the above error analysis also confirms the feasibility of studying the mechanical response of asphalt pavement based on variational inequality.     

Numerical solution of some classes of integral equations using Bernstein polynomials

This paper is concerned with obtaining approximate numerical solutions of some classes of integral equations by using Bernstein polynomials as basis. The integral equations considered are Fredholm integral equations of second kind, a simple hypersingular integral equation and a hypersingular integral equation of second kind. The method is explained with illustrative examples. Also, the convergence of the method is established rigorously for each class of integral equations considered here.     

On the solution of a Schrödinger type equation by a projection-difference method with an implicit Euler scheme with respect to time

A linear nonstationary Schrödinger type problem in a separable Hilbert space is approximately solved by a projection-difference method. The problem is discretized in space by the Galerkin method using finite-dimensional subspaces of finite-element type, and an implicit Euler scheme is used with respect to time. We establish error estimates uniform with respect to the time grid for the approximate solutions; as to the spatial variables, the estimates are given in the norm of the original space as well as in the energy norm. The estimates considered here not only permit one to prove the convergence of approximate solutions to the exact solution but also give a numerical characterization of the convergence rate.     

Dynamically-consistent non-standard finite difference method for an epidemic model

This paper considers the problem of constructing finite-difference methods that are qualitatively consistent with the original continuous-time model they approximate. To achieve this goal, a deterministic continuous-time model for the transmission dynamics of two strains of an arbitrary disease, in the presence of an imperfect vaccine, is considered. The model is rigorously analysed, first of all, to gain insights into its dynamical features. The analysis reveal that it undergoes a vaccine-induced backward bifurcation when the associated reproduction threshold is less than unity. For the case where the vaccine is 100% effective, the disease-free equilibrium of the model is shown to be globally-asymptotically stable if the reproduction number is less than unity. The model also exhibits the phenomenon of competitive exclusion, where the strain with the higher reproduction number dominates (and drives out) the other. Two finite-difference methods are presented for numerically solving the model. The central objective is to determine which of the two methods gives solutions that are dynamically consistent with those of the continuous-time model. The first method, an implicitly-derived explicit finite-difference method, is considered for its computational simplicity, being a Gauss–Seidel-like algorithm. However, this method is shown to suffer numerous scheme-dependent numerical instabilities and spurious behaviour (such as convergence to the wrong steady-state solutions and failing to preserve many of the main essential dynamical features of the model), particularly when relatively large step-sizes are used in the simulations. On the other hand, the second numerical method, constructed based on Mickens’ non-standard finite-difference discretization framework, is shown to be free of any numerical instabilities and contrived behaviour regardless of the size of the step-size used in the numerical simulations. In other words, unlike the first method, the non-standard method is shown to be dynamically consistent with the original continuous-time model, and, therefore, it is more suited for use to study the asymptotic dynamics of the disease transmission model being considered.