the chain collocation method a spectrally accurate calculus of forms preserving in the discrete realm the underlying geometric topological and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity electromagnetism or fluid mechanics however structure preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms yet in many problems where solutions are smoothly varying in space a spectral numerical treatment is called for in an effort to provide structure preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains we present a spectral extension of the discrete exterior calculus dec with resulting computational tools extending well known collocation based spectral methods its efficient implementation using fast fourier transforms is provided as well

a spectral chebyshev method for linear stability analysis of one dimensional exact solutions of gas dynamics we present a spectral numerical method for solving one dimensional systems of partial differential equations pdes which arise from linearization of the euler equations about an exact solution depending on space and time a two domain chebyshev collocation method is used matching of quantities is performed in the space of characteristic variables as suggested by kopriva appl numer math 2 1986 221 j comput phys 125 1996 244 time dependent boundary conditions are handled following an approach proposed by thompson j comput phys 68 1987 1 89 1990 439 an exact numerical stability analysis valid for any explicit three step third order nondegenerate runge kutta scheme is provided the numerical method is tested against exact solutions for the three fundamental modes of a compressible flow entropy vorticity and acoustic modes

on a generalized max type difference equation from automatic control theory abstract this paper studies the boundedness character of positive solutions of the following generalization of a max type difference equation from automatic control theory see mishkis 1977 18 and popov 1966 21 x n 1 max a x n p x n 1 q x n 2 r n n 0 where the parameters a p q and r are positive numbers in the study of the equation we also introduce a new method called oachkatzlschwoif

the periodic nature of the positive solutions of a nonlinear fuzzy max difference equation we investigate the periodic nature of the positive solutions of the fuzzy difference equation x n maxa 0x n k a 1x n m where k m are positive integers a 0 a 1 are positive fuzzy numbers and the initial values x i i d d 1 1 d max k m are positive fuzzy numbers in addition we give conditions so that the solutions of this equation are unbounded

mixed discrete fuzzy multiobjective programming for engineering optimization using hybrid genetic algorithm although much attention has been focused on the development and applications of fuzzy optimization multiobjective programming and mixed discrete optimization methods separately fuzzy multiobjective optimization problems in mixed discrete design space have not been addressed in the literature it is mainly because of the lack of mature and robust theories of mixed discrete and multiobjective optimization in most practical applications designers often encounter problems involving imprecise or fuzzy information multiple objectives and mixed discrete design variables a new method is presented in which the fuzzy formulation and game theory techniques are combined with a mixed discrete hybrid genetic algorithm for solving mixed dixcrete fuzzy multiobjective programming problems three example problems dealing with the optimal designs of a two bar truss a conical convective spine and a 25 bar truss demonstrate that the method can be flexibly and effectively applied to various kinds of engineering design problems to obtain more realistic and satisfactory results in an imprecise environment nomenclature d fuzzy feasible solution domain d f avorable search direction fiti x fitness function fi x ith objective function f max i upper bound of ith objective function f min i l ower bound of ith objective function g j allowable interval of the constraint function g j g j x jth inequality constraint function k number of objective functions m size of the population m number of inequality constraints n total number of design variables nd number of discrete design variables nq number of discrete design variables with equal spacing x design vector x c centroid of the composite polygon xw v ertex with the lowest fitness value xi ith design variable d x membership function of the design vector fi x membership function of the ith objective gj x membership function of the jth constraint

multidomain spectral solution of the euler gas dynamics equations abstract we present interface treatments for computing the euler gas dynamics equations by a multidomain chebyshev spectral collocation method these treatments are suitable for use at the corners of subdomains and for patched or overlapping subdomains they can be applied to interfaces placed in subsonic supersonic or transonic regions of a flow computed results indicate that the solutions are spectrally accurate can be more accurate and more efficient than a single domain calculation and that reflections of waves at interfaces are not significant

fuzzy programming in multiobjective linear programming a parametric approach abstract zimmermann s fuzzy approach to the compromise solution concept in the multi objective linear programming problem is considered it is shown that given a class of membership functions of fuzzy goals assigned to objective functions in the problem wider than primarily proposed by zimmermann the use of classical linear programming methods to solve and analyse the problem is also possible as a result of application of the method based on the parametric programming technique one can obtain a fuzzy solution of the problem this solution is a certain fuzzy subset of the set of weakly efficient solutions of the problem the solution which belongs to this set to the highest degree is a maximizing one in bellman and zadeh s terminology it may also be obtained by use of the usual non parametric simplex method

an efficient correction procedure via reconstruction for simulation of viscous flow on moving and deforming domains in this paper we report the development of a new parallel solver using the correction procedure via reconstruction cpr for viscous flows on moving and deforming grids by employing an accurate treatment of flux derivatives for moving and deforming unstructured grids consisting of all quadrilateral cells it is found that the geometric conservation law is not explicitly required the free stream preservation is automatically satisfied the cpr code is verified using a benchmark case for a moving inviscid vortex on moving and deforming grids the optimal orders of accuracy are obtained it is subsequently employed to study viscous flows on moving and deforming grids the cpr method is faster than and nearly as accurate as the sd method for solving viscous flow problems with moving boundaries

towards efficient tracking of inertial particles with high order multidomain methods this paper develops an efficient particle tracking algorithm to be used in fluid simulations approximated by a high order multidomain discretization of the navier stokes equations we discuss how to locate a particle s host subdomain how to interpolate the flow field to its location and how to integrate its motion in time a search algorithm for the nearest subdomain and quadrature point tuned to a typical quadrilateral isoparametric spectral subdomain takes advantage of the inverse of the linear blending equation we show that to compute particle laden flows a sixth order lagrangian polynomial that uses points solely within a subdomain is sufficiently accurate to interpolate the carrier phase variables to the particle position time integration of particles with a lower order adams bashforth scheme rather than the fourth order runge kutta scheme often used for the integration of the carrier phase increases computational efficiency while maintaining engineering accuracy we verify the tracking algorithm with numerical tests on a steady channel flow and an unsteady backward facing step flow

a simple efficient and high order accurate curved sliding mesh interface approach to spectral difference method on coupled rotating and stationary domains this paper presents a simple efficient and high order accurate sliding mesh interface approach to the spectral difference sd method we demonstrate the approach by solving the two dimensional compressible navier stokes equations on quadrilateral grids this approach is an extension of the straight mortar method originally designed for stationary domains 7 8 our sliding method creates curved dynamic mortars on sliding mesh interfaces to couple rotating and stationary domains on the nonconforming sliding mesh interfaces the related variables are first projected from cell faces to mortars to compute common fluxes and then the common fluxes are projected back from the mortars to the cell faces to ensure conservation to verify the spatial order of accuracy of the sliding mesh spectral difference ssd method both inviscid and viscous flow cases are tested it is shown that the ssd method preserves the high order accuracy of the sd method meanwhile the ssd method is found to be very efficient in terms of computational cost this novel sliding mesh interface method is very suitable for parallel processing with domain decomposition it can be applied to a wide range of problems such as the hydrodynamics of marine propellers the aerodynamics of rotorcraft wind turbines and oscillating wing power generators etc

reduced navier stokes equations near a flow boundary we derive a hierarchy of pdes for the leading order evolution of wall based quantities such as the skin friction and the wall pressure gradient in two dimensional fluid flows the resulting reduced navier stokes rns equations are defined on the boundary of the flow and hence have reduced spatial dimensionality compared to the navier stokes equations this spatial reduction speeds up numerical computations and makes the equations attractive candidates for flow control design we prove that members of the rns hierarchy are well posed if appended with boundary conditions obtained from wall based sensors we also derive the lowest order rns equations for three dimensional flows for several benchmark problems our numerical simulations show close finite time agreement between the solutions of rns and those of the full navier stokes equations c 2006 elsevier b v all rights reserved

