stability and convergence of the peaceman rachford adi method for initial boundary value problems etude des proprietes de stabilite et de convergence de la methode des directions alternees implicite losrsqu elle est appliquee aux problemes aux valeurs initiales dans un espace bidimensionnel

design and implementation of two dimensional fully recursive digital filters the two dimensional 2 d fully recursive filter was recently introduced by the authors as a more general 2 d recursive filter in this paper we present a design algorithm and an implementation method for this class of filters the design algorithm incorporates a novel stability test we discuss the boundary condition problem which occurs in the implementation of fully recursive filters we propose a direct fully recursive implementation method which has been verified in software several design examples and comparisons are provided

coset sum an alternative to the tensor product in wavelet construction a multivariate biorthogonal wavelet system can be obtained from a pair of multivariate biorthogonal refinement masks in multiresolution analysis setup some multivariate refinement masks may be decomposed into lower dimensional refinement masks tensor product is a popular way to construct a decomposable multivariate refinement mask from lower dimensional refinement masks we present an alternative method which we call coset sum for constructing multivariate refinement masks from univariate refinement masks the coset sum shares many essential features of the tensor product that make it attractive in practice 1 it preserves the biorthogonality of univariate refinement masks 2 it preserves the accuracy number of the univariate refinement mask and 3 the wavelet system associated with it has fast algorithms for computing and inverting the wavelet coefficients the coset sum can even provide a wavelet system with faster algorithms in certain cases than the tensor product these features of the coset sum suggest that it is worthwhile to develop and practice alternative methods to the tensor product for constructing multivariate wavelet systems some experimental results using 2 d images are presented to illustrate our findings

chebyshev approximations for the direct design of 2 d quarter plane iir filters the development of various direct design techniques for inherently stable causal recursive two dimensional 2 d digital filters is described and illustrated by examples these techniques center around the development of 2 d z domain functions for use as arguments in the chebyshev function and provide for the design of low pass bandpass and high pass filters the specifications that can be prescribed are passband ripple filter order and normalized passband position parameters in addition to being inherently stable the filters possess an approximately flat group delay in most of the filter s passband a feature necessary for most applications

a filter bank for the directional decomposition of images theory and design the authors introduce a directionally oriented 2 d filter bank with the property that the individual channels may be critically sampled without loss of information the passband regions of the component filters are wedge shaped and thus provide directional information it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed the authors discuss the theory for directional decomposition and reconstruction in addition implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered

self organization in systems of self propelled particles we investigate a discrete model consisting of self propelled particles that obey simple interaction rules we show that this model can self organize and exhibit coherent localized solutions in one and in two dimensions in one dimension the self organized solution is a localized flock of finite extent in which the density abruptly drops to zero at the edges in two dimensions we focus on the vortex solution in which the particles rotate around a common center and show that this solution can be obtained from random initial conditions even in the absence of a confining boundary furthermore we develop a continuum version of our discrete model and demonstrate that the agreement between the discrete and the continuum model is excellent

spontaneously ordered motion of self propelled particles we study a biologically inspired inherently non equilibrium model consisting of self propelled particles in the model particles move on a plane with a velocity of constant magnitude they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours thus in the limit of vanishing velocities the model becomes analogous to a monte carlo realization of the classical xy ferromagnet we show by large scale numerical simulations that unlike in the equilibrium xy model a long range ordered phase characterized by non vanishing net flow emerges in this system in a phase space domain bordered by a critical line along which the fluctuations of the order parameter diverge the corresponding phase diagram as a function of two parameters the amplitude of noise and the average density of the particles is calculated and is found to have the form we also find that scales as a function of the external bias h field or wind according to a power law in the ordered phase the system shows long range correlated fluctuations and 1 f noise

estimation of linear parametric models using inverse filter criteria and higher order statistics considers the problem of estimating the parameters of a stable scalar arma p q signal model causal or noncausal minimum phase or mixed phase driven by an i i d non gaussian sequence the driving noise sequence is not observed the wiggins donoho 1978 1991 class of inverse filter criteria for estimation of model parameters are analyzed and extended these criteria have been considered in the past only for moving average inverse filters these criteria are extended to general arma inverses computer simulation examples are presented to illustrate the proposed approaches

