time discretization of an integro differential equation of parabolic type the stability and convergence properties of two time discretizations of an integro differential equation of parabolic type are studied the methods reduce to the backward euler and crank nicolson methods if the integral term is absent the integral term is approximated in each case by a quadrature rule with relatively high order truncation error so that a relatively large time step can be used for the quadrature in order to reduce the memory and computational requirements of the method

approximation of solutions of hammerstein equations with bounded strongly accretive nonlinear operators abstract suppose x is a real q uniformly smooth banach space and f k x x are bounded strongly accretive maps with d k f x x let u denote the unique solution of the hammerstein equation u k f u 0 a new explicit coupled iteration process is shown to converge strongly to u no invertibility assumption is imposed on k and the operators k and f need not be defined on compact subsets of x furthermore our new technique of proof is of independent interest finally some interesting open questions are included

existence and multiplicity of non negative solutions for systems of perturbed hammerstein integral equations abstract we study the existence of positive solutions for a system of perturbed hammerstein integral equations our setting is quite general and covers a wide class of systems of boundary value problems the main ingredient in our theory is the classical fixed point index theory for compact maps

halpern s iteration for bregman strongly nonexpansive mappings in reflexive banach spaces we investigate strong convergence for bregman strongly nonexpansive mappings by halpern s iteration in the framework of reflexive banach spaces using the obtained result convergence for a family of bregman strongly nonexpansive mappings is also discussed as applications we apply our main result to problems of finding zeros of maximal monotone operators and equilibrium problems in reflexive banach spaces

right bregman nonexpansive operators in banach spaces abstract we introduce and study new classes of bregman nonexpansive operators in reflexive banach spaces these classes of operators are associated with the bregman distance induced by a convex function in particular we characterize sunny right quasi bregman nonexpansive retractions and as a consequence we show that the fixed point set of any right quasi bregman nonexpansive operator is a sunny right quasi bregman nonexpansive retract of the ambient banach space

two strong convergence theorems for bregman strongly nonexpansive operators in reflexive banach spaces abstract we study the convergence of two iterative algorithms for finding common fixed points of finitely many bregman strongly nonexpansive operators in reflexive banach spaces both algorithms take into account possible computational errors we establish two strong convergence theorems and then apply them to the solution of convex feasibility variational inequality and equilibrium problems

an adi fdtd method for periodic structures in this communication the alternating direction implicit finite difference time domain adi fdtd method is extended to analyze periodic structures in the implicit updates of the adi fdtd method the periodic boundary condition leads to a cyclic matrix instead of inverting the cyclic matrix directly the problem is converted into two auxiliary linear systems that can be solved using the tridiagonal matrix solver consequently only 7n arithmetic operations are required for each implicit update and the efficiency of the adi fdtd method is retained numerical examples further demonstrate the effectiveness of this periodic adi fdtd method

on the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel ii nonsmooth initial data abstract backward euler methods are considered for a parabolic integrodifferential equation with a memory term containing a weakly singular kernel the integral term is treated by means of a convolution quadrature suggested by lubich some results from lubich s discretized fractional calculus play a crucial role in error analyses the stability and convergence properties of the time discretizations are derived and are applied to the semidiscrete equations built by the galerkin finite element methods in the space variables

unconditionally stable fdtd method based on lod scheme for analysis of 2 d periodic structures for modeling periodic structures at oblique incidence an unconditionally stable finite difference time domain technique is presented by applying the locally one dimensional lod scheme to the field transformation technique by splitting the space operator matrix in an appropriate way the transformed maxwell s equations can be subdivided into two sub steps for an efficient implementation the accuracy and efficiency of the proposed method are verified by comparing with the results of the reference 4 and the split field method respectively

efficient implementation of 2 d split field fdtd method for analyzing periodic structures this communication presents an efficient implementation of the 2 d split field method for solving problems of the oblique incident plane wave on periodic structures first by only splitting one field quantity q x and adopting the locally one dimensional scheme the transformed maxwell s equations are reformulated into a concise form and then by some matrix operation the field updating of the proposed method is implemented in the explicit scheme compared with the traditional split field method the courant friedrich levy stability condition of the proposed method is weaker and the cpu time and memory are saved numerical results demonstrate that the proposed method is more efficient

