s semantics for logic programming a retrospective look the paper provides an overview of the s semantic approach to the semantics of logic programs which had been developed about twenty years ago the aim of such an approach was that of providing a suitable base for program analysis by means of a semantics which really captures the operational behavior of logic programs and thus offers useful notions of observable program equivalences the semantics is given in terms of extended interpretations which are more expressive than herbrand interpretations extends the standard herbrand semantics and can be obtained as a result of both top down and bottom up constructions the approach has been applied to several extensions of positive logic programs and used to develop semantic based techniques for program analysis verification and transformation

numerical methods for systems of nonlinear parabolic equations with time delays abstract the purpose of this paper is to investigate some numerical aspects of a class of coupled nonlinear parabolic systems with time delays the system of parabolic equations is discretized by the finite difference method which yields a coupled system of nonlinear algebraic equations the mathematical analysis of the nonlinear system is by the method of upper and lower solutions and its associated monotone iterations three monotone iterative schemes are presented and it is shown that the sequence of iterations from each one of these iterative schemes converges monotonically to a unique solution of the finite difference system a theoretical comparison result for the various monotone sequences and error estimates for the three monotone iterative schemes are obtained it is also shown that the finite difference solution converges to the classical solution of the parabolic system as the mesh size decreases to zero

accelerated monotone iterative methods for finite difference equations of reaction diffusion this paper is concerned with numerical methods for a finite difference system of reaction diffusion convection equation under nonlinear boundary condition various monotone iterative methods are presented and each of these methods leads to an existence comparison theorem as well as a computational algorithm for numerical solutions the monotone property of the iterations gives improved upper and lower bounds of the solution in each iteration and the rate of convergence of the iterations is either quadratic or nearly quadratic depending on the property of the nonlinear function application is given to a model problem from chemical engineering and some numerical results including a test problem with known analytical solution are presented to illustrate the various rates of convergence of the iterations

monotone iterative methods for finite difference system of reaction diffusion equations this paper presents an existence comparison theorem and an iterative method for a nonlinear finite difference system which corresponds to a class of semilinear parabolic and elliptic boundary value problems the basic idea of the iterative method for the computation of numerical solutions is the monotone approach which involves the notion of upper and lower solutions and the construction of monotone sequences from a suitable linear discrete system using upper and lower solutions as two distinct initial iterations two monotone sequences from a suitable linear system are constructed it is shown that these two sequences converge monotonically from above and below respectively to a unique solution of the nonlinear discrete equations this formulation leads to a well posed problem for the nonlinear discrete system applications are given to several models arising from physical chemical and biological systems numerical results are given to some of these models including a discussion on the rate of convergence of the monotone sequences

monotone iterates for solving nonlinear integro parabolic equations of volterra type the paper deals with numerical solving of nonlinear integro parabolic problems based on the method of upper and lower solutions a monotone iterative method is constructed existence and uniqueness of a solution to the nonlinear difference scheme are established an analysis of convergence rates of the monotone iterative method is given construction of initial upper and lower solutions is discussed numerical experiments are presented

periodic solutions of parabolic systems with time delays existence of maximal and minimal periodic solutions of a coupled system of parabolic equations with time delays and with nonlinear boundary conditions is discussed the proof of the existence theorem is based on the method of upper and lower solutions and its associated monotone iterations this method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic parabolic system an application is given to a competitor competitor mutualist model which consists of a coupled system of three reaction diffusion equations with time delays

uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems this paper deals with discrete monotone iterative methods for solving semilinear singularly perturbed parabolic problems monotone sequences based on the accelerated monotone iterative method are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem this monotone convergence leads to the existence uniqueness theorem an analysis of uniform convergence of the monotone iterative method to the solutions of the nonlinear difference scheme and continuous problem is given numerical experiments are presented

a uniform monotone alternating direction scheme for nonlinear singularly perturbed parabolic problems this paper deals with a monotone alternating direction adi scheme for solving nonlinear singularly perturbed parabolic problems monotone sequences based on the method of upper and lower solutions are constructed for a nonlinear difference scheme which approximates the nonlinear parabolic problem the monotone sequences possess quadratic convergence rate an analysis of uniform convergence of the monotone adi scheme to the solutions of the nonlinear difference scheme and to the continuous problem is given numerical experiments are presented