stable boundary conditions and difference schemas for navier stokes equations the navier stokes equations at high reynolds numbers can be viewed as an incompletely elliptic perturbation of the euler equations by using the entropy function for the euler equations as a measure of energy for the navier stokes equations we are able to obtain nonlinear energy estimates for the mixed initial boundary value problem these estimates are used to derive boundary conditions that guarantee l 2 boundedness even when the reynolds number tends to infinity finally we propose a new difference scheme for modeling the navier stokes equations in multidimensions for which we are able to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation

global behavior of the max type difference equation x n max 1 x n m a n x n r in this paper we study the global behavior of the following max type difference equation x n max 1 x n m a n x n r n 0 1 2 where a n n 0 is a sequence of positive numbers with a n 0 1 for every n 0 and sup a n 1 and m r 1 2 3 and the initial values x d x d 1 x 1 0 with d max m r we show that 1 if x n n d is a positive solution of this equation then for every 0 k 2 m 1 x 2 mn k n 0 is eventually monotone 2 if a n n 0 is a periodic sequence then every positive solution of this equation is eventually periodic with period 2 m

subharmonic solutions of systems of difference equations with periodic perturbations part i existence we consider the existence of subharmonic solutions of systems of difference equations with periodic perturbations the theory of coincidence degree coupled with some detailed a priori estimates is applied to show that the perturbed system admits subharmonic solutions near a hyperbolic periodic orbit of the unperturbed system if the perturbation is sufficiently small

a high order solver for unsteady incompressible navier stokes equations using the flux reconstruction method on unstructured grids with implicit dual time stepping we report development of a high order compact flux reconstruction method for solving unsteady incompressible flow on unstructured grids with implicit dual time stepping the method falls under the class of methods now referred to as flux reconstruction correction procedure via reconstruction the governing equations employ chorin s classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems an implicit non linear lower upper symmetric gauss seidel scheme with backward euler discretization is used to efficiently march the solution in pseudo time while a second order backward euler discretization is used to march in physical time we verify and validate implementation of the high order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems the current implicit time stepping scheme is proven effective in satisfying the divergence free constraint on the velocity field in the artificial compressibility formulation within the context of the high order flux reconstruction method this compact high order method is very suitable for parallel computing and can easily be extended to moving and deforming grids

a staggered grid multidomain spectral method for the compressible navier stokes equations we present a flexible non conforming staggered grid chebyshev spectral multidomain method for the solution of the compressible navier stokes equations in this method subdomain corners are not included in the approximation thereby simplifying the subdomain connectivity to allow for local refinement of the polynomial order or subdomain subdivision non conforming subdomains are treated by a mortar method spectral accuracy is shown in one and two dimensional linear and non linear problems application is made to four compressible flow problems the couette flow a steady boundary layer over a flat plate steady transonic flow in a nozzle and unsteady flow over a cylinder at a reynolds number of 75

on a max difference equation abstract in this paper we study the existence of generalized invariants and the periodicity of the positive solutions of max equations x n 1 max a n n i n k 1 x i b n n i n k x i n 0 1 where an bn are sequences of positive numbers x k x k 1 x0 0 and k 2 3

on the eventual periodicity of xn 1 max 1xn anxn 1 with a period five parameter in this paper we will study the max difference equation x n 1 max 1x n a nx n 1 when a n is a period five sequence of real numbers greater than one we will prove that every solution is eventually periodic with period twenty

the theory of approximate prices analytical foundations of experimental cost benefit analysis in a fuzzy decision space abstract the essay presents a theory of efficient prices for cost benefit analysis in a fuzzy space the approach proceeds by taking consumers income and producers outputs and costs as given the price preferences of consumers and producers are elicited and then embedded in a fuzzy space through fuzzy mappings to obtain a fuzzy compact price space where fuzzy price decisions are constructed solutions to the fuzzy price decision problems are abstracted through fuzzy mathematical programming to obtain fuzzy equilibrium prices from the fuzzy price space measures of price disagreement fuzzy consumer surplus and fuzzy producer surplus are advanced theorems of existence and uniqueness are stated the total result is a theory of fuzzy prices for cost benefit analysis for decision problem in general including cases where market imputations of prices may not be available to us as well as those cases where market failure may yield price distortions the theory is not only compactible with either contigent variation method direct information elicitation and revealed preference method market based evaluation but provides a direction for cases where problems may exist in both a computational example is provided to illustrate the working mechanism of the theory