some properties of generalized factorable 2 d fir filters factorable m dimensional filters are interesting because they can be implemented efficiently their computational complexity is o mn instead of o n sup m as in the case of generic non factorable filters unfortunately the passband support of a factorable filter can assume only very simple shapes parallelepipeds with edges pairwise parallel to the axes which are not adequate for most applications in a recent paper chen and vaidyanathan 1991 1993 proposed a new class of non factorable m dimensional filters whose passband support can be any parallelepiped which can be realized with complexity o mn in addition they are designed starting from 1 d prototypes which makes for a very simple design procedure in this paper we show that such filters belong to the class of generalized factorable gf filters whose formal definition we introduce here and derive some properties of theirs relative to the 2 d case our review includes issues such as the relation between minimax frequency response parameters and filter size which is nontrivial in the multidimensional case symmetries 2 d step response and frequency response constraints

design of multidimensional fir digital filters using the symmetrical decomposition technique a technique for the design of multidimensional fir filters based on symmetrical decomposition is described along with this technique a procedure to decompose a frequency response into symmetrical components is also discussed it is proved that the design based on the symmetrical decomposition technique when the cost function is chosen as the weighted square error yields the same optimal solution as the classical method that does not use the decomposition technique the l sub 2 norm design is discussed as a special case of weighted l sub 2 norm design it is also shown that the decomposition technique is advantageous when the weight function satisfies some symmetry properties examples are also provided to illustrate the application and the effectiveness of applying the decomposition in the design of 2 d and 3 d fir filters

two dimensional iir filter design with magnitude and phase error criteria two dimensional iir filters are designed using an error criterion consisting of the weighted sum of magnitude phase and stability errors thereby extending the spectral factorization based method to complex approximation the weights are adjusted to effectively constrain stability while minimizing a weighted sum of frequency domain magnitude and phase errors we use a derivative free variant of the marquardt optimization algorithm augmented by a one dimensional search we present examples of approximation of both linear and nonlinear phase ideal transfer functions and conduct comparisons across a range of numerator and denominator orders from fir to all pole while keeping the total number of coefficients approximately constant we find that the designed iir filters offer better magnitude response in the case of linear phase ideal functions even considering coefficient reflection symmetry but of course the fir filter has the better zero phase error when the ideal transfer function has nonlinear phase and hence no coefficient reflection symmetry we find that the designed iir filter can perform better than the fir filter with regard to both magnitude and phase error when magnitude error is weighted more heavily than phase error

numerical analyses of operator splitting algorithms for the two dimensional advection diffusion equation abstract holly and preissmann s hp scheme has been the basis of a large number of operator splitting algorithms for the solution of the advection diffusion equation however these algorithms including hp are first order accurate in time due to splitting errors error analyses of these algorithms incorporating splitting error and errors resulting from numerical solutions of the split advection and diffusion equations are lacking in this paper error analysis of a second order accurate adaptation of the hp scheme ahp is presented for the two dimensional advection diffusion equation a modified ahp scheme mahp is suggested to remove the ad hoc nature of boundary conditions during the diffusion step of computations in both hp and ahp as boundary conditions specified for the advection diffusion equation are not applicable to the split equations second order accurate boundary conditions for the split advection and diffusion equations are derived an analysis of numerical dispersion and dissipation associated with the numerical procedure for the advection equation is presented the analysis establishes a criterion so that computational errors are small in two dimensional advection dominated transport problems several numerical examples are presented to verify the numerical analyses presented in the paper in addition a review of the current status of operator splitting algorithms for the advection diffusion equation is presented the objective of the review is to identify the issues that have not been addressed in the previous studies

