artificial boundary conditions for one dimensional cubic nonlinear schrodinger equations this paper addresses the construction of nonlinear integro differential artificial boundary conditions for one dimensional nonlinear cubic schrodinger equations several ways of designing such conditions are provided and a theoretical classification of their accuracy is given semidiscrete time schemes based on the method developed by duran and sanz serna ima j numer anal 20 2000 pp 235 261 are derived for these unusual boundary conditions stability results are stated and several numerical tests are performed to analyze the capacity of the proposed approach

an initial and boundary value problem for the zakharov kuznestov equation in a bounded domain motivated by the study of boundary control problems for the zakharov kuznetsov equation we study in this article the initial and boundary value problem for the zk short for zakharov kuznetsov equation posed in a limited domain 0 1 x 2 2 d d 1 2 this article is related to saut and temam an initial boundary value problem for the zakharov kuznetsov equation adv differ equ 15 11 12 1001 1031 2010 in which the authors studied the same problem in the band 0 1 x rd d 1 2 but this article is not a straightforward adaptation of saut and temam an initial boundary value problem for the zakharov kuznetsov equation adv differ equ 15 11 12 1001 1031 2010 indeed many new issues arise in particular for the function spaces due to the loss of the fourier transform in the tangential directions orthogonal to 0x in this article after studying a number of suitable function spaces we show the existence and uniqueness of solutions for the linearized equation using the

technical communique sliding mode control of singular stochastic hybrid systems this paper is concerned with the sliding mode control smc of nonlinear singular stochastic systems with markovian switching an integral sliding surface function is designed and the resulting sliding mode dynamics is a full order markovian jump singular stochastic system by introducing some specified matrices a new sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic stability of the sliding mode dynamics then a smc law is synthesized for reaching motion moreover when there exists an external disturbance the 2 disturbance attenuation performance is analyzed for the sliding mode dynamics some related sufficient conditions are also established

admissibility and dissipativity analysis for discrete time singular systems with mixed time varying delays abstract the problems of admissibility and dissipativity are studied for discrete time singular systems with mixed time varying delays the mixed time delays consist of both discrete and distributed delays by taking advantage of the delay partitioning technique a criterion that warrants the admissibility of the considered systems is established based on the criterion a dissipativity condition is also given all the results presented depend upon not only discrete delay and distributed delay but also depend upon the number of delay partitions some numerical examples are included to demonstrate the improvement and effectiveness of the proposed methods

absorbing boundary conditions for general nonlinear schrodinger equations this paper addresses the construction of different families of absorbing boundary conditions for the one and two dimensional schrodinger equations with a general variable nonlinear potential various semidiscrete time schemes are built for the associated initial boundary value problems finally some numerical simulations give a comparison of the various absorbing boundary conditions and associated schemes to analyze their accuracy and efficiency

accurate boundary treatment for transient schrodinger equation under polar coordinates abstract a new local boundary condition is designed for the two dimensional schrodinger equation under polar coordinates based on an approximate linear relation among the kernel functions for a free one dimensional schrodinger equation of a new variable it takes a simple form of ordinary differential equation that relates the neighboring grid points numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment

transparent boundary condition for numerical modeling of intense laser molecule interaction this article addresses the problem of constructing transparent boundary conditions for the schrodinger maxwell system where the interacting electromagnetic field is treated classically in the dipole approximation the problem essentially boils down to constructing transparent boundary condition for the schrodinger equation with time dependent linear potential the transparent boundary maps obtained are not purely of the convolution type however they are amenable to numerical methods like convolution quadrature for implementation

theoretical aspects of the application of convolution quadrature to scattering of acoustic waves in this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non homogeneous obstacles using convolution quadrature cq techniques for the time variable and coupled boundary element method finite element method for the space variable the applicability of cq to waves requires polynomial type bounds for operators related to the operator s 2 in the right half complex plane we propose a new systematic way of dealing with this problem both at the continuous and semidiscrete in space cases we apply the technique to three different situations scattering by a group of sound soft and hard obstacles by homogeneous and non homogeneous obstacles

