three step iterative algorithm for a system of set valued variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of set valued variational inclusions with h monotone operators we prove the convergence of a new three step iterative algorithm for this system of set valued variational inclusions the results in this paper extend and improve some known results from the literature

on an iterative method for variational inequalities a number of numerical solutions are presented as examples of a new iterative method for variational inequalities the iterative method is based on the reduction of variational inequalities to the wiener hopf equations for obstacle problems the convergence is guaranteed inw 1 p spaces forp 2 the examples presented are one and two dimensional obstacle problems in cases when the greens function is known but the method is very general

boundary spectral method for acoustic scattering and radiation problems the spectral method is considered in solving boundary integral equations by subtracting known solutions from the helmholtz integral equation the singularities of the helmholtz integral equation are removed therefore any order of basis functions used in spectral methods that times nonsingular kernels in the modified helmholtz integral equation can be integrated easily and efficiently instead of solving the variables at collocation points using conventional methods the generalized fourier coefficients are solved by the spectral method which reduces the number of unknowns and the storage of matrix elements in computation scattering and radiation problems from a sphere are used to illustrate the technique in the present paper

a new system of generalized mixed quasi variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of generalized mixed quasi variational inclusions with h monotone operators we prove the convergence of a new iterative algorithm for this system of generalized mixed quasi variational inclusions the results in this paper extend and improve some known results in the literature

iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities in this paper we study iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities which include as a special case some known results in this field our results are the extension and improvements of the results of siddiqi and ansari ding and zeng

a study on the stability and numerical dispersion of the lumped network fdtd method the lumped network finite difference time domain ln fdtd technique is an extension of the conventional fdtd method that enables the incorporation of linear one port lns in a single fdtd cell this paper studies the stability and the numerical dispersion of this technique to this end an isotropic medium that is uniformly loaded with lns in the x direction is considered as a working model the stability analysis based on the von neumann method is performed for general mth order lns and closed form stability conditions are derived for some particular cases the numerical dispersion relation is obtained for plane wave propagation in the proposed ln loaded medium it is shown that lns can be interpreted in terms of an effective frequency dependent permittivity and as a consequence the ln loaded medium can be viewed as a uniaxial medium the numerical admittance of the lns is also obtained showing that as a side effect of the time discretization the ln parameters become frequency dependent e g for the resistor case the resistance becomes a function of the frequency

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

a perturbed algorithm for variational inclusions a perturbed method for solving a new class of variational inclusions is presented and a convergence result which includes as a special case some known results in this field is given

a system of generalized variational inclusions involving generalized h accretive mapping in real q uniformly smooth banach spaces abstract in this paper we consider a class of accretive mappings called generalized h accretive mappings in banach spaces we prove that the proximal point mapping of the generalized h accretive mapping is single valued and lipschitz continuous further we consider a system of generalized variational inclusions involving generalized h accretive mappings in real q uniformly smooth banach spaces using proximal point mapping method we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions furthermore we discuss the convergence criteria of the iterative algorithm under some suitable conditions our results can be viewed as a refinement and improvement of some known results in the literature

implementation of a continuation method for normal maps this paper presents an implementation of a nonsmooth continuation method of which the idea was originally put forward by alexander et al we show how the method can be computationally implemented and present numerical results for variational inequality problems in up to 96 variables

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

a method to overcome computational difficulties in the exterior acoustics problem when the boundary integral equation method is applied to exterior acoustics problems singularities occur in the resulting algebraic equations at various frequencies associated with the eigenvalues of an interior problem these frequencies are referred to as forbidden and various methods have been devised to overcome the computational difficulties presented at these frequencies the work presented here is an extension to the chief method in that higher derivatives in addition to the function itself are constrained to be zero at selected points in the interior domain whereas the relative success of either method depends on the quantity and selection of interior points the superchief method requires fewer interior points and is less sensitive to point selection resulting in improved robustness without a significant increase in computational complexity

acoustic scattering by a modified werner method a modified integral werner method is used to calculate pressure scattered by an axisymmetric body immersed in a perfect and compressible fluid subject to a harmonic acoustic field this integral representation is built as the sum of a potential of a simple layer and a potential of volume it is equivalent to the exterior helmholtz problem with neumann boundary condition for all real wave numbers of the incident acoustic field for elastic structure scattering problems the modified werner method is coupled with an elastodynamic integral formulation in order to account for the elastic contribution of the displacement field at the fluid structure interface the resulting system of integral equations is solved by the collocation method with a quadratic interpolation the introduction of a weighting factor in the modified werner method decreases the number of volume elements necessary for a good convergence of results this approach becomes very competitive when it is compared with other integral methods that are valid for all wave numbers a numerical comparison with an experiment on a tungsten carbide end capped cylinder allows a glimpse of the interesting possibilities for using the coupling of the modified werner method and the integral elastodynamic equation used in this research