a weak legendre collocation spectral method for the solution of the incompressible navier stokes equations in unstructured quadrilateral subdomains a weak legendre spectral method is developed for the solution of the primitive variable formulation of the unsteady incompressible navier stokes equations in general two dimensional and axisymmetric geometries a semi implicit projection method is utilized for the temporal approximation and for decoupling the velocity field from the pressure field a series of elliptic boundary value problems arises from the above procedure each of which is spatially discretized by a weak collocation method in multiple nonoverlapping subdomains in particular a modified variational formulation of the partial differential equations is presented which leads after discretization to a weak multidomain approximation of the corresponding problems a weak formalism for the influence matrix technique is also developed which is consistent with the spatial discretization scheme and successfully separate the equations for the internal nodes from the ones governing the interface unknowns a method of dealing with the singularity problem faced by the weak formulation at axisymmetric problems is proposed while a combination of direct methods is studied for tackling effectively the linear algebraic systems resulting from the full discretization exponential convergence is demonstrated for a plethora of stokes and navier stokes simulations

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

on subharmonic solutions of systems of difference equations with periodic perturbations part ii multiplicity and stability we consider the multiplicity and stability of subharmonic solutions of discrete dynamic systems with periodic perturbations whose existence was established in the first part of this series under the hypotheses that the perturbation is locally lipschitz continuous we determine the precise number of subharmonic solutions and we also show that these subharmonic solutions are stable unstable provide the periodic orbit of the unperturbed system is stable unstable

a fuzzy decision theory of optimal social discount rate collective choice theoretic abstract in this essay we present a fuzzy decision theory of the optimal social discount rate by combining methods of fuzzy logic consensus combination of expert judgments and fuzzy aggregation algorithms are developed for computing optimal social discount rates from individual and collective time preferences the results are examined against the computation of social discount rate on individual preferences as measured by utilities an example is provided to illustrate the applicational mechanism of the theory the essay is concluded with an appendix which is devoted to examining the properties of the required time set for the construction of the social discount

multiple goal non cooperative conflicts under uncertainty a fuzzy set approach abstract this paper investigates strategy selection for a participant in a two party non cooperative conflict which involves both uncertainty and multiple goals uncertainty arises from the players not knowing the utility functions multiple objectives appear as the result of the payoff being a vector of prizes and the players attempt to attain various goals for each prize separately the main objective is to present a fuzzy set fuzzy programming solution concept to the conflict situation in doing so we compare a bayesian player to one that employs fuzzy set techniques we point out some of the advantages of the fuzzy set method the necessary computations in the fuzzy set method are explained in detail through an example

global stability of a difference equation with maximum we prove that every positive solution to the difference equationx n maxa 1x n 1 a 1 a 2x n 2 a 2 a kx n k a k email protected n 0 where email protected n a i 0 a email protected 0 1 i 1 k converges to the following quantity maxa 1 1 a 1 1 a k 1 a k 1 confirming a quite recent conjecture of interest we also prove another result on global convergence which concerns some cases when not all a i i 1 k belong to the interval 0 1

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

a spectrally accurate method for overlapping grid solution of incompressible navier stokes equations an overlapping mesh methodology that is spectrally accurate in space and up to third order accurate in time is developed for solution of unsteady incompressible flow equations in three dimensional domains the ability to decompose a global domain into separate but overlapping subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries the methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally accurate spatial interpolation and high order accurate temporal extrapolation and requires few if any iterations yet maintains the global accuracy and stability of the underlying flow solver the overlapping mesh methodology is thoroughly validated using two dimensional and three dimensional benchmark problems in laminar and turbulent flows the spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver the influence of long integration times as well as inflow outflow global boundary conditions on the performance of the overlapping grid solver is assessed in a turbulent benchmark of fully developed turbulent pipe flow the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data scaling tests are presented that show near linear strong scaling even for moderately large processor counts a novel overlapping grid method for incompressible flow equations is developed the overlapping grid method is based on spectral element discretization the method maintains global spectral accuracy with polynomial refinement an explicit interface extrapolation scheme for temporal coupling is proposed the scheme allows for high order temporal accuracy with only a few iterations