new tools for characterizing swarming systems a comparison of minimal models abstract we compare three simple models that reproduce qualitatively the emergent swarming behavior of bird flocks fish schools and other groups of self propelled agents by using a new set of diagnosis tools related to the agents spatial distribution two of these correspond in fact to different implementations of the same model which had been previously confused in the literature all models appear to undergo a very similar order to disorder phase transition as the noise level is increased if we only compare the standard order parameter which measures the degree of agent alignment when considering our novel quantities however their properties are clearly distinguished unveiling previously unreported qualitative characteristics that help determine which model best captures the main features of realistic swarms additionally we analyze the agent clustering in space finding that the distribution of cluster sizes is typically exponential at high noise and approaches a power law as the noise level is reduced this trend is sometimes reversed at noise levels close to the phase transition suggesting a non trivial critical behavior that could be verified experimentally finally we study a bi stable regime that develops under certain conditions in large systems by computing the probability distributions of our new quantities we distinguish the properties of each of the coexisting metastable states our study suggests new experimental analyses that could be carried out to characterize real biological swarms

l 0 stable splitting methods for the simple heat equation in two space dimensions with homogeneous boundary conditions l 0 stable splitting methods which are third and fourth order accurate in time are developed for the numerical solution of the simple diffusion equation in two space dimensions the methods are seen to evolve from first and second order pade approximants to the exponential function the local truncation errors of the methods are compared and the costs of implementing the algorithms are estimated by arithmetic operations counts the methods are tested on a constant coefficients problem for which there is a discontintlty between initial conditions and boundary conditions

an efficient approach for the synthesis of 2 d recursive fan filters using 1 d prototypes an elliptic approximation based design approach is proposed for obtaining 2 d recursive fan filters the 1 d elliptic filter is reduced to a cascade parallel combination of all pass sections and is then used as a prototype for fan filter synthesis resulting in final realization of 2 d transfer functions using allpass filters it is shown that the synthesis procedure not only gives a filter that has far fewer coefficients but also enjoys a very low computational complexity

exactly conservative integrators traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of any nonlinear invariants in this work we present a general approach for developing explicit nontraditional algorithms that conserve such invariants exactly we illustrate the method by applying it to the three wave truncation of the euler equations the lotka volterra predator prey model and the kepler problem the ideas are discussed in the context of symplectic phase space conserving integration methods as well as nonsymplectic conservative methods we comment on the application of our method to general conservative systems

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

on the numerical solution of multi dimensional parabolic problem by the additive splitting up method several numerical methods arising from the difference methods for certain classes of two dimensional parabolic equation are based on an operator slitting from the theoretical point of view the success and the evaluation of the splitting approach is primarily determined by the accuracy and the stability constrained most of the splitting methods defined in the past decades were of multiplicative non parallel types with respect to the spatial variables in 1994 lui tai and neittaanmaki presented a parallelisable implicit splitting type of methods of different order of approximation and its of additive type with regard to the solution at the advanced time step in this paper the stability analysis will be presented for the implicit splitting methods by lu et al and also we presented a parallelisable explicit splitting algorithm several model problems are solved by the splitting up algorithms to enhance the theoretical results and the concluding remarks

unconditional convergence of some crank nicolson lod methods for initial boundary value problems in this paper convergence properties are discussed for some locally one dimensional lod splitting methods applied to linear parabolic initialboundary value problems we shall consider unconditional convergence where both the stepsize in time and the meshwidth in space tend to zero independently of each other

phase equalization of one and two dimensional recursive filers an effective optimization algorithm is proposed to design multidimensional recursive phase equalizers the optimization algorithm uses the modified version of the rosenbrock 1960 pattern search method to minimize the maximum group delay ripple this numerical method eliminates the increased complexity that derivative methods show when multiple variables are to be found the criteria used to guarantee the stability of the equalizer are based on the decarlo strintzis theorem by applying this theorem the stability test procedure in m dimensions is reduced to m one dimensional stability test routines using this stabilization technique and the rosenbrock pattern search method for optimization the intensity of computations is considerably reduced in higher dimensions

phase transitions in self driven many particle systems and related non equilibrium models a network approach we investigate the conditions that produce a phase transition from an ordered to a disordered state in a family of models of two dimensional elements with a ferromagnetic like interaction this family is defined to contain under the same framework among others the xy model and the self driven particles model introduced by vicsek et al each model is distinguished only by the rules that determine the set of elements with which each element interacts we propose a new member of the family the vectorial network model in which a given fraction of the elements interact through direct random connections this model is analogous to an xy system on a network and as such can be of interest for a wide range of problems it captures the main aspects of the interaction dynamics that produce the phase transition in other models of the family the network approach allows us to show analytically the existence of a phase transition in this vectorial network model and to compute its relevant parameters for the case in which all elements are randomly connected finally we study numerically the conditions required for a phase transition to exist for different members of the family our results show that a qualitatively equivalent phase transition appears whenever even a small amount of long range interactions are present or built over time regardless of other equilibrium or non equilibrium properties of the system

algebraic approach to two dimensional recursive digital filter synthesis an effective algorithm is developed for synthesizing two dimensional recursive digital filters which approximate prescribed ideal frequency response specifications the algorithm is based on an algebraic approach that uses the eigenvalue eigenvector decomposition of the ideal filter s excitation response matrix in conjunction with a recently developed signal enhancement method this results in a recursive filter which has a unit impulse that closely approximates the ideal filter s unit impulse response illustrative examples and comparisons to an existing technique are included

an operator splitting algorithm for coupled one dimensional advection diffusion reaction equations abstract an operator splitting algorithm for a system of one dimensional advection diffusion reaction equations describing the transport of non conservative pollutants is presented in this paper the algorithm is a strang type splitting procedure incorporating contributions from the inhomogeneous terms by the duhamel s principle the associated homogeneous equations are split into advection diffusion and reaction equations and solved by a backward method of characteristic a finite element method and an explicit runge kutta method respectively the boundary conditions applicable to the split equations are derived numerical analyses of the algorithm consisting of the stability the accuracy and the convergence of the solution procedure are presented the composite algorithm is second order accurate in time and space and conditionally stable the numerical characteristics of the algorithm are demonstrated by several examples

on the treatment of time dependent boundary conditions in splitting methods for parabolic differential equations splitting methods for time dependent partial differential equations usually exhibit a drop in accuracy if boundary conditions become time dependent this phenomenon is investigated for a class of splitting methods for two space dimensional parabolic partial differential equations a boundary value correction discussed in a paper by fairweather and mitchell for the laplace equation with dirichlet conditions is generalized for a wide class of initial boundary value problems a numerical comparison is made for the adi method of peaceman rachford and the lod method of yanenko applied to problems with dirichlet boundary conditions and non dirichlet boundary conditions

fourfold rotational symmetry in two dimensional functions the presence of various types of symmetry in the frequency responses of a two dimensional filter function reflects as constraints on its coefficients in this paper such constraints are derived for two dimensional analog and digital transfer functions so that the magnitude functions of the frequency responses of these transfer functions possess fourfold rotational symmetry the relationship between fourfold rotational symmetry and quadrantal diagonal and octagonal symmetries is also discussed

short note a high order pade adi method for unsteady convection diffusion equations a high order alternating direction implicit adi method for computations of unsteady convection diffusion equations is proposed by using fourth order pade schemes for spatial derivatives the present scheme is fourth order accurate in space and second order accurate in time the solution procedure consists of a number of tridiagonal matrix operations which make the computation cost effective the method is unconditionally stable and shows higher accuracy and better phase and amplitude error characteristics than the standard second order adi method d w peaceman h h rachford jr the numerical solution of parabolic and elliptic differential equations journal of the society of industrial and applied mathematics 3 1959 28 41 and the fourth order adi scheme of karaa and zhang high order adi method for solving unsteady convection diffusion problem journal of computational physics 198 2004 1 9

a norm estimate for the adi method for nonsymmetric problems abstract we give a norm estimate for the alternating direction implicit method for nonsymmetric elliptic convection diffusion problems on a rectangular domain we estimate a certain form of the iteration matrix in terms of the coefficients of convective terms and the mesh size the norm is shown to be asymptotically of the form 1 ch 1 ch where c is the same constant as in the symmetric case we also show that the optimal size of the parameter is the same as in the symmetric case as a consequence we conclude that the convergence behavior is as good as that of the symmetric case and does not deteriorate as the size of convective terms grows numerical experiment shows that our analysis is sharp

symmetry in two dimensional rectangularly sampled digital filters it is well known that exploiting the quadrantal diagonal or octagonal symmetry existing in the 2 d filter frequency response results in a reduction in the design and implementation complexities this paper introduces new symmetries that could possibly exist in the frequency response the symmetries are presented in a general framework that encompasses all previously known and newly discovered symmetries the commonly found cases such as displacement rotation and reflection symmetries are discussed in some detail to present their geometric properties in the frequency plane two examples are solved at the end to illustrate the significant savings resulting from exploiting those previously unknown symmetries

a fractional step ellam approach to high dimensional convection diffusion problems with forward particle tracking in this paper a fractional step method combined with an eulerian lagrangian localized adjoint method ellam is proposed to solve high dimensional convection diffusion problems the method reduces high dimensional problems to a series of uncoupled one dimensional problems in each time step interval in which one dimensional ellam is used to solve the one dimensional splitting equations the approach takes the attractive advantages of the ellam method and the fractional step technique it reduces computational complexities large memory requirements and long computation durations due to the application of the splitting technique it reduces temporal errors and generates accurate numerical solutions even if large time and coarse spatial step sizes are used in computation it effectively eliminates non physical oscillation or excessive numerical dispersion and treats boundary conditions well and in a natural way numerical experiments show the efficient performance of the approach

a multi block adi finite volume method for incompressible navier stokes equations in complex geometries an efficient second order accurate finite volume method is developed for a solution of the incompressible navier stokes equations on complex multi block structured curvilinear grids unlike in the finite volume or finite difference based alternating direction implicit adi methods where factorization of the coordinate transformed governing equations is performed along generalized coordinate directions in the proposed method the discretized cartesian form navier stokes equations are factored along curvilinear grid lines the new adi finite volume method is also extended for simulations on multi block structured curvilinear grids with which complex geometries can be efficiently resolved the numerical method is first developed for an unsteady convection diffusion equation then is extended for the incompressible navier stokes equations the order of accuracy and stability characteristics of the present method are analyzed in simulations of an unsteady convection diffusion problem decaying vortices flow in a lid driven cavity flow over a circular cylinder and turbulent flow through a planar channel numerical solutions predicted by the proposed adi finite volume method are found to be in good agreement with experimental and other numerical data while the solutions are obtained at much lower computational cost than those required by other iterative methods without factorization for a simulation on a grid with o 10 5 cells the computational time required by the present adi based method for a solution of momentum equations is found to be less than 20 of that required by a method employing a biconjugate gradient stabilized scheme

a comparative study of adi splitting methods for parabolic equations in two space dimensions abstract the main purpose of the paper is a numerical comparison of three integration methods for semi discrete parabolic partial differential equations in two space variables linear as well as nonlinear equations are considered the integration methods are the well known adi method of peaceman and rachford a global extrapolation scheme of the classical adi method to order four and a fourth order four step adi splitting method

classical theory of runge kutta methods for volterra functional differential equations abstract for solving volterra functional differential equations vfdes a class of discrete runge kutta methods based on canonical interpolation is studied which was first presented by the same author in a previous published paper classical stability and convergence theories for this class of methods are established the methods studied and the theories established in this paper can be directly applied to non stiff non linear initial value problems in delay differential equations ddes integro differential equations ides delay integro differential equations dides and vfdes of other type which appear in practice and can be used as a necessary basis for the study of splitting methods for complex nonlinear stiff vfdes

interaction ruling animal collective behavior depends on topological rather than metric distance evidence from a field study numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals however very little is known about the nature of such interaction so that models and theories mostly rely on aprioristic assumptions by reconstructing the three dimensional positions of individual birds in airborne flocks of a few thousand members we show that the interaction does not depend on the metric distance as most current models and theories assume but rather on the topological distance in fact we discovered that each bird interacts on average with a fixed number of neighbors six to seven rather than with all neighbors within a fixed metric distance we argue that a topological interaction is indispensable to maintain a flock s cohesion against the large density changes caused by external perturbations typically predation we support this hypothesis by numerical simulations showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one

piecewise linearized and linearized θ methods for ordinary and partial differential equations lnitial and boundary value problems appear frequently in many branches of physics in this paper several numerical methods based on linearization techniques for solving these prob lems are reviewed first piecewise linearized methods and linearized 0 methods are considered for the solution of initial value problems in ordinary differential equations second piecewise linearized techniques for two point boundary value problems in ordinary differential equations are developed and used in conjunction with a shooting method in order to overcome the lack of convergence asso ciated with shooting piecewise linearized methods which provide piecewise analytical solutions and yield nonstandard finite difference schemes axe presented third methods of lines in either space or time for the solution of one dimensional convection reaction diffusion problems that transform the original problem into an initial or boundary value one are reviewed methods of lines in time that result in boundary value problems at each time step can be solved by means of the techniques described here whereas methods of lines in space that yield initial value problems and employ ei ther piecewise linearized techniques or linearized 0 methods in time are also developed finally for multidimensional problems approximate factorization methods are first used to transform the multi dimensional problem into a sequence of one dimensional ones which are then solved by means of the linearized and piecewise linearized methods presented here 2003 elsevier science ltd all rights reserved

adams methods for neutral functional differential equations in this paper adams type methods for the special case of neutral functional differential equations are examined it is shown thatk step methods maintain orderk 1 for sufficiently small step size in a sufficiently smooth situation however when these methods are applied to an equation with a non smooth solution the order of convergence is only one some computational considerations are given and numerical experiments are presented

hierarchical cluster structures in a one dimensional swarm oscillator model swarm oscillator model derived by one of the authors tanaka where interacting motile elements form various kinds of patterns is investigated we particularly focus on the cluster patterns in one dimensional space we mathematically derive all static and stable configurations in final states for a particular but a large set of parameters in the derivation we introduce renormalized expression of this model we find that the static final states are hierarchical cluster structures in which a cluster consists of smaller clusters in a nesting manner

stability of runge kutta methods for the generalized pantograph equation this paper deals with stability properties of runge kutta rk methods applied to a non autonomous delay differential equation dde with a constant delay which is obtained from the so called generalized pantograph equation an autonomous dde with a variable delay by a change of the independent variable it is shown that in the case where the rk matrix is regular stability properties of the rk method for the dde are derived from those for a difference equation which are examined by similar techniques to those in the case of autonomous ddes with a constant delay as a result it is shown that some rk methods based on classical quadrature have a superior stability property with respect to the generalized pantograph equation stability of algebraically stable natural rk methods is also considered

a modified vicsek model for self propelled agents with exponential neighbor weight and restricted visual field abstract large flocks of wild beings can have coordinated motion with neither leading center nor global information the vicsek model and its new versions explained such collective behavior of self propelled agents with the mechanism of un weighted influence of neighbors and global visual field gvf which may not always fit the reality in the present work we take both exponential neighbor weight enw and restricted visual field rvf into account and investigate the combinatory effect of them based on this mechanism in most cases of our simulation stationary direction consensus v a exhibits a maximum or decreases with v f and a minimum convergence time t m i n appears in rvf which demonstrates that gvf is not necessary for coordinated motion while rvf matched enw would be reasonable moreover we simulated various recipes for optimizing v a and t in unfavorable cases and found critical points separating inverse dependent variations of t the present work may be useful in improving the efficiency of direction consensus of large flocks of artificial individuals besides the understanding of biological collective motion in nature

k cyclic symmetries in multidimensional sampled signals in this paper k cyclic frequency domain symmetry conditions for n dimensional sampled signals are introduced it is shown that these frequency domain symmetry conditions result in certain interrelationships between the sample values a theorem is given that specifies these interrelationships several interesting properties of k cyclic symmetries are discussed also a systematic approach is given for finding the parameters of several commonly encountered symmetry conditions certain implications to multidimensional digital filtering are discussed including l p optimality and the reduction in computation for design and implementation

geometric integrators for odes geometric integration is the numerical integration of a differential equation while preserving one or more of its geometric properties exactly i e to within round off error many of these geometric properties are of crucial importance in physical applications preservation of energy momentum angular momentum phase space volume symmetries time reversal symmetry symplectic structure and dissipation are examples in this paper we present a survey of geometric numerical integration methods for ordinary differential equations our aim has been to make the review of use for both the novice and the more experienced practitioner interested in the new developments and directions of the past decade to this end the reader who is interested in reading up on detailed technicalities will be provided with numerous signposts to the relevant literature

error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems abstract we study space and time discretizations for mixed formulations of parabolic problems the spatial approximation is based on the multipoint flux mixed finite element method which reduces to an efficient cell centered pressure system on general grids including triangles quadrilaterals tetrahedra and hexahedra the time integration is performed by using a domain decomposition time splitting technique combined with multiterm fractional step diagonally implicit runge kutta methods the resulting scheme is unconditionally stable and computationally efficient as it reduces the global system to a collection of uncoupled subdomain problems that can be solved in parallel without the need for schwarz type iteration convergence analysis for both the semidiscrete and fully discrete schemes is presented

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

symmetry exploitation in the design and implementation of recursive 2 d rectangularly sampled digital filters it is well known that exploiting the symmetries existing in the frequency response of 2 d filters results in a reduction in design and implementation complexities in this paper we explore how to exploit a general class of symmetries in the design and implementation of recursive two dimensional 2 d filters three types of filters are being studied namely causal factorizable noncausal and unfactorizable noncausal the capability of each of these filters to exhibit symmetries is discussed a method is then proposed to obtain the required form of the filter transfer function for exhibiting the different types of symmetries examples are solved both to illustrate the proposed method and to compare the performance of these filter types for the same implementation complexity

stability of runge kutta methods for delay integro differential equations we study stability of runge kutta rk methods for delay integro differential equations with a constant delay on the basis of the linear equation du dt lu t mu t k t t u d where l m k are constant complex matrices in particular we show that the same result as in the case k 0 koto bit 34 1994 262 267 holds for this test equation i e every a stable rk method preserves the delay independent stability of the exact solution whenever a step size of the form h m is used where m is a positive integer

design of 2 d recursive digital filters using nonsymmetric half plane allpass filters a novel structure using recursive nonsymmetric half plane nshp digital allpass filters dafs is presented for designing 2 d recursive digital filters first several important properties of 2 d recursive dafs with nshp support regions for filter coefficients are investigated the stability of the 2 d recursive nshp dafs is guaranteed by using a spectral factorization based algorithm then the important characteristics regarding the proposed novel structure are discussed the design problem of 2 d recursive digital filters using the novel structure is considered we formulate the problem by forming an objective function consisting of the weighted sum of magnitude group delay and stability related errors a design technique using a trust region newton conjugate gradient method in conjunction with the analytic derivatives of the objective function is presented to efficiently solve the resulting optimization problem the novelty of the presented 2 d structure is that it possesses the advantage of better performance in designing a variety of 2 d recursive digital filters over existing 2 d filter structures finally several design examples are provided for conducting illustration and comparison

a fourth order adi method for semidiscrete parabolic equations abstract a fourth order fourstep adi method is described for solving the systems of ordinary differential equations which are obtained when a nonlinear parabolic initial boundary value problem in two dimensions is semi discretized the local time discretization error and the stability conditions are derived by numerical experiments it is demonstrated that the asymptotic fourth order behaviour does not degenerate if the time step increases to relatively large values also a comparison is made with the classical adi method of peaceman and rachford showing the superiority of the fourth order method in the higher accuracy region particularly in nonlinear problems