error estimation and step size control for delay differential equation solvers based on continuously embedded runge kutta sarafyan methods abstract this paper considers the use of continuously embedded runge kutta sarafyan methods for the solution of delay differential equations it discusses simple ways to improve the error estimation and step size selection strategies for delay solvers based on sarafyan methods numerical results are given which demonstrate the manner in which these estimates improve the accuracy of the solvers in a natural way

existence and convergence theorems for a class of multi valued variational inclusions in banach spaces abstract an existence theorem for a new class of multi valued variational inclusion problems is established in smooth banach spaces further it is shown that a sequence of a mann type iteration algorithm is strongly convergent to the solutions in this class of variational inclusion problems

perturbed ishikawa type iterative algorithm for generalized quasivariational inclusions in this paper a perturbed ishikawa type iterative algorithm of solving a new class of generalized nonlinear implicit quasivariational inclusions are suggested and analysed first an existence theorem of solutions for generalized nonlinear implicit quasivariational inclusion is proved under suitable assumptions then the convergence of the perturbed ishikawa type iterative sequences generated by the new algorithm is proved as special cases some known results are also discussed

an iterative method for a system of generalized mixed quasi variational inclusions with a η monotone mappings in this paper we introduce and consider a new system of generalized mixed quasi variational inclusions with a h monotone mappings we prove the convergence of a new iterative algorithm for this system of generalized mixed quasi variational inclusions our results can be viewed as a refinement and improvement of the previously known results in the literature

set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions without compactness condition in banach spaces by using michael s selection theorem and nadler s theorem an existence theorem and an iterative algorithm for solving this kind of set valued variational inclusions in banach spaces are established and suggested

on generalized set valued variational inclusions abstract we point out a basic flaw made by m a noor 1998 j math anal appl 228 206 220 construct a new iterative algorithm for a class of variational inclusions involving non monotone set valued mappings with noncompact values and study the convergence of the perturbed ishikawa iterative process for solving a class of the generalized single valued variational inclusions

existence and iterative approximation of solutions of generalized mixed equilibrium problems in this paper we consider a generalized mixed equilibrium problem involving non monotone set valued mappings in real hilbert space we extend the notions of the yosida approximation and its corresponding regularized operator given by moudafi and thera a moudafi m thera proximal and dynamical approaches to equilibrium problems in lecture notes in econom and math system vol 477 springer verlag berlin 2002 pp 187 201 and discuss some of their properties further we consider a generalized wiener hopf equation problem and show its equivalence with the generalized mixed equilibrium problem using a fixed point formulation of the generalized wiener hopf equation problem we construct an iterative algorithm furthermore we extend the notion of stability given by harder and hick a m harder t l hicks stability results for fixed point iteration procedures math japonica 33 5 1998 693 706 we prove the existence of a solution and discuss the convergence and stability of the iterative algorithm for the generalized wiener hopf equation problem since the generalized mixed equilibrium problems include variational inequalities as special cases the results presented in this paper continue to hold for these problems

piecewise smoothness local invertibility and parametric analysis of normal maps this paper is concerned with properties of the euclidean projection map onto a convex set defined by finitely many smooth convex inequalities and affine equalities under a constant rank constraint qualification we show that the projection map is piecewise smooth pc1 hence bouligand differentiable or directionally differentiable and a relatively simple formula is given for the b derivative these properties of the projection map are used to obtain inverse and implicit function theorems for associated normal maps using a new characterization of invertibility of a pc1 function in terms of its b derivative an extension of the implicit function theorem which does not require local uniqueness is also presented degree theory plays a major role in the analysis of both the locally unique case and its extension

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

examination clarification and simplification of stability and dispersion analysis for adi fdtd and cnss fdtd schemes we describe a rigorous analysis of unconditional stability for the alternating direction implicit finite difference time domain adi fdtd and crank nicholson split step cnss fdtd schemes avoiding use of the von neumann spectral criterion the proof is performed in the spectral domain and uses skew hermitivity of matrix terms in the adi and cnss total amplification matrices a bound for the total adi amplification matrix is provided while the cn and cnss fdtd amplification matrices are unitary the bound on the adi fdtd depends on the courant number importantly we have found that the adi fdtd amplification matrix is not normal i e the unit spectral radius alone cannot be used to prove the adi fdtd unconditional stability the paper also shows that the adi fdtd and cnss fdtd schemes share the same dispersion equation by a similarity of their total amplification matrices and the two schemes have identical numerical dispersion in the frame of plane waves