iterative approximation of solutions of nonlinear equations of hammerstein type abstract suppose x is a real q uniformly smooth banach space and f k x x are lipschitz strongly accretive maps with d k f x x let u denote the unique solution of the hammerstein equation u k f u 0 an iteration process recently introduced by chidume and zegeye is shown to converge strongly to u no invertibility assumption is imposed on k and the operators k and f need not be defined on compact subsets of x furthermore our new technique of proof is of independent interest finally some interesting open questions are included

space time spectral method for a weakly singular parabolic partial integro differential equation on irregular domains abstract the spectral method is proposed for the partial integro differential equations with a weakly singular kernel on irregular domains the space discretization is based on the nodal spectral element method using the lagrange polynomials basis associated with the gauss lobatto legendre quadrature nodes also the model is discretized in time with the legendre spectral galerkin method the discretization leads to conversion of the problem to a sylvester matrix equation which can be solved efficiently by the qz algorithm gardiner et al 1992 the convergence of the method is proven by providing a priori l 2 error estimate numerical results illustrate the efficiency and spectral accuracy of the proposed method

finite element methods for parabolic and hyperbolic partial integro differential equations on formule plusieurs methodes de galerkin a temps discret pour des equations integrodifferentielles paraboliques

implementation of the periodic boundary condition in the finite difference time domain algorithm for fss structures a method for implementing the general floquet boundary condition in the finite difference time domain algorithm fdtd is presented the floquet type of phase shift boundary condition is incorporated into the time domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step with this approach the characteristics of periodic structures comprised of arbitrarily shaped inhomogeneous geometries can be computed for an arbitrary angle of incidence theoretical results are compared for various planar frequency selective surfaces fss and for one with a three dimensional element e g a thick double concentric square loop

numerical solution of nonlinear weakly singular partial integro differential equation via operational matrices in this paper we propose and analyze an efficient matrix method based on shifted legendre polynomials for the solution of non linear volterra singular partial integro differential equations pides the operational matrices of integration differentiation and product are used to reduce the solution of volterra singular pides to the system of non linear algebraic equations some useful results concerning the convergence and error estimates associated to the suggested scheme are presented illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method

fundamental schemes for efficient unconditionally stable implicit finite difference time domain methods generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite difference time domain fdtd methods are presented the fundamental schemes constitute a family of implicit schemes that feature similar fundamental updating structures which are in simplest forms with most efficient right hand sides the formulations of fundamental schemes are presented in terms of generalized matrix operator equations pertaining to some classical splitting formulae including those of alternating direction implicit locally one dimensional and split step schemes to provide further insights into the implications and significance of fundamental schemes the analyses are also extended to many other schemes with distinctive splitting formulae detailed algorithms are described for new efficient implementations of the unconditionally stable implicit fdtd methods based on the fundamental schemes a comparative study of various implicit schemes in their original and new implementations is carried out which includes comparisons of their computation costs and efficiency gains

error estimates for semidiscrete finite element methods for parabolic integro differential equations application des methodes d elements finis aux equations integro differentielles de type parabolique avec un noyau integral forme par un operateur aux derivees partielles d ordre 2

a generalized proximal point algorithm for the variational inequality problem in a hilbert space we consider a generalized proximal point method for solving variational inequality problems with monotone operators in a hilbert space it differs from the classical proximal point method as discussed by rockafellar for the problem of finding zeroes of monotone operators in the use of generalized distances called bregman distances instead of the euclidean one these distances play not only a regularization role but also a penalization one forcing the sequence generated by the method to remain in the interior of the feasible set so that the method becomes an interior point one under appropriate assumptions on the bregman distance and the monotone operator we prove that the sequence converges weakly if and only if the problem has solutions in which case the weak limit is a solution if the problem does not have solutions then the sequence is unbounded we extend similar previous results for the proximal point method with bregman distances which dealt only with the finite dimensional case and which applied only to convex optimization problems or to finding zeroes of monotone operators which are particular cases of variational inequality problems

bregman monotone optimization algorithms a broad class of optimization algorithms based on bregman distances in banach spaces is unified around the notion of bregman monotonicity a systematic investigation of this notion leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block iterative surrogate bregman projection schemes another key contribution is the introduction of a class of operators that is shown to be intrinsically tied to the notion of bregman monotonicity and to include the operators commonly found in bregman optimization methods special emphasis is placed on the viability of the algorithms and the importance of legendre functions in this regard various applications are discussed

cα regularity for non autonomous linear integrodifferential equations of parabolic type abstract linear integrodifferential equations in general banach space are studied and applications are given to linear integrodifferential partial differential equations