numerical methods for nonlinear integro parabolic equations of fredholm type abstract this paper is concerned with iterative methods for numerical solutions of a class of nonlocal reaction diffusion convection equations under either linear or nonlinear boundary conditions the discrete approximation of the problem is based on the finite difference method and the computation of the finite difference solution is by the method of upper and lower solutions three types of quasi monotone reaction functions are considered and for each type a monotone iterative scheme is obtained each of these iterative schemes yields two sequences which converge monotonically from above and below respectively to a unique solution of the finite difference system this monotone convergence leads to an existence uniqueness theorem as well as a computational algorithm for the computation of the solution an error estimate between the computed approximations and the true finite difference solution is obtained for each iterative scheme these error estimates are given in terms of the strength of the reaction function and the effect of diffusion convection and are independent of the true solution applications are given to three model problems to illustrate some basic techniques for the construction of upper and lower solutions and the implementation of the computational algorithm

monotone iterates with quadratic convergence rate for solving weighted average approximations to semilinear parabolic problems this paper deals with discrete monotone iterative methods for solving semilinear singularly perturbed parabolic problems monotone sequences based on the accelerated monotone iterative method are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem this monotone convergence leads to the existence uniqueness theorem an analysis of convergence of the monotone iterative method to the solutions of the nonlinear difference scheme is given numerical experiments are presented

asymptotic behavior of solutions for a cooperation diffusion model with a saturating interaction this paper is concerned with a lotka volterra cooperation diffusion model with a saturating interaction term for one species the goal of the paper is to investigate the asymptotic behavior of the time dependent solution in relation to the corresponding steady state solutions under homogeneous neumann boundary condition some simple and easily verifiable conditions are given to the rate constants so that for every nontrivial nonnegative initial function the corresponding time dependent solution converges to one of the nonnegative constant steady state solutions as time tends to infinity this convergence result leads to the existence and uniqueness of a positive or nonnegative steady state solution and the global asymptotic stability of a given nonnegative constant steady state solution in terms of ecological dynamics it also gives some coexistence permanence and extinction results for the model

differentiable structure of the set of controllable a b t invariant subspaces abstract given a b t hom c n c n m observable we prove that the set of a b t invariant subspaces having a fixed brunovsky kronecker structure is a connected manifold and we compute its dimension also we include some applications of these results

nonstationary monotone iterative methods for nonlinear partial differential equations a simple technique is given in this paper for the construction and analysis of monotone iterative methods for a class of nonlinear partial differential equations with the help of the special nonlinear property we can construct nonstationary parameters which can speed up the iterative process in solving the nonlinear system picard gauss seidel and jacobi monotone iterative methods are presented and analyzed for the adaptive solutions the adaptive meshes are generated by the 1 irregular mesh refinement scheme which together with the m matrix of the finite element stiffness matrix lead to existence uniqueness comparison theorems with simple upper and lower solutions as initial iterates some numerical examples including a test problem with known analytical solution are presented to demonstrate the accuracy and efficiency of the adaptive and monotone properties numerical results of simulations on a mosfet with the gate length down to 34 nm are also given

finite difference reaction diffusion systems with coupled boundary conditions and time delays abstract this paper is concerned with finite difference solutions of a coupled system of reaction diffusion equations with nonlinear boundary conditions and time delays the system is coupled through the reaction functions as well as the boundary conditions and the time delays may appear in both the reaction functions and the boundary functions the reaction diffusion system is discretized by the finite difference method and the investigation is devoted to the finite difference equations for both the time dependent problem and its corresponding steady state problem this investigation includes the existence and uniqueness of a finite difference solution for nonquasimonotone functions monotone convergence of the time dependent solution to a maximal or a minimal steady state solution for quasimonotone functions and local and global attractors of the time dependent system including the convergence of the time dependent solution to a unique steady state solution also discussed are some computational algorithms for numerical solutions of the steady state problem when the reaction function and the boundary function are quasimonotone all the results for the coupled reaction diffusion equations are directly applicable to systems of parabolic ordinary equations and to reaction diffusion systems without time delays

monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem in this paper we consider monotone explicit iterations of the finite element schemes for the nonlinear equations associated with the boundary value problem u bu 2 based on piecewise linear polynomials and the lumping operator these iterations construct the monotonically decreasing and increasing sequences and convergence proofs are given finally we present some numerical examples verifying the effectiveness of the theory

a modified accelerated monotone iterative method for finite difference reaction diffusion convection equations this paper is concerned with monotone algorithms for the finite difference solutions of a class of nonlinear reaction diffusion convection equations with nonlinear boundary conditions a modified accelerated monotone iterative method is presented to solve the finite difference systems for both the time dependent problem and its corresponding steady state problem this method leads to a simple and yet efficient linear iterative algorithm it yields two sequences of iterations that converge monotonically from above and below respectively to a unique solution of the system the monotone property of the iterations gives concurrently improving upper and lower bounds for the solution it is shown that the rate of convergence for the sum of the two sequences is quadratic under an additional requirement quadratic convergence is attained for one of these two sequences in contrast with the existing accelerated monotone iterative methods our new method avoids computing local maxima in the construction of these sequences an application using a model problem gives numerical results that illustrate the effectiveness of the proposed method

an accelerated monotone iterative method for the quantum corrected energy transport model a non stationary monotone iterative method is proposed and analyzed for the quantum corrected energy transport model in nanoscale semiconductor device simulation for the density gradient equations it is analytically and numerically shown that the convergence rate of the method is optimal in the sense of gummel s decoupling iteration this is a globally convergent method in the sense that the initial guess can be taken as a lower or an upper solution which is independent of applied voltages the method integrates the monotone parameters grid sizes and scharfetter gummel fitting in an adaptive and automatic way to treat the singularly perturbed nature of the model that incurs boundary junction and quantum potential layers in the device

numerical methods for semilinear parabolic equations the method of upper lower solutions for continuous parabolic equations is extended to some finite difference system for numerical solutions the idea of this method is that by using the upper or lower solution as the initial iteration one can obtain a monotone sequence that converges to a unique solution of the problem the aim of this paper is to present two iterative schemes for the construction of the monotone sequence and to show that both schemes are numerically stable these two schemes are modified jacobi method and gauss seidel method for nonlinear algebraic equations an advantage of this approach is that each of the two methods yields an error estimate between the true solution and the computed mth iteration on the other hand the standard picard type of iterative scheme is used to show that the finite difference system converges to the continuous parabolic equations

time delayed finite difference reaction diffusion systems with nonquasimonotone functions this paper is concerned with finite difference solutions of a system of reaction diffusion equations with coupled nonlinear boundary conditions and time delays the reaction functions and the boundary functions are not necessarily quasimonotone and the time delays may appear in the reaction functions as well as in the boundary functions the investigation is devoted to the finite difference system for both the time dependent problem and its corresponding steady state problem some monotone iteration processes for the finite difference systems are given and the asymptotic behavior of the time dependent solution in relation to the steady state solution is discussed the asymptotic behavior result leads to some local and global attractors of the time dependent problem including the convergence of the time dependent solution to a unique steady state solution an application and some numerical results to an enzyme substrate reaction diffusion problem are given all the results are directly applicable to parabolic ordinary systems and to reaction diffusion systems without time delays

monotone iterative methods for nonlinear equations involving a noninvertible linear part we study monotone iterative methods for the numerical solution of a class of nonlinear elliptic boundary value problems by applying a theorem of ortega and rheinboldt this generalizes the work of earlier authors to the case of nonlinear perturbations of linear problems with a nontrivial kernel

finite difference reaction diffusion equations with nonlinear diffusion coefficients a monotone iterative method for numerical solutions of a class of finite difference reaction diffusion equations with nonlinear diffusion coefficient is presented it is shown that by using an upper solution or a lower solution as the initial iteration the corresponding sequence converges monotonically to a unique solution of the finite difference system it is also shown that the solution of the finite difference system converges to the solution of the continuous equation as the mesh size decreases to zero

numerical solving nonlinear integro parabolic equations by the monotone weighted average method the paper deals with numerical solving nonlinear integro parabolic problems of volterra type based on the weighted average method a monotone iterative method is presented construction of initial upper and lower solutions is given existence and uniqueness of a solution to the nonlinear difference scheme are established an analysis of convergence rates of the monotone iterative method is given numerical experiments are presented