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

a simple method avoiding non uniqueness in the boundary element method for acoustic scattering problem the boundary element method bem is widely used for sound field analysis problems however it has a non uniqueness problem in the exterior domain various methods to avoid this problem have been developed however these are not easily applied to the bem in this paper a simple method called the ica ring inner cavity ringing method is proposed for avoiding the non uniqueness problem and this method is applied to the bem in both single and plural domains the concept of the ica ring method is that a scatterer in free space is hollowed as a shell and the volume is smaller the eigenfrequencies are shifted to a higher range next the mechanism of the non uniqueness problem in plural domains and a reason of the application of the ica ring method to the case of plural domains are explained finally some results calculated by the bem using the ica ring method are shown the calculational condition is that a cylinder with radius 0 125m floats in two dimensional free space in this case no calculationa

generalized set valued variational inclusions in q uniformly smooth banach spaces abstract in this paper a class of generalized set valued variational inclusions in banach spaces are introduced and studied which include many variational inclusions studied by others in recent years by using some new and innovative techniques several existence theorems for the generalized set valued variational inclusions in q uniformly smooth banach spaces are established and some perturbed iterative algorithms for solving this kind of set valued variational inclusions are suggested and analyzed our results improve and generalize many known algorithms and results

the mann and ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings abstract the purpose of this paper is to introduce and study the existence of solutions and convergence of mann and ishikawa iterative processes for a class of variational inclusions with accretive type mappings in banach spaces the results presented in this paper extend and improve the corresponding results of 1 9

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

some resolvent iterative methods for variational inclusions and nonexpansive mappings in this paper we suggest and analyze three step iterations for finding the common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions using the resolvent operator technique we also study the convergence criteria of three step iterative method under some mild conditions our results include the previous results of noor m aslam noor general variational inequalities and nonexpansive mappings j math anal appl 331 2007 810 822 and noor and huang m aslam noor zhenyu huang three step methods for nonexpansive mappings and variational inequalities appl math comput in press doi 10 1016 j amc 2006 08 088 as special cases and may be considered as an improvement and refinement of the previously known results

parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings a new class of parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings is introduced by applying resolvent operator technique of h maximal monotone mapping and the property of fixed point set of set valued contractive mappings the behavior and sensitivity analysis of the solution set of the parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings are studied the continuity and lipschitz continuity of the solution set with respect to the parameter are proved under suitable assumptions our approach and results are new and improve unify and extend previous many known results in this field

hypersingular boundary integral equations for exterior acoustic problems a bounded form of the hypersingular helmholtz integral equation for 3 d acoustic problems is developed in this paper all integrals with singular kernels are regularized within each regular surface element in the sense of kellogg with twice continuous differentiability the standard gaussian quadrature formula is applied without any special treatment for all the computational points the collocation points are chosen to be the gauss legendre nodes and no interpolation function is assumed for acoustic variables

resolvent operator technique for generalized implicit variational like inclusion in banach space a new class of g accretive mappings is introduced and studied in banach space by using the properties of g accretive mappings the concept of resolvent operators associated with the classical m accretive operators is extended and an iterative algorithm for a new class of generalized implicit variational like inclusion involving g accretive mappings and its convergence results are established in banach space

three step iterative algorithms for multivalued quasi variational inclusions in this paper we suggest and analyze some new classes of three step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique new iterative algorithms include the ishikawa mann and noor iterations for solving variational inclusions inequalities and optimization problems as special cases the results obtained in this paper represent an improvement and a significant refinement of previously known results

approximation solvability of nonlinear random a η resolvent operator equations with random relaxed cocoercive operators in this paper we introduce and study a new class of nonlinear random a h resolvent operator equations with random relaxed cocoercive operators in hilbert spaces by using chang s lemma theorem 3 1 of liu and li and the resolvent operator technique for a h monotone operators due to lan we also prove the existence theorems of the solutions and convergence theorems of the new generalized random iterative procedures with errors for this nonlinear random a h resolvent operator equations involving non monotone random set valued operators in hilbert spaces the results presented in this paper improve and generalize some known corresponding results in the literature