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

convergence theorems for maximal monotone operators and fixed point problems in banach spaces our purpose in this paper is to prove strong convergence theorems for approximation of a common zero of a finite family of maximal monotone operators which is also a fixed point for a left bregman strongly relatively nonexpansive mapping in a reflexive banach space we also apply our results to approximation of solutions of nonlinear integral equations of hammerstein type in reflexive banach spaces

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

strong convergence of a proximal type algorithm in a banach space in this paper we study strong convergence of the proximal point algorithm it is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator but it fails to converge strongly then in math program 87 2000 pp 189 202 solodov and svaiter introduced the new proximal type algorithm to generate a strongly convergent sequence and established a convergence property for it in hilbert spaces our purpose is to extend solodov and svaiter s result to more general banach spaces using this we consider the problem of finding a minimizer of a convex function

finite element approximation of a parabolic integro differential equation with a weakly singular kernel we give error estimates for the numerical solution by means of the galerkin finite element method of an integro differential equation of parabolic type with a memory term containing a weakly singular kernel optimal order estimates are shown for spatially semidiscrete and completely discrete methods special attention is paid to the regularity of the exact solution

numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data error estimates are derived for the discretization in space by finite elements and in time by the backward euler method of a parabolic equation with a semilinear memory term special attention is paid to the case of nonsmooth data and the computation of the memory term by quadrature

numerical analysis of nonlinear subdiffusion equations we present a general framework for the rigorous numerical analysis of time fractional nonlinear parabolic partial differential equations with a fractional derivative of order alpha in 0 1 in time it relies on three technical tools a fractional version of the discrete gronwall type inequality discrete maximal regularity and regularity theory of nonlinear equations we establish a general criterion for showing the fractional discrete gronwall inequality and verify it for the l1 scheme and convolution quadrature generated by backward difference formulas further we provide a complete solution theory e g existence uniqueness and regularity for a time fractional diffusion equation with a lipschitz nonlinear source term together with the known results of discrete maximal regularity we derive pointwise l 2 omega norm error estimates for semidiscrete galerkin finite element solutions and fully discrete solutions which are of order o h 2 up to a logarithmic factor and o tau alpha

spectral fdtd a novel technique for the analysis of oblique incident plane wave on periodic structures this paper introduces a new technique which calculates the reflection coefficient for the plane wave incident on planar periodic structures the method referred to as spectral finite difference time domain sfdtd replaces the conventional single angle incident wave with a constant transverse wavenumber ctw wave because the transverse wavenumbers are constant the fields have no delay in the transverse plane x y plane and pbc periodic boundary condition can be directly implemented in the time domain for both oblique and normal incident waves the stability criterion for this new fdtd technique is angle independent and therefore this method works well for incident angles close to grazing spl theta 90 spl deg as well as normal incident spl theta 0 spl deg this shows the efficiency of the method compared to other available fdtd techniques for the same purpose that force a more restricted stability criterion as angles turns to grazing the validity of this method is verified by comparing the reflection coefficient calculated by this method with the analytical results of a grounded slab the results of this technique are also compared with method of moments for a periodic array of metallic patches and a good agreement is observed a periodic array of metallic patches above a pec plate is analyzed and the reflection coefficient is calculated over a wide frequency band for angles varying from 0 spl deg to close to 90 spl deg

analysis of a temporal discretization for a semilinear fractional diffusion equation abstract this paper considers a temporal discretization of a semilinear fractional diffusion equation with nonsmooth initial data with appropriately graded temporal grids first order temporal accuracy in the norm of l 2 0 t l 2 is derived by a new discrete gronwall s inequality and then first order temporal accuracy in the norm of l 0 t l 2 is established for 1 2 1 finally numerical results are provided to verify the theoretical results

positive solvability of systems of nonlinear hammerstein integral equations the paper deals with the existence of positive continuous solutions to systems of nonlinear hammerstein integral equations the main tool used in the proofs is fixed point index theory in a cone the results obtained here are essentially different from existing ones in the literature