time discretization of parabolic boundary integral equations in time dependent boundary integral equations a boundary element method in space can be coupled with a different type of discretization in time for the latter a procedure based on linear multistep methods is proposed which is applicable whenever the laplace transform of the fundamental solution is known the stability properties of the method are obtained from those of the underlying multistep method in the absence of a space discretization the numerical solution given by the proposed method is identical to that of a semi discretization in time of the partial differential equation by the underlying multistep method the theory is presented for the single layer potential equation of the heat equation convergence estimates which are pointwise in time and expressed in terms of the boundary data are obtained for full discretizations using galerkin or collocation boundary element methods in space numerical examples are included

on the nonreflecting boundary operators for the general two dimensional schrodinger equation of the two main objectives we pursue in this paper the first one consists in the studying operators of the form t i 1 2 1 2 1 where is the laplace beltrami operator these operators arise in the context of nonreflecting boundary conditions in the pseudo differential approach for the general schrodinger equation the definition of such operators is discussed in various settings and a formulation in terms of fractional operators is provided the second objective consists in deriving corner conditions for a rectangular domain in order to make such domains amenable to the pseudo differential approach the stability and uniqueness of the solution is investigated for each of these novel boundary conditions

new insight into reachable set estimation for uncertain singular time delay systems abstract this paper investigates the problem of reachable set estimation for a class of uncertain singular systems with time varying delays from a new point of view our consideration is centered on the design of a proportional derivative state feedback controller pdsfc such that the considered singular system is robustly normalizable and all the states of the closed loop system can be contained by a bounded set under zero initial conditions first a nominal singular time delay system is considered and sufficient conditions are obtained in terms of matrix inequalities for the existence of a pdsfc and an ellipsoid in this case the considered system is guaranteed to be normalizable and the reachable set of the closed loop systems is contained by the ellipsoid then the result is extended to the case of singular time delay systems with polytopic uncertainties and relaxed conditions are derived by introducing some weighting matrix variables furthermore based on the obtained results the reachable set of the considered closed loop singular system can be contained in a prescribed ellipsoid finally the effectiveness of our results are demonstrated by two numerical examples

fast calculation of energy and mass preserving solutions of schrodinger poisson systems on unbounded domains this paper deals with the numerical solution of the time dependent schrodinger poisson system in the spherically symmetric case since the problem is posed on an unbounded domain one has to introduce artificial boundary conditions to confine the computational domain the main topic of this work is the construction of a so called discrete transparent boundary condition tbc for a crank nicolson type predictor corrector scheme for solving the schrodinger poisson system this scheme has the property of mass and energy conservation exactly on the discrete level we propose different strategies for the discrete tbc and present an efficient implementation finally a numerical example illustrate the findings and shows the comparison results between the different approaches

a note on the 2d generalized zakharov kuznetsov equation local global and scattering results abstract we consider the generalized two dimensional zakharov kuznetsov equation u t x u x u k 1 0 where k 3 is an integer number for k 8 we prove local well posedness in the l 2 based sobolev spaces h s r 2 where s is greater than the critical scaling index s k 1 2 k for k 3 we also establish a sharp criteria to obtain global h 1 r 2 solutions a nonlinear scattering result in h 1 r 2 is also established assuming the initial data is small and belongs to a suitable lebesgue space

a new physiological boundary condition for hemodynamics we propose a new physiologically based outflow boundary condition for hemodynamics under general transient regimes this is in contrast to previous studies that impose restrictions of temporal periodicity the new condition is analyzed and its numerical implementation is discussed in detail we show that existing impedance boundary conditions can be viewed as numerical approximations of the new condition our study provides a partial justification for using some of these existing conditions beyond the periodic problems for which they were designed moreover the new condition has better stability properties the theoretical results are illustrated by numerical experiments pertaining to cerebral blood flow