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

stability and phase error analysis of fd td in dispersive dielectrics four fd td extensions for the modeling of pulse propagation in debye or lorentz dispersive media are analyzed through studying the stability and phase error properties of the coupled difference equations corresponding to maxwell s equations and to the equations for the dispersion for good overall accuracy the author shows that all schemes should be run at their courant stability limit and that the timestep should finely resolve the medium timescales particularly for debye schemes it should be at least spl delta t 10 sup spl minus 3 spl tau while for lorentz schemes it should be spl delta t 10 sup spl minus 2 spl tau where spl tau is a typical medium relaxation time a numerical experiment with a debye medium confirms this the author has determined that two of the discretizations for debye media are totally equivalent in the lorentz medium case the author establishes that the method that uses the polarization differential equation to model dispersion is stable for all wavenumbers and that the method using the local in time constitutive relation is weakly unstable for modes with wavenumber k such that k spl delta x spl pi 2

generalized nonlinear quasi variational inclusions in banach spaces this paper introduces a new class of generalized nonlinear quasi variational inclusions involving generalized m accretive mappings in p uniformly smooth real banach spaces by using the resolvent operator technique for generalized m accretive mappings due to huang et al n j huang y p fang c x deng nonlinear variational inclusions involving generalized m accretive mappings in proceedings of the bellman continuum international workshop on uncertain systems and soft computing beijing china july 24 27 2002 pp 323 327 and nadler theorem s b nadler jr multivalued contraction mappings pacific j math 30 1969 475 488 we construct an iterative algorithm for solving generalized nonlinear quasi variational inclusions with strongly accretive and relaxed accretive mappings in p uniformly smooth real banach spaces then we prove the existence of solutions for our inclusions without compactness assumption and convergence of the iterative sequences generated by the algorithm in p uniformly smooth real banach spaces some special cases are also discussed

the generalized quasi variational inequality problem with applications a new problem called the generalized quasi variational inequality problem is introduced this new problem extends all the existing variational inequality problems in finite dimensional spaces and enlarges the class of problems that can be approached by the variational inequality theory some existence results without convexity assumptions are presented applications to mathematical and equilibrium programming are given

on variational inclusion and common fixed point problems in hilbert spaces with applications abstract the purpose of this paper is to introduce a general iterative method for finding a common element of the solution set of quasi variational inclusion problems and of the common fixed point set of an infinite family of nonexpansive mappings in the framework hilbert spaces strong convergence of the sequences generated by the purposed iterative scheme is obtained

a bem fmm approach applied to the combined convected helmholtz integral formulation for the solution of aeroacoustic problems abstract exterior and interior acoustic calculations often exploit the advantages of boundary element method bem numerical scheme due to the large dimension of dense matrices arising in real case applications direct matrix vector products become prohibitive since the computational cost of standard methods increases quadratically in this work the black box fast multipole method bbfmm based on the chebyshev interpolation is extended to the integral solution of the convective helmholtz equation stabilized using the combined helmholtz integral equation formulation chief the chief approach relies on the solution of an over determined linear system achieved by adding a set of points internal to the scattering body in order to handle the distribution of the chief points within the body volume a robust stochastic approach has been also developed moreover an adaptive bbfmm abbfmm is presented for handling the oscillating kernels such as those arising in the solution of the convective helmholtz equation the proposed approach which has a complexity of o n l o g n is interesting for industrial applications especially in the aeroacoustic field

iterative approximation of solutions for a class of completely generalized set valued quasi variational inclusions in this paper we study a new class of completely generalized set valued quasi variational inclusion problems in banach spaces this inclusion problem is a generalization of the generalized set valued variational inclusion problem studied by chang et al we show that chang et al s algorithm can be modified for finding approximate solutions to this class of quasi variational inclusion problems moreover the modified algorithm generalizes and improves a number of results in the literature

generalized set valued variational inclusions and resolvent equations in banach spaces abstract in this paper we construct a new iterative algorithm for set valued variational inclusions without the compactness condition and study the convergence of the perturbed ishikawa iterative process for solving a class of the generalized single valued variational inclusions in banach spaces the result obtained in this paper is a generalization and improvement of noor s theorem 1

a boundary integral method for acoustic radiation and scattering in this article a computational method is proposed for computing the helmholtz integral equation for acoustic radiation and scattering problems with a three dimensional body shape unlike the previous boundary element method the integration of acoustic properties is based on the global body surface instead of local elements the approximation function of body geometry and the weighting function of numerical integration are independently chosen when the singular kernels of helmholtz equation are regularized as bounded discontinuous functions the order of integration polynomials for acoustic properties can be arbitrarily chosen therefore the accuracy and efficiency of computation can be increased

on the generalized implicit quasivariational inequalities abstract in the present paper we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set valued mappings and construct some new iterative algorithms we prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set valued mappings without compactness and the convergence of iterative sequences generated by the algorithms we also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities