numerical investigation on the stability of singular driven cavity flow by applying the singularity subtraction technique to the unsteady driven cavity problem the stability of the impulsively started flow is investigated without smoothing the corner singularity a second order spectral projection method allows localization of the critical reynolds number for the first hopf bifurcation in the interval 8017 6 8018 8

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

accurate three dimensional lid driven cavity flow a chebyshev collocation method in space is introduced which allows an accurate calculation of three dimensional lid driven cavity flows the time integration is carried out by an adams bashforth backward euler scheme the accuracy of the method relies on the representation of the solution as a superposition of stationary local asymptotic solutions and a residual flow field this way the most severe discontinuities in the boundary conditions which arise along the lines where moving and stationary walls meet are taken care of analytically and thus do not spoil the numerical part of the solution calculations are carried out for no slip boundary conditions at the cavity end walls as well as for periodic end wall conditions in general the spatial accuracy is better than fifth order for rigid end wall conditions the accuracy is reduced near the end walls to o n 3 2 but recovers in the bulk tabulated data are provided for the most interesting flow properties

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

on the periodicity of non homogeneous markov chains and systems abstract we firstly recall the concept of an nhms and introduce concepts and known results necessary for the study of asymptotic periodicity of the vector of expectations variances and covariances of the state sizes this sequence of vectors is called the variability of population structures we then proceed to prove some useful propositions and lemmas for the establishment of the basic results that follow note that some of these lemmas have a power and usefulness of their own finally we provide two theorems where we study the asymptotic periodicity of the variability of population structures when the inherent non homogeneous markov chain is uniquely determined by a sequence of arbitrary stochastic matrices all with the same incidence matrix following that an illustrative example from the area of manpower systems is provided in this example the results in the basic theorems of the previous section are illustrated numerically we conclude with an appendix where we firstly introduce the necessary concepts and known results needed in order to study the periodicity and asymptotic periodicity of an infinite product of finite arbitrary stochastic matrices we then proceed to study the periodicity and asymptotic periodicity of non homogeneous markov chains in their full possible generality it is very important to note that similar results hold also for an infinite product of non negative matrices

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

uniform boundedness and stability criteria in terms of two measures for impulsive integro differential equations1research supported by nserc canada 1 this paper establishes several criteria on uniform boundedness and stability in terms of two measures for impulsive integro differential equations by the method of lyapunov functions the interplay of two different measures and the discontinuities of solutions create additional difficulties in choosing suitable minimal set of functions along which the derivative of the lyapunov function is estimated consequently very complicated analysis is required in the proof of the theorems

a high order compact scheme for the pure streamfunction vector potential formulation of the 3d steady incompressible navier stokes equations abstract in this paper a high order compact finite difference algorithm is proposed for the pure streamfunction vector potential formulation of the three dimensional steady incompressible navier stokes equations in which the grid values of the streamfunction vector potential its first order and second order derivatives are carried as the unknown variables the numerical boundary schemes are also established for a general set of flow problems with no normal speed on the boundaries numerical examples including a test problem with an analytical solution and three types of lid driven cubic cavity flow problems are solved numerically by the newly proposed scheme the results obtained prove that the present numerical method has the ability to solve the three dimensional incompressible flow with high accuracy

a multi dimensional high order discontinuous galerkin method based on gas kinetic theory for viscous flow computations this paper presents a high order discontinuous galerkin dg method based on a multi dimensional gas kinetic evolution model for viscous flow computations generally the dg methods for equations with higher order derivatives must transform the equations into a first order system in order to avoid the so called non conforming problem in the traditional dg framework the inviscid and viscous fluxes are numerically treated differently differently from the traditional dg approaches the current method adopts a kinetic evolution model for both inviscid and viscous flux evaluations uniformly by using a multi dimensional gas kinetic formulation we can obtain a spatial and temporal dependent gas distribution function for the flux integration inside the cell and at the cell interface which is distinguishable from the gaussian quadrature point flux evaluation in the traditional dg method besides the initial higher order non equilibrium states inside each control volume a linear least square lls method is used for the reconstruction of smooth distributions of macroscopic flow variables around each cell interface in order to construct the corresponding equilibrium state instead of separating the space and time integrations and using the multistage runge kutta time stepping method for time accuracy the current method integrates the flux function in space and time analytically which subsequently saves the computational time many test cases in two and three dimensions which include high mach number compressible viscous and heat conducting flows and the low speed high reynolds number laminar flows are presented to demonstrate the performance of the current scheme