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

rational square root approximations for parabolic equation algorithms in this article stable pade approximations to the function 1 z are derived by choosing a branch cut in the negative half plane the pade coefficients are complex and may be derived analytically to arbitrary order from the corresponding real coefficients associated with the principal branch defined by z 1 i z 0 i z denotes the imaginary part of z the characteristics of the corresponding square root approximation are illustrated for various segments of the complex plane in particular for waveguide problems it is shown that an increasingly accurate representation may be obtained of both the evanescent part of the mode spectrum for the acoustic case and the complex mode spectrum for the elastic case an elastic parabolic equation algorithm is used to illustrate the application of the new pade approximations to a realistic ocean environment including elasticity in the ocean bottom

on the quadrature error in operational quadrature methods for convolutions we analyze the quadrature error associated with operational quadrature methods for convolution equations the assumptions are that the convolution kernel is inl 1 and that its laplace transform is analytic and bounded in an obtuse sector of the complex plane under these circumstances the laplace transform has a slow variation property which admits a fourier analysis of the quadrature error we provide generall p error estimates assuming suitable smoothness conditions on the function under convolution

on the multistep time discretization of linear initial boundary value problems and their boundary integral equations convergence estimates in terms of the data are shown for multistep methods applied to non homogeneous linear initial boundary value problems similar error bounds are derived for a new class of time discrete and fully discrete approximation schemes for boundary integral equations of such problems e g for the single layer potential equation of the wave equation in both cases the results are obtained from convergence and stability estimates for operational quadrature approximations of convolutions these estimates which are also proved here depend on bounds of the laplace transform of the distributional convolution kernel outside the stability region scaled by the time stepsize and on the smoothness of the data

local and global well posedness for the 2d generalized zakharov kuznetsov equation this paper addresses well posedness issues for the initial value problem ivp as sociated with the generalized zakharov kuznetsov equation namely ut xu u k ux 0 x y 2 r 2 t 0 u x y 0 u0 x y for 2 k 7 the ivp above is shown to be locally well posed for data in h s r 2 s 3 4 for k 8 local well posedness is shown to hold for data in h s r 2 s sk where sk 1 3 2k 4 furthermore for k 3 if u0 2 h 1 r 2 and satisfies ku0kh1 1 then the solution is shown to be global in h 1 r 2 for k 2 if u0 2 h s r 2 s 53 63 and satisfies ku0kl2 p 3k kl2 where is the corresponding ground state solution then the solution is shown to be global in h s r 2

operational quadrature methods for wiener hopf integral equations we study the numerical solution of wiener hopf integral equations by a class of quadrature methods which lead to discrete wiener hopf equations with quadrature weights constructed from the fourier transform of the kernel or rather from the laplace transforms of the kernel halves as the analytical theory of wiener hopf equations is likewise based on the fourier transform of the kernel this approach enables us to obtain results on solvability and stability and error estimates for the discretization the discrete wiener hopf equations are solved by using an approximate wiener hopf factorization obtained with fft numerical experiments with the milne equation of radiative transfer are included

absorbing boundary conditions for relativistic quantum mechanics equations this paper is devoted to the derivation of absorbing boundary conditions for the klein gordon and dirac equations modeling quantum and relativistic particles subject to classical electromagnetic fields microlocal analysis is the main ingredient in the derivation of these boundary conditions which are obtained in the form of pseudo differential equations basic numerical schemes are derived and analyzed to illustrate the accuracy of the derived boundary conditions

the zakharov kuznetsov equation in weighted sobolev spaces abstract in this work we consider the initial value problem ivp associated to the two dimensional zakharov kuznetsov equation u t x 3 u x y 2 u u x u 0 x y r 2 t r u x y 0 u 0 x y we study the well posedness of the ivp in the weighted sobolev spaces h s r 2 l 2 1 x 2 y 2 r d x d y with s r r

on the rate of convergence of schwarz waveform relaxation methods for the time dependent schrodinger equation this paper is dedicated to the analysis of the rate of convergence of the classical and quasi optimal schwarz waveform relaxation swr method for solving the linear schrodinger equation with space dependent potential the strategy is based on i the rewriting of the swr algorithm as a fixed point algorithm in frequency space and ii the explicit construction of contraction factors thanks to pseudo differential calculus some numerical experiments illustrating the analysis are also provided

regular solutions of the 2d zakharov kuznetsov equation on a half strip abstract we formulate on a half strip an initial boundary value problem for the zakharov kuznetsov equation existence and uniqueness of a regular solution as well as the exponential decay rate of small solutions as t are proven

stability and convergence of collocation schemes for retarded potential integral equations time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations solving such equations numerically is both complicated and computationally intensive and numerical methods often prove to be unstable collocation schemes are easier to implement than full finite element formulations but little appears to be known about their stability and convergence here we derive and analyze some new stable collocation schemes for the single layer equation for transient acoustic scattering and use spatial fourier and temporal laplace transform techniques to demonstrate that such stable schemes are second order convergent

method of lines for hyperbolic differential equations runge kutta methods are applied to the numerical solution of hyperbolic partial differential equations conditions that they are locally stable are derived

initial boundary value problems in a rectangle for two dimensional zakharov kuznetsov equation abstract initial boundary value problems in a bounded rectangle with different types of boundary conditions for two dimensional zakharov kuznetsov equation are considered results on global well posedness in the classes of weak and regular solution are established as applications of the developed technique results on boundary controllability and long time decay of weak solutions are also obtained

robust sliding mode control for uncertain discrete singular systems with time varying delays and external disturbances in this paper a sliding mode control smc of uncertain discrete singular systems with external disturbances and time varying delays is under consideration by use of the free weighting matrices and the lyapunov krasovskii functional a delay dependent sufficient condition is given in strict linear matrix inequality lmi format to guarantee the sliding mode dynamics to be admissible regular causal and stable furthermore a proposed smc law and an adaptive smc law are synthesized to make sure that the trajectories of system can be driven to a region near equilibrium point in finite time finally a numerical example is designed to display the effectiveness of the control scheme all these results are expected to propose a new approach for the research on smc of discrete time delay singular systems

an analysis of schwarz waveform relaxation domain decomposition methods for the imaginary time linear schrodinger and gross pitaevskii equations the aim of this paper is to derive and numerically validate some asymptotic estimates of the convergence rate of classical and quasi optimal schwarz waveform relaxation swr domain decomposition methods applied to the computation of the stationary states of the one dimensional linear and nonlinear schrodinger equations with a space dependent potential although swr methods are currently used for efficiently solving high dimensional partial differential equations their convergence analysis and most particularly obtaining expressions of their convergence rate remains largely open even in one dimension except in simple cases in this work we tackle this problem for linear and nonlinear one dimensional schrodinger equations by developing techniques which can be extended to higher dimensional problems and other types of pdes the approach combines the method developed in gander and halpern siam j num anal 45 2 666 697 2007 for the linear advection reaction diffusion equation and the theory of inhomogeneous pseudodifferential operators in conjunction with the associated symbolic asymptotic expansions for computing the stationary states we consider the imaginary time formulation of the schrodinger equation based on the normalized gradient flow ngf method and use a semi implicit euler scheme for the discretization some numerical results in the one dimensional case illustrate the analysis for both the linear schrodinger and gross pitaevskii equations

controller design for time delay system with stochastic disturbance and actuator saturation via a new criterion abstract this paper deals with the problem of controller design for time delay system with stochastic disturbance and actuator saturation by use of more appropriate lyapunov krasovskii functional lkf and a new criterion for the domain of attraction less conservative conditions for stochastic stability are proposed then the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome these sufficient conditions are derived in terms of linear matrix inequality lmi finally two practical examples demonstrate the validity of the given results

an initial boundary value problem in a strip for two dimensional zakharov kuznetsov burgers equation abstract an initial boundary value problem in a strip with homogeneous dirichlet boundary conditions for two dimensional zakharov kuznetsov burgers equation is considered results on global well posedness and large time decay of solutions in the spaces h s for s 0 2 are established