on the periodic nature of the solutions of the reciprocal difference equation with maximum abstract we prove that every positive solution of the third order difference equation x n max a x n 1 b x n 2 c x n 3 n 0 1 is eventually periodic of not necessarily prime period t which is explicitly determined by the coefficients a b and c

two classes of piecewise linear difference equations with eventual periodicity three in this paper we will study two classes of difference equations which are piecewise linear and of similar forms we will show that all nontrivial solutions of one equation are eventually periodic with prime period three we will show this result for one case of the second equation

an exponential membership function for fuzzy multiple objective linear programming abstract the operator min is one of the most frequently used aggregation operators in fuzzy decision however this operator is the softest operator and no allowance is made for any compensation the product and other operators some of them may be compensatory are seldom used because of the nonlinearity of the resulting problem in this paper an exponential instead of linear membership function is proposed the advantages of using exponential membership are two fold first the resulting problems can be transformed to linear ones when the product and several other nonlinear aggregate operators are used secondly exponential representation is more realistic than the linear ones usually used for some practical applications

on finding compromise solutions in multicriteria problems using the fuzzy min operator abstract this paper presents an application of fuzzy approaches to the linear vectormaximum problem it shows that using the fuzzy min operator together with linear as well as special nonlinear membership functions the obtained solutions are always compromise solutions of the original multicriteria problem

a conservative staggered grid chebyshev multidomain method for compressible flows ii a semi structured method we present a chebyshev multidomain method that can solve systems of hyperbolic equations in conservation form on an unrestricted quadrilateral subdivision of a domain within each subdomain the solutions and fluxes are approximated by a staggered grid chebyshev method thus the method is unstructured in terms of the subdomain decomposition but strongly structured within the subdomains communication between subdomains is done by a mortar method in such a way that the method is globally conservative the method is applied to both linear and nonlinear test problems and spectral accuracy is demonstrated

boundedness character of a class of difference equations abstract a complete picture regarding the boundedness character of positive solutions to the following difference equation x n max a x n 1 p x n k p n n 0 where k 2 and the parameters a and p are positive real numbers is given in particular for the case p k 1 0 k k k 1 k 1 we prove that all solutions to the equation are bounded we also present corresponding results concerning the following closely related difference equation x n a x n 1 p x n k p n n 0

a note of fuzzy programming and the pareto optimal set abstract we indicate some errors made in buckley s paper on fuzzy programming and the pareto optimal set 1

joint solution to fuzzy programming problems we propose a new solution concept for fuzzy programming problems it is based on our new method of solving fuzzy equations 101 for simplicity we discuss in detail only fuzzy linear programming in this paper we define and obtain the basic properties of the joint solution a fuzzy vector in rn and the optimal value of the objective function a fuzzy number three examples are presented illustrating these concepts

on a system of difference equations with maximum in this paper we study the periodic character of the solutions of the system of difference equations with maximum x n 1 max a y n x n 1 y n 1 max b x n y n 1 where a b are positive constants and the initial values x 1 x 0 y 1 y 0 are positive numbers we prove that every solution is eventually periodic

on a difference equation with maximum abstract this paper studies the asymptotic behavior of positive solutions to the difference equation x n max 1 x n 1 a x n 2 n 0 1 where 0 0 we prove that every positive solution of this equation approaches x 1 or is eventually periodic with period 4 according as a 1 or a 1

a direct solver for variable coefficient elliptic pdes discretized via a composite spectral collocation method a numerical method for variable coefficient elliptic problems on two dimensional domains is presented the method is based on high order spectral approximations and is designed for problems with smooth solutions the resulting system of linear equations is solved using a direct solver with o n 1 5 complexity for the pre computation and o nlogn complexity for the solve the fact that the solver is direct is a principal feature of the scheme and makes it particularly well suited to solving problems for which iterative solvers struggle in particular for problems with highly oscillatory solutions numerical examples demonstrate that the scheme is fast and highly accurate for instance using a discretization with 12 points per wavelength a helmholtz problem on a domain of size 100x100 wavelengths was solved to ten correct digits the computation was executed on a standard laptop it involved 1 6m degrees of freedom and required 100 s for the pre computation and 0 3 s for the actual solve