algebraic approximation of sub grid scales for the variational multiscale modeling of transport problems abstract variational multiscale vms finite element methods fems are robust for the development of general formulations for the solution of multiphysics and multiscale transport problems to obtain a tractable and computationally efficient model vms methods often rely on a residual based algebraic approximation of the sub grid scales small or unresolved features of the solution field not captured by the discretization using a so called intrinsic time scales matrix which depends on the problem s overall differential operator and represents the main model parameter a novel technique for approximating the intrinsic time scales matrix for generic transport problems in a relatively inexpensive manner e g does not rely on eigenvalue computations is presented the method is denoted transport equivalent scaling tes and is based on the monolithic casting of the transport problem as a system of transient advective diffusive reactive tadr equations and a subsequent scaling of the coefficient matrices such to preserve each type of transport flux an algebraic vms formulation incorporating the tes method is complemented with a discontinuity capturing dc approach and implemented within a fem solver for the solution of tadr problems the solution of the global discrete system is accomplished using a generalized alpha time stepper together with a globalized inexact newton krylov nonlinear solver the effectiveness of the tes formulation is verified with the simulation of benchmark incompressible compressible and magnetohydrodynamic flow problems the results demonstrate that the tes method seamlessly handles incompressible compressible flows in a unified manner e g without assessing the compressibility of the flow the convergence process using the tes approach and a more standard approximation for the intrinsic time scales as well as the effect of the dc approach are also investigated analysis of the intrinsic time scales for a one dimensional incompressible flow model reveals the similitudes and differences between the tes formulation and other conventional methods

asymptotic behavior of nonhomogeneous semi markov systems abstract we study the asymptotic behavior of a nonhomogeneous semi markov system population in discrete time after a series of definitions lemmas and theorems we firstly establish the conditions under which the ergodic behavior of a nonhomogeneous semi markov chain exists and then find the limit of the basic matrix of the chain q n s in closed form finally the existence of the asymptotic population structure of the nonhomogeneous semi markov system is studied and the limit is provided in closed analytic form

stochastic equilibria in nonhomogeneous markov population replacement processes this paper is an exposition on the dynamic stochastic equilibria in multi type time dependent markov population processes for different types of environmental behaviour the joint multivariate cumulant generating function of the various population sizes at any time is derived together with the covariance structure both with and without time lags an asymptotic analysis shows that there are either one or several equilibria of dynamic character depending critically on the behaviour of the system parameters as well as on the total population size the possible stochastic equilibria are characterized as stable or unstable according to whether or not they are independent of initial conditions

the behavior of solutions of linear integro differential equations with unbounded delay abstract a basic theorem on the behavior of solutions of scalar linear integro differential equations with unbounded delay is established as a consequence of this theorem a stability criterion is obtained

nonstationary cyclic behavior in markov systems abstract we introduce the concept of the nonstationary cyclic markov system as a natural extension of the cyclic systems found in recent literature we find the sets of d cyclic asymptotically attainable structures and establish the relationships that exist between these structures for a nonhomogeneous markov system in a deterministic or stochastic environment the inherent connection between nonstationary cyclicity and stochastic environment is examined also we investigate the conditions under which there exists a geometric convergence to the equilibrium

a new approach to stability of impulsive functional differential equations in this work a new approach to stability theory of impulsive functional differential equations is proposed instead of putting all components of the state variable x in one liapunov function several functions of partial components of x which can be much easier constructed are used so that the conditions ensuring that stability are simpler and less restrictive also an example is given to illustrate the advantages of the obtained results

a pressure correction scheme for convection dominated incompressible flows with discontinuous velocity and continuous pressure in this work we present a pressure correction scheme for the incompressible navier stokes equations combining a discontinuous galerkin approximation for the velocity and a standard continuous galerkin approximation for the pressure the main interest of pressure correction algorithms is the reduced computational cost compared to monolithic strategies in this work we show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high reynolds regimes the proposed spatial velocity pressure approximation is lbb stable for equal polynomial orders and it allows adaptive p refinement for velocity and global p refinement for pressure the method is validated against a large set of classical two and three dimensional test cases covering a wide range of reynolds numbers in which it proves effective both in terms of accuracy and computational cost

the treatment of spurious pressure modes in spectral incompressible flow calculations algorithms for the transient and steady state simulation of incompressible newtonian and non newtonian flows are described for the primitive variable formulation of the governing equations spectral approximations are used for the spatial discretization attention is given to the satisfaction of the incompressibility constraint and the determination of the pressure spurious pressure modes are removed by means of a singular value decomposition the corresponding velocity field is divergence free at all the collocation points numerical results are presented for newtonian flow in a regularized driven square cavity and for non newtonian flow in a planar channel and in a journal bearing for a realistic range of material parameters

global exponential stability of impulsive integro differential equation abstract in this paper an impulsive integro differential equation is considered by establishing an integro differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive integro differential equation are obtained the results extend and improve the earlier publications an example is given to demonstrate the effectiveness of the theory

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

driven cavity flows by efficient numerical techniques abstract efficient and reliable numerical techniques of high order accuracy are presented for solving problems of steady viscous incompressible flow in the plane and are used to obtain accurate solutions for the driven cavity a solution is obtained at reynolds number 10 000 on a 180 180 grid the numerical methods combine an efficient linear system solver an adaptive newton like method for nonlinear systems and a continuation procedure for following a branch of solutions over a range of reynolds numbers

an element by element bicgstab iterative method for three dimensional steady navier stokes equations construction of a stabilized galerkin upwind finite element model for steady and incompressible navier stokes equations in three dimensions is the main theme of this study in the time independent context the weighted residuals statement is kept biased in favor of the upstream flow direction by adding an artificial damping term of physical plausibility to the galerkin framework this upwind approach has significant advantage of seeking solutions free from cross stream diffusion error finite element solutions have been found by mixed formulation implemented in quadratic cubic elements which are characterized as possessing the so called lbb ladyzhenskaya babuska brezzi condition an element by element bicgstab solution solver is intended to alleviate difficulties regarding the asymmetry and indefiniteness arising from the use of a mixed formulation for incompressible fluid flows the developed three dimensional finite element code is first rectified by solving a problem amenable to analytic solution a well known lid driven cavity flow problem in a cubical cavity is also studied

semi markov migration process in a stochastic market in credit risk abstract in the present the idea of stochastic market environment comes into play to express the changes in general economy which affects any industry in small or great amounts of turbulence we model the evolution of the market among its possible states as an f inhomogeneous semi markov process this idea leads us to modeling the migration process of defaultable bonds as different f inhomogeneous semi markov process the survival probabilities of a defaultable bond in every credit grade are found the asymptotic behaviour of the survival probabilities is established under certain conditions also it is proved under what conditions the convergence is geometrically fast the stochastic foundation of the general stochastic discrete time market is provided by proving that the market is viable if and only if there exists an equivalent martingale measure from which we construct the forward probability measure and under which the discounted default free bond price process for all possible states of the market is a martingale the term structure of credit spread and the change of real world probability measure to forward probability measure are studied in the form of a theorem it is proved that under certain conditions changing the real probability measure to a forward probability measure does not affect the inhomogeneous semi markov process modeling the migration of defaultable bonds that is it is proved that it only changes the basic parameters and we provide a relation among the transition probabilities under the two measures finally parameter estimation and calibration of the inhomogeneous semi markov chain in stochastic environment is being provided

fuzzy semi markov migration process in credit risk we explore the rating system used by credit agencies with a focus on problems that justify the use of fuzzy set theory we prove that a fuzzy market is viable if and only if an equivalent martingale measure exists from which we construct the forward probability measure and under which the discounted price of a default free bond is a martingale we model the evolution of credit migration of a defaultable bond as an inhomogeneous semi markov process with fuzzy states we study the effects of changing the real probability measure to a forward probability measure in addition we investigate the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default finally we discuss parameter estimation and calibration of the inhomogeneous markov chain with fuzzy states

an alternative lattice boltzmann model for three dimensional incompressible flow abstract in this work an alternative lattice boltzmann lb model for three dimensional 3d incompressible flow is proposed the equilibrium distribution function edf of the present model is directly derived in accordance with the incompressibility conditions by applying the hermite expansion moreover an alternative formula for pressure computation is designed from the second order moment of the distribution function the present 3d lb model inherits the advantageous features of guo s lb model the density is a constant the fluid pressure is independent of density and the navier stokes n s equations for incompressible flow can be derived two benchmark tests flow over a backward facing step and the lid driven cavity flow are applied to validate the present model accurate results for these tests are obtained with the present model and further comparisons with the previous lb models the standard lb model the he luo model and guo s lb model demonstrate that the present model provides better accuracy in the region of high deviatoric stress and such advantage is further enhanced by using the d3q27 lattice

semi implicit discontinuous galerkin methods for the incompressible navier stokes equations on adaptive staggered cartesian grids in this paper a new high order semi implicit discontinuous galerkin method si dg is presented for the solution of the incompressible navier stokes equations on staggered space time adaptive cartesian grids amr in two and three space dimensions the pressure is written in the form of piecewise polynomials on the main grid which is dynamically adapted within a cell by cell amr framework according to the time dependent main grid different face based spatially staggered dual grids are defined for the piece wise polynomials of the respective velocity components although the resulting adaptive staggered grids are more complex than classical uniform cartesian meshes the numerical scheme can still be written in a rather compact form thanks to the use of a tensor product formulation for the definition of the nodal basis in the d dimensional space d 2 3 all the discrete operators can be efficiently written as a combination of linear one dimensional operators acting in the d space directions separately arbitrary high order of accuracy is achieved in space while a very simple semi implicit time discretization is obtained via an explicit discretization of the nonlinear convective terms and an implicit discretization of the pressure gradient in the momentum equation and of the divergence of the velocity field in the continuity equation the real advantages of the staggered grid arise in the solution of the schur complement associated with the saddle point problem of the discretized incompressible navier stokes equations i e after substituting the discrete momentum equations into the discrete continuity equation this leads to a linear system for only one unknown the scalar pressure indeed the resulting linear pressure system is shown to be symmetric and positive definite in order to avoid a quadratic stability condition for the parabolic terms given by the viscous stress tensor an implicit discretization is also used for the diffusive terms in the momentum equation a particular feature of our staggered dg approach is that the viscous stress tensor is discretized on the dual mesh this corresponds to the use of a lifting operator but on the staggered grid both linear systems for pressure and velocity are very efficiently solved by means of a classical matrix free conjugate gradient method for which fast convergence is observed moreover it should be noticed that all test cases shown in this paper have been performed without the use of any preconditioner due to the explicit discretization of the nonlinear convective terms the final algorithm is stable within the classical cfl type time step restriction for explicit dg methods based on the fluid velocity moreover by using a suitable local time stepping technique based on the ader dg framework each element can use its optimal local time step also within the amr context the new space time adaptive staggered dg scheme has been thoroughly verified for polynomial degrees up to n 9 for a large set of non trivial test problems in two and three space dimensions for which analytical numerical or experimental reference solutions exist the high order of accuracy of the scheme is shown by means of a numerical convergence table obtained by comparing the numerical solution against a smooth analytical solution to the knowledge of the authors this is the first staggered semi implicit dg scheme for the incompressible navier stokes equations on space time adaptive meshes in two and three space dimensions

periodicity of asymptotically attainable structures in nonhomogeneous markov systems we find the sets of d periodic asymptotically attainable structures and we establish the periodicities that exist between these structures for a nonhomogeneous markov system in the case where the imbedded nonhomogeneous markov chain is periodic with period d also it is proved that under certain conditions each converging subsequence of the sequence of relative structures has a geometric rate of convergence

asymptotic variability of nonhomogeneous markov systems under cyclic behaviour abstract in this paper the asymptotic variability of nonhomogeneous markov systems under cyclic behaviour is studied it is found that the sequence of vectors of means variances and covariances splits into d subsequences which converge where d is the period of the cyclic finally an illustration of the present results with data from a manpower system is given

chebyshev 3 d spectral and 2 d pseudospectral solvers for the helmholtz equation two chebyshev solvers are presented for the linear helmholtz equation the first algorithm is a 3 d direct spectral solver based on a diagonalization technique whilst the second performs an iterative pseudospectral 2 d calculation with finite difference preconditioning both techniques handle general nonhomogeneous boundary conditions computing times and accuracies of the two methods are compared

existence and stability of almost periodic solutions for quasilinear delay systems and the halanay inequality abstract we present some easily verifiable conditions for the existence and global asymptotical stability of almost periodic solutions to systems of delay differential equations in the form u t au t wg t ut f t where a w l r n and f t g t are almost periodic in t uniformly on from bounded subsets of c h 0 r n with this purpose we use the exponential dichotomy theory together with usual positivity arguments in particular the semigroup version of the so called perron frobenius theorem is applied to study the generalized halanay inequality finally systems with maxima are studied in detail

accurate ω ψ spectral solution of the singular driven cavity problem this article provides accurate spectral solutions of the driven cavity problem calculated in the vorticity stream function representation without smoothing the corner singularities a prima facie impossible task as in a recent benchmark spectral calculation by primitive variables of botella and peyret closed form contributions of the singular solution for both zero and finite reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form the method employed is based on a split approach to the vorticity and stream function equations a galerkin legendre approximation of the problem for the perturbation and an evaluation of the nonlinear terms by gauss legendre numerical integration results computed for re 0 100 and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation chebyshev projection method the validity of the proposed singularity subtraction scheme for computing time dependent solutions is also established

variable resolution for sph in three dimensions towards optimal splitting and coalescing for dynamic adaptivity abstract as smoothed particle hydrodynamics sph becomes increasingly popular for complex flow analysis the need to improve efficiency particularly for 3 d problems is becoming greater automatic adaptivity with variable particle size is therefore desirable in this paper a novel 3 d splitting and coalescing algorithm is developed which minimizes density error while conserving both mass and momentum using a variational principle accuracy is increased in refined areas unaffected by coarser particle distributions elsewhere for particle splitting the key criteria are the number of split daughter particles their distribution spacing and kernel size four different splitting arrangements are investigated including a cubic stencil with 8 particles a cubic stencil with an additional 6 located at the face centres an icosahedron shaped arrangement with 14 particles and a dodecahedron shaped arrangement with 20 particles where particles are located at the vertices the error analysis also examines whether retaining a particle at the centre of the arrangement is necessary revealing that regardless of the stencil adopted to minimize the density error a daughter particle should be placed at the same position of the original particle the optimum configuration is found to be the icosahedron shaped arrangement while commonly used smoothing kernels such as the cubic and quintic splines and wendland produce similar density errors so that the optimal refinement stencil is effectively independent of the kernel choice a new 3 d coalescing scheme completes the algorithm such that the particle resolution can be either increased or reduced locally the sph splitting and coalescing scheme is tested with poiseuille flow showing negligible loss of convergence accuracy in the refined area and the lid driven cavity for a wide range of reynolds number showing good agreement with reference solutions again with local accuracy defined by particle distribution

hopf bifurcation of the unsteady regularized driven cavity flow abstract a numerical simulation of the unsteady incompressible flow in the unit cavity is performed by using a chebyshev tau approximation for the space variables the high accuracy of the spectral methods and the condensed distribution of the chebyshev collocation points near the boundary enable us to obtain reliable results for high reynolds numbers with a moderate number of modes it is found that the flow converges to a stationary state for reynolds numbers re up to 10 000 for reynolds numbers larger than a critical value 10 000

a hybrid high order method for the incompressible navier stokes equations based on temam s device abstract in this work we propose a novel hybrid high order method for the incompressible navier stokes equations based on a formulation of the convective term including temam s device for stability the proposed method has several advantageous features it supports arbitrary approximation orders on general meshes including polyhedral elements and non matching interfaces it is inf sup stable it is locally conservative it supports both the weak and strong enforcement of velocity boundary conditions it is amenable to efficient computer implementations where a large subset of the unknowns is eliminated by solving local problems inside each element particular care is devoted to the design of the convective trilinear form which mimicks at the discrete level the non dissipation property of the continuous one the possibility to add a convective stabilisation term is also contemplated and a formulation covering various classical options is discussed the proposed method is theoretically analysed and an energy error estimate in h k 1 with h denoting the meshsize is proved under the usual data smallness assumption a thorough numerical validation on two and three dimensional test cases is provided both to confirm the theoretical convergence rates and to assess the method in more physical configurations including in particular the well known two and three dimensional lid driven cavity problems

splitting techniques for the unsteady stokes equations a pseudospectral or collocation approximation of the unsteady stokes equations is presented using the uzawa algorithm the spectral system is decoupled into helmholtz equations for the velocity components and an equation with the pseudo laplacian for the pressure both the velocity components and the pressure are approximated by polynomials of the same degree n compatible velocity and pressure approximations are constructed to ensure that the discrete problem is well posed the resulting discrete velocity field is identically divergence free only one grid no staggered grids with the standard chebyshev gauss lobatto nodes is used here we further compare our treatment with an inhomogeneous neumann condition for the pressure this scheme was proposed in g karniadakis m israeli and s a orszag j comp phys 97 1991 pp 414 443 the comparison shows that the neumann condition yields somewhat better approximations for the pressure in the time discretization a high order backward differentiation scheme for the intermediate velocity is combined with a high order extrapolant for the pressure it is numerically shown that a stable third order method in time can be achieved in the case of periodic boundary conditions this result is confirmed by fourier analysis

exponential stability of nonlinear impulsive neutral differential equations with delays abstract in this article a nonlinear impulsive neutral differential equation with time varying delays is considered by establishing a singular impulsive delay differential inequality and transforming the n dimensional impulsive neutral delay differential equation to a 2 n dimensional singular impulsive delay differential equation some sufficient conditions ensuring the global exponential stability in pc 1 of the zero solution of an impulsive neutral differential equation are obtained the results extend and improve on earlier publications an example is given to illustrate the theory

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

a pseudospectral method for solution of the three dimensional incompressible navier stokes equations abstract a new chebyshev pseudospectral technique based on the projection method that was previously applied by the authors to the solution of two dimensional incompressible navier stokes equations in primitive variables for nonperiodic boundary conditions is extended to solve the three dimensional navier stokes equations the crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain on the boundaries as well as in the interior the key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition the method was tested on a two dimensional driven cavity flow and the results were compared with those of the most accurate finite difference calculation the three dimensional driven cavity flow was then calculated at the same reynolds numbers as the two dimensional cases i e re 100 400 and 1000 in the calculated results three dimensional boundary effects were observed in all cases and became more apparent with increasing reynolds number

stability results for impulsive functional differential equations with infinite delays abstract this paper studies the stability problems for a class of impulsive functional differential equations with infinite delays of the form x t f t x t t x t k j k x t k k 1 2 by using the liapunov functions and razumikhin technique some new razumikhin type theorems on stability are obtained

solution of high reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing the objective of this paper is to show that anisotropic meshes with highly stretched elements can be used to compute high reynolds number flows in particular it will be shown that boundary layers flow detachments and all vortices are well captured automatically by the mesh we present an anisotropic meshing based on a posteriori estimation for the incompressible navier stokes equations the proposed a posteriori estimate is based on the length distribution tensor approach and the associated edge based error analysis the finite element flow solver is based on a variational multiscale vms method which consists in here of decomposing both the velocity and the pressure fields into coarse resolved and fine unresolved scales this choice of decomposition is shown to be efficient for simulating flows at high reynolds number the stabilization parameters are determined taking into account the anisotropy of the mesh using a directional element diameter the adaptation algorithm is applied to high reynolds number flows inside the 2d and 3d lid driven cavities and compared to accurate reference solutions

on the limiting behaiour of a nonhomogeneour markov chain model in manpower systems summary we study the limiting structure of an expanding manpower system where the nonhomogeneous markov chain model proposed by young vassiliou 1974 is applicable the limiting structure and the relative limiting structure exist under certain conditions which are easily met in practical situations finally the problem of weak ergodicity in the above manpower systems is studied necessary and sufficient conditions are provided for weak ergodicity

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

hopf bifurcation in the driven cavity abstract incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two the algorithm is based on the time dependent stream function equation with a crank nicolson differencing scheme for the diffusion terms and with an adams bashforth scheme for the convection terms a multigrid method is used to solve the linear implicit equations at each time step periodic asymptotic solutions have been found for re 10000 and for re 5000 the re 5000 results are validated by grid refinement calculations the solutions are shown to be precisely periodic and care is taken to demonstrate that asymptotic states have been reached a discussion is included about the indicators that are used to show that an asymptotic state has been reached and to show that the asymptotic state is indeed periodic

existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay abstract in this paper we discuss local and global existence and uniqueness results for first order impulsive functional differential equations with multiple delay we shall rely on a nonlinear alternative of leray schauder for the global existence and uniqueness we apply a recent nonlinear alternative of leray schauder type in frechet spaces due to m frigon and a granas resultats de type leray schauder pour des contractions sur des espaces de frechet ann sci math quebec 22 2 1998 161 168 the goal of this paper is to extend the problems considered by a ouahab local and global existence and uniqueness results for impulsive differential equations with multiple delay j math anal appl 323 2006 456 472

asymptotic behavior of solutions of impulsive delay differential equations abstract effective sufficient conditions for the asymptotic stability of the trivial solution of impulsive delay differential equation formula are obtained by investigating respectively the asymptotic behavior of the nonoscillatory solutions and oscillatory solutions of the equation