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

energy estimates for galerkin semidiscretizations of time domain boundary integral equations in this paper we present a battery of results related to how galerkin semidiscretization in space affects some formulations of wave scattering and propagation problems when retarded boundary integral equations are used

multistep and multistage convolution quadrature for the wave equation algorithms and experiments we describe how a time discretized wave equation in a homogeneous medium can be solved by boundary integral methods the time discretization can be a multistep runge kutta or a more general multistep multistage method the resulting convolutional system of boundary integral equations belongs to the family of convolution quadratures of lubich the aim of this work is twofold it describes an efficient robust and easily parallelizable method for solving the semidiscretized system the resulting algorithm has the main advantages of time stepping methods and of fourier synthesis at each time step a system of linear equations with the same system matrix needs to be solved yet computations can easily be done in parallel the computational cost is almost linear in the number of time steps and only the laplace transform of the time domain fundamental solution is needed the new aspect of the algorithm is that all this is possible without ever explicitly constructing the weights of the convolution quadrature this approach also readily allows the use of modern data sparse techniques to efficiently perform computation in space we investigate theoretically and numerically to which extent hierarchical matrix mathcal h matrix techniques can be used to speed up the space computation the second aim of this article is to perform a series of large scale 3d experiments with a range of multistep and multistage time discretization methods the backward difference formula of order 2 bdf2 the trapezoid rule and the 3 stage radau iia methods are investigated in detail one of the conclusions of the experiments is that the radau iia method often performs overwhelmingly better than the linear multistep methods especially for problems with many reflections yet in connection with hyperbolic problems bdfs have so far been predominant in the literature on convolution quadrature

frozen gaussian approximation based domain decomposition methods for the linear schrodinger equation beyond the semi classical regime the paper is devoted to develop efficient domain decomposition methods for the linear schrodinger equation beyond the semiclassical regime which does not carry a small enough rescaled planck constant for asymptotic methods e g geometric optics to produce a good accuracy but which is too computationally expensive if direct methods e g finite difference are applied this belongs to the category of computing middle frequency wave propagation where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy motivated by recent works of the authors on absorbing boundary conditions antoine et al 2014 13 and yang and zhang 2014 43 we introduce semiclassical schwarz waveform relaxation methods sswr which are seamless integrations of semiclassical approximation to schwarz waveform relaxation methods two versions are proposed respectively based on herman kluk propagation and geometric optics and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods

potential evaluation in space time bie formulations of 2d wave equation problems in this paper we examine the computation of the potential generated by space time bie representations associated with dirichlet and neumann problems for the 2d wave equation in particular we consider the efficient evaluation of the convolution time integral that appears in the potential representation for this we propose two simple quadrature rules which appear more efficient than the currently used ones both are of gaussian type the classical gauss jacobi quadrature rule in the case of a dirichlet problem and the classical gauss radau quadrature rule in the case of a neumann problem both of them give very accurate results by using a few quadrature nodes as long as the potential is evaluated at a point not very close to the boundary of the pde problem domain to deal with this latter case we propose an alternative rule which is defined by a proper combination of a gauss legendre formula with one of product type the latter having only 5 nodes the proposed quadrature formulas are compared with the second order bdf lubich convolution quadrature formula and with two higher order lubich formulas of runge kutta type an extensive numerical testing is presented this shows that the new proposed approach is very competitive from both the accuracy and efficiency points of view

absorbing boundary conditions for the two dimensional schrodinger equation with an exterior potential four families of abcs where built in antoine et al math models methods appl sci 22 10 2012 for the two dimensional linear schrodinger equation with time and space dependent potentials and for general smooth convex fictitious surfaces the aim of this paper is to propose some suitable discretization schemes of these abcs and to prove some semi discrete stability results furthermore the full numerical discretization of the corresponding initial boundary value problems is considered and simulations are provided to compare the accuracy of the different abcs

transparent boundary conditions for parabolic equation solutions of radiowave propagation problems perfectly transparent boundary conditions are derived for truncating the integration domain when solving radiowave propagation problems with a parabolic equation pe method the boundary conditions are nonlocal they are expressed as a convolution integral involving the field at all previous ranges the convolution kernel is matched to the refractive index vertical gradient at the boundary the boundary conditions include an incoming energy term which can model an arbitrary incident field in particular they may be used with plane wave incidence or with a point source located below or above the domain boundary if required the solution can be extended to heights above the boundary with a generalized horizontal pe method closed form solutions for the incoming energy term are given for plane wave incidence and for gaussian sources when the refractive index above the boundary is constant or linear the resulting finite difference algorithms provide efficient solutions to problems involving airborne sources numerical examples are given showing excellent agreement with a pure split step fourier pe algorithm

absorbing boundary conditions for the one dimensional schrodinger equation with an exterior repulsive potential mathematical constructions and comparisons of accurate absorbing boundary conditions for the one dimensional schrodinger equation with a general variable repulsive potential are developed stable semi discretization schemes are built for the associated initial boundary value problems finally some numerical simulations give a comparison of the various absorbing boundary conditions and show that they yield accurate computations

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

exact artificial boundary conditions for problems with periodic structures based on the work of zheng on the artificial boundary condition for the schrodinger equation with sinusoidal potentials at infinity an analytical impedance expression is presented for general second order ode problems with periodic coefficients and its validity is shown to be strongly supported by numerical evidences this new expression for the kernel of the dirichlet to neumann mapping of the artificial boundary conditions is then used for computing the bound states of the schrodinger operator with periodic potentials at infinity other potential applications are associated with the exact artificial boundary conditions for some time dependent problems with periodic structures as an example a two dimensional hyperbolic equation modeling the tm polarization of the electromagnetic field with a periodic dielectric permittivity is considered

solutions to the discrete airy equation application to parabolic equation calculations in the case of the equidistant discretization of the airy differential equation discrete airy equation the exact solution can be found explicitly this fact is used to derive a discrete transparent boundary condition tbc for a schrodinger type equation with linear varying potential which can be used in parabolic equation simulations in underwater acoustics and for radar propagation in the troposphere we propose different strategies for the discrete tbc and show an efficient implementation finally a stability proof for the resulting scheme is given a numerical example in the application to underwater acoustics shows the superiority of the new discrete tbc

a state dependent boundary layer design for sliding mode control the use of a boundary layer in sliding mode control has been a common technique to reduce chattering of the control signal however different choices of the boundary layer width lead to conflicting effects a large small boundary layer width can more less effectively alleviate the chattering phenomenon but leads to less more accurate control results this note proposes online adjusting the width of the boundary layer based on the state norm for an uncertain linear system the proposed state dependent boundary layer design can effectively eliminate chattering while at the same time ensuring almost perfect control accuracy

an energy approach to space time galerkin bem for wave propagation problems in this paper we consider dirichlet or neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential starting from a natural energy identity a space time weak formulation for 1d integral problems is briefly introduced and continuity and coerciveness properties of the related bilinear form are proved then a theoretical analysis of an extension of the introduced formulation for 2d problems is proposed pointing out the novelty with respect to existing literature results at last various numerical simulations will be presented and discussed showing unconditional stability of the space time galerkin boundary element method applied to the energetic weak problem copyright 2009 john wiley sons ltd

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

exponential mean square stability of time delay singular systems with markovian switching and nonlinear perturbations abstract this paper considers exponential stability in mean square of singular markovian jump systems the systems under consideration involve nonlinear perturbation and time varying delays by using the lyapunov krasovskii functional delay dependent stability conditions in terms of linear matrix inequality lmi are addressed which guarantee exponential mean square stability and a prescribed h performance index for the considered systems two numerical examples are given to illustrate the effectiveness of the proposed main results

microlocal approach towards construction of nonreflecting boundary conditions abstract this paper addresses the problem of construction of non reflecting boundary condition for certain second order nonlinear dispersive equations it is shown that using the concept of microlocality it is possible to relax the requirement of compact support of the initial data the method is demonstrated for a class of initial data such that outside the computational domain it behaves like a continuous wave the generalization is detailed for two existing schemes in the framework of pseudo differential calculus namely szeftel s method szeftel 2006 1 and gauge transformation strategy antoine et al 2006 2 efficient numerical implementation is discussed and a comparative performance analysis is presented the paper also briefly surveys the possibility of extension of the method to higher dimensional pdes

artificial boundary conditions for certain evolution pdes with cubic nonlinearity for non compactly supported initial data the paper addresses the problem of constructing non reflecting boundary conditions for two types of one dimensional evolution equations namely the cubic nonlinear schrodinger nls equation email protected u 2u 0 with email protected x 2 and the equation obtained by letting email protected x 3 the usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain we adapt the pseudo differential approach developed by antoine et al 2006 5 for the nls equation to the second type of evolution equation and further extend the scheme to the aforementioned class of initial data for both of the equations in addition we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness

runge kutta convolution quadrature for the boundary element method abstract time domain boundary element formulations can be established either directly in time domain or via laplace or fourier domain somewhere in between are the convolution quadrature based boundary element formulations which utilize the laplace domain fundamental solution but establish a time stepping procedure up to now in applications mostly backward differential formulas of second order are used as the underlying multistep method however in recent mathematical literature also runge kutta methods have been applied here the use of runge kutta methods is explained in detail and some numerical studies are given in these studies the backward difference based procedures are compared to runge kutta methods for a non smooth problem an l 2 norm of the error is used as the basis of comparison the convergence of which is investigated theoretically as well the results confirm that the usage of the new techniques is preferable with regard to less numerical oscillations in the solution and better representation of wave fronts

unconditionally stable discretization schemes of non reflecting boundary conditions for the one dimensional schrodinger equation this paper addresses the problem of the construction of stable approximation schemes for the one dimensional linear schrodinger equation set in an unbounded domain after a study of the initial boundary value problem in a bounded domain with a transparent boundary condition some unconditionally stable discretization schemes are developed for this kind of problem the main difficulty is linked to the involvement of a fractional integral operator defining the transparent operator the proposed semi discretization of this operator yields with a very different point of view the one proposed by yevick friese and schmidt j comput phys 168 2001 433 two possible choices of transparent boundary conditions based on the dirichlet neumann dn and neumann dirichlet nd operators are presented to preserve the stability of the fully discrete scheme conform galerkin finite element methods are employed for the spatial discretization finally some numerical tests are performed to study the respective accuracy of the different schemes

well posedness for the two dimensional generalized zakharov kuznetsov equation in anisotropic weighted sobolev spaces abstract we consider the well posedness of the initial value problem associated to the k generalized zakharov kuznetsov equation in fractional weighted sobolev spaces h s r 2 l 2 x 2 r 1 y 2 r 2 d x d y s r 1 r 2 r our method of proof is based on the contraction mapping principle and it mainly relies on the well posedness results recently obtained for this equation in the sobolev spaces h s r 2 and a new pointwise commutator type formula involving the group induced by the linear part of the equation and the fractional anisotropic weights to be considered

decay of regular solutions for the critical 2d zakharov kuznetsov equation posed on rectangles an initial boundary value problem for the critical generalized 2d zakharov kuznetsov equation posed on rectangles is considered the existence uniqueness and exponential decay rate of global regular solutions for small initial data are established

sliding mode control for markovian jump repeated scalar nonlinear systems with packet dropouts the uncertain occurrence probabilities case abstract this paper studies the sliding mode based control problem for a class of delayed markovian jump repeated scalar nonlinear systems rsnss subject to packet dropouts pds and randomly occurring uncertainties rous here the phenomenon of the markovian pds is modeled by utilizing a random variable obeying markov process by using the bernoulli distributed random variables the rous under uncertain occurrence probabilities uops are characterized from the mathematical perspective in addition the time delay considered is bounded time varying with known upper and lower bounds the attention is on designing a sliding mode based control method for markovian jump rsnss in the simultaneous presence of markovian pds rous and time varying delays specifically the robustly asymptotically mean square stability is ensured for corresponding sliding mode dynamics by proposing new sufficient criterion moreover the reachability in discrete setting is analyzed i e the state trajectories of the system from any initial condition are globally driven onto a small region nearby the pre designed sliding surface in mean square sense by synthesizing a robust sliding mode control smc law finally the effectiveness of developed control method is verified by some simulations

exponential decay of the h1 norm for the 2d zakharov kuznetsov equation on a half strip abstract we formulate on a half strip an initial boundary value problem for the 2d zakharov kuznetsov equation the existence of a unique weak solution was proven as well as exponential decay of the h 1 norm for small initial data