on the asymptotic behavior and periodic nature of a difference equation with maximum in this paper we investigate the asymptotic behavior and periodic nature of positive solutions of the difference equation x n max ax n 1 1xn 2 a n 0 where a 0 and 0 a 1 we prove that every positive solution of this difference equation approaches x 1 or is eventually periodic with a period 2 3 or 4

possibility and necessity in optimization abstract we employ possibility and necessity in fuzzy programming and in other optimization problems that traditionally use random variables the possibility approach to multiobjective programming produces the same results as fuzzy programming a detailed example is presented to illustrate the use of possibility and necessity in optimization problems that usually employ random variables to describe uncertainty

a multicriteria fuzzy linear programming method for water supply system development planning abstract a method is presented for solving a multicriteria linear program where the coefficients of the objective functions and the constraints are fuzzy numbers of the l r type assuming the aspiration levels for particular criteria to be fuzzy and basing on comparison of fuzzy numbers the original problem is transformed into a multicriteria linear fractional program the latter is solved using an interactive technique involving a linear programming procedure in the calculation phase this method has been elaborated with a view to the application to the development of a water supply system

on the boundedness of positive solutions of the reciprocal max type difference equation xn max a1n 1 xn 1 a2n 1 xn 2 atn 1 xn t with periodic parameters we investigate the boundedness of positive solutions of the reciprocal max type difference equation xn max a1n 1 xn 1 a2n 1 xn 2 atn 1 xn t where for each value of i the sequence ain n 0 of positive numbers is periodic with period pi we give both sufficient conditions on the pi s for the boundedness of all solutions and sufficient conditions for all solutions to be unbounded this work essentially complements the work by bidwell and franke who showed that as long as every positive solution of our equation is bounded then every positive solution is eventually periodic thereby leaving open the question as to when solutions are bounded

a stable penalty method for the compressible navier stokes equations i open boundary conditions the purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible navier stokes equations in three spatial dimensions the treatment uses the conservation form of the navier stokes equations and utilizes linearization and localization at the boundaries based on these variables the proposed boundary conditions are applied through a penalty procedure thus ensuring correct behavior of the scheme as the reynolds number tends to infinity the versatility of this method is demonstrated for the problem of a compressible flow past a circular cylinder

multiobjective possibilistic linear programming abstract this paper presents two solutions to multiobjective linear programs when all the parameters may be fuzzy variables whose values are restricted by a possibility distribution in the first solution we first find possibility distribution of the objective function and then a solution consists of those values of the decision variables which produce the largest undominated values of the objective function where these values also have maximum possibility in the second solution we first find the possibility distribution of the undominated sets and then a solution consists of those values of the decision variables which are undominated with maximum possibility but also produce the largest undominated values of the objective function for certain multiobjective possibilistic linear programs we show that the two solution concepts are identical

periodicity of a second order switched difference system over integers abstract in this paper a second order switched difference system which consists of two linear difference equations with a switching rule is proposed to study specifically the periodicity of a particular case is addressed deriving the appropriate rational values for parameter r which possess periodic integer solutions by the transformation method the particular second order difference system is transformed into a first order switched system and we prove that 1 this system possesses periodic integer solutions of prime period two if and only if r 1 2 2 any rational r except for the integers arises periodic integer solutions of prime period three 3 periodic integer solutions of prime period four exist if and only if r 1 2 4 this system possesses no periodic solutions of prime period five we also prove that if r 0 and the system has periodic integer solutions of prime period k 6 then the only possible values of r are reciprocals of integers

fuzzy programming and the pareto optimal set it is shown how fuzzy programming using either the min or product operator may be used to generate the whole pareto optimal set for nonlinear concave or convex multiobjective programming problems also a new solution procedure for a fuzzy program when the min operator is employed is presented

on a nonlinear generalized max type difference equation abstract the boundedness character of positive solutions of the following max type difference equation x n max a x n 1 p x n k r n n 0 where k n 1 the parameters a and r are positive and p is a nonnegative real number is studied in this paper our main results considerably improve results appearing in the literature

multidomain spectral solution of compressible viscous flows abstract we develop a nonoverlapping multidomain spectral collocation method to solve compressible viscous flows at the interfaces the advection terms are treated with a characteristic correction method the diffusion terms are treated with a penalty method spectral accuracy is demonstrated on linear model problems in one and two space dimensions the method is applied to a subsonic and a supersonic flow over a flat plate the results are compared to solutions of the boundary layer equations which show that two digit accuracy in the adiabatic plate temperature is obtained with 16 points in the boundary layer for a freestream mach number of two a second application is to a transonic flow in a two dimensional converging diverging nozzle where the computed results are compared to experimental data

a strategy for the efficient simulation of viscous compressible flows using a multi domain pseudospectral method abstract a new multi domain pseudospectral method is developed to simulate viscous compressible flow in a quasi one dimensional nozzle the flow variables at the interface points are advanced in time using the same second order time marching scheme as the interior points the spatial derivatives of the inviscid flux vector are evaluated at the interface points using a spectrally accurate modification of van leer s flux vector splitting method the derivatives of the viscous flux vector are evaluated alternately from neighboring sub domains the scheme is found to be spectrally accurate shock waves are resolved without oscillations for moderate reynolds numbers

global stability of a max type difference equation we show that every positive solution to the difference equationx n maxa 1x n p 1 a 1 a 2x n p 2 a 2 a kx n p k a k n n 0 where p i i 1 k are natural numbers such that 1 0 a i 1 1 i 1 k converges to max 1 i ka i 1 a i 1 this result improves and complements the main result in our recent note s stevic global stability of a difference equation with maximum appl math comput 210 2009 525 529 since it also considers the case when a i 1 0 i 1 k

a new approach to uncertain parameter linear programming abstract a novel method for solving uncertain linear programming is put forward in this paper in contrast to stochastic linear programming and most fuzzy linear programming models the parameters of the problem discussed here are neither random variables with known probability distributions nor fuzzy parameters with known possibility distributions all we know about the parameters is merely their intervals of existence to solve this kind of uncertain linear programming might be very attractive since many actual decision problems could be formulated as such if we do not have enough information about the parameters in this paper the concept of a confidence function for inequalities is introduced based on this definition the problem is solved by an iterative algorithm then the convergence of the algorithm is proved and the decision risk grades for different confidence functions are discussed finally an illustrative example is given to demonstrate the actual application of thismethod

on the max type equation xn 1 max axn xn 2 abstract we show that every well defined solution of the difference equation x n 1 max a x n x n 2 n n 0 where a r is eventually periodic with period three

a direct solver with o n complexity for variable coefficient elliptic pdes discretized via a high order composite spectral collocation method a numerical method for solving elliptic pdes with variable coefficients on two dimensional domains is presented the method is based on high order composite spectral approximations and is designed for problems with smooth solutions the resulting system of linear equations is solved using a direct as opposed to iterative solver that has optimal o n complexity for all stages of the computation when applied to problems with nonoscillatory solutions such as the laplace and the stokes equations numerical examples demonstrate that the scheme is capable of computing solutions with a relative accuracy of 10 10 or better for challenging problems such as highly oscillatory helmholtz problems and convection dominated convection diffusion equations in terms of speed it is demonstrated that a problem with a nonoscillatory solution that was discretized using 10 8 nodes can be solved in 115 minutes on a personal workstation with two quad core 3 3 ghz cpus since the solver is direct and the solution

computation of electromagnetic scattering with a non conforming discontinuous spectral element method in this paper we solve electromagnetic scattering problems by approximating maxwell s equations in the time domain with a high order quadrilateral discontinuous spectral element method dsem the method is a collocation form of the discontinuous galerkin method for hyperbolic systems where the solution is approximated by a tensor product legendre expansion and inner products are replaced with gauss legendre quadratures to increase flexibility of the method we use a mortar element method to couple element faces mortars provide a means for coupling element faces along which the polynomial orders differ which allows the flexibility to choose the approximation order within an element by considering only local resolution requirements mortars also permit local subdivision of a mesh by connecting element faces that do not share a full side we present evidence showing that the convergence of the non conforming approximations is spectral along with examples of their use copyright 2001 john wiley sons ltd

stability of multiobjective nlp problems with fuzzy parameters in the objectives and constraints functions abstract this paper deals with the stability of multiobjective nonlinear programming problems with fuzzy parameters in the objectives and constraints functions these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the qualitative analysis of the notions solvability set stability sets of the first kind and of the second kind in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of pareto optimality an algorithm for obtaining any subset of the parametric space which has the same corresponding pareto optimal solution is also presented an illustrative example is given to clarify the obtained results

a difference equation with eventually periodic solutions we show that every solution of the difference equation xn 1 max 1xn axn 1 n 0 1 where the parameter a and the initial conditions x 1 and x0 are nonzero real numbers is eventually periodic with period 2 3 or 4 we also give a precise description of the period in terms of a and the initial conditions

a conservative staggered grid chebyshev multidomain method for compressible flows we present a new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems the solution unknowns are defined at the nodes of a gauss quadrature rule the fluxes are evaluated at the nodes of a gauss lobatto rule the method is conservative free stream preserving and exponentially accurate a significant advantage of the method is that subdomain corners are not included in the approximation making solutions in complex geometries easier to compute

periodicity of a class of nonautonomous max type difference equations abstract in this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x n max f 1 x n k 1 n f m x n k m n x n s n n 0 and x n min f 1 x n k 1 n f m x n k m n x n s n n 0 where 1 k 1 k m m s n and where the functions f i 0 n 0 0 1 i m satisfy some additional conditions these results considerably extend and unify numerous results on max type difference equations existing in the literature

short note a comparison of computational efficiencies of spectral difference method and correction procedure via reconstruction we report computational efficiencies of two types of numerical solvers the first type uses the spectral difference sd method and the second one uses the correction procedure via reconstruction cpr in this paper we employ the lumped g 2 scheme proposed by huynh as an example of the cpr approach the solvers deal with both inviscid euler equations and navier stokes equations on 2d unstructured grids which are comprised of all quadrilateral cells both types of solvers are programmed using fortran 90 with similar management of data structures we employ identical time marching schemes for both sd and cpr methods spatial 3rd and 4th order of accuracy for both methods is demonstrated by a study of a moving inviscid vortex the comparisons were directed to measure the computational efficiency of both sd and cpr methods in spatial discretization with respect to the fourth order methods cpr is 27 faster than sd for inviscid flow and more promisingly cpr is over 40 faster than sd for viscous flow

a stable penalty method for the compressible navier stokes equations iii multidimensional domain decomposition schemes this paper concluding the trilogy develops schemes for the stable solution of wave dominated unsteady problems in general three dimensional domains the schemes utilize a spectral approximation in each subdomain and asymptotic stability of the semidiscrete schemes is established the complex computational domains are constructed by using nonoverlapping quadrilaterals in the two dimensional case and hexahedrals in the three dimensional space to illustrate the ideas underlying the multidomain method a stable scheme for the solution of the three dimensional linear advection diffusion equation in general curvilinear coordinates is developed the analysis suggests a novel yet simple stable treatment of geometric singularities like edges and vertices the theoretical results are supported by a two dimensional implementation of the scheme the main part of the paper is devoted to the development of a spectral multidomain scheme for the compressible navier stokes equations on conservation form and a unified approach for dealing with the open boundaries and subdomain boundaries is presented well posedness and asymptotic stability of the semidiscrete scheme is established in a general curvilinear volume with special attention given to a hexahedral domain the treatment includes a stable procedure for dealing with boundary conditions at a solid wall the efficacy of the scheme for the compressible navier stokes equations is illustrated by obtaining solutions to subsonic and supersonic boundary layer flows with various types of boundary conditions the results are found to agree with the solution of the compressible boundary layer equations