on local convergence of a symmetric semi discrete scheme for an abstract analogue of the kirchhoff equation the present work considers a nonlinear abstract hyperbolic equation with a self adjoint positive definite operator which represents a generalization of the kirchhoff string equation a symmetric three layer semi discrete scheme is constructed for an approximate solution of a cauchy problem for this equation value of the gradient in the nonlinear term of the scheme is taken at the middle point it makes possible to find an approximate solution at each time step by inverting the linear operator local convergence of the constructed scheme is proved numerical calculations for different model problems are carried out using this scheme

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

solving a singular system of two nonlinear odes abstract in this paper a new method is given in order to solve a singular system of two nonlinear ordinary differential equations having multiple solutions and we may give a special solution by imposing an additional condition representation of the exact solution is given in the form of series in the reproducing kernel space its approximate solution is obtained by truncating the series the error of the approximate solution is monotone decreasing in the sense of w 2 0 1 and the intrinsic merit of the method given in the paper lies in its speedy convergence some numerical examples are studied to demonstrate the accuracy of the present method

solving integro differential equations with cauchy kernel a simple method for solving the fredholm singular integro differential equations with cauchy kernel is proposed based on a new reproducing kernel space using a transformation and modifying the traditional reproducing kernel method the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space the advantage of the approach lies in the fact that on the one hand by improving the definition of traditional inner product the representation of new reproducing kernel function becomes simple and requirement for image space of operator is weakened comparing with traditional reproducing kernel method on the other hand the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives some examples are displayed to demonstrate the validity and applicability of the proposed method

global solvability for the kirchhoff equations in exterior domains of dimension three abstract we consider the initial boundary value problem for the kirchhoff equations in exterior domains or in the whole space of dimension three and show that these problems admit time global solutions provided the norms of the initial data in the usual sobolev spaces of appropriate order are sufficiently small we obtain uniform estimates of the l 1 r norms with respect to time variable at each point in the domain of solutions of initial boundary value problem for the linear wave equations we then show that the estimates above yield the unique global solvability for the kirchhoff equations

the relationship between real poles and real zeros in siso sampled data systems a relationship between real poles and real zeros of siso single input single output sampled data systems is presented which is independent of the sampling period the relation is stated in terms of a parity property involving the number of real zeros between any two real poles this property allows the investigation of conditions for the preservation of stable or unstable zeros under sampling a sufficient condition for stability of a sampled system with a continuous time plant having all real zeros and a sufficient condition for instability of a two sampled system with an unstable plant is developed

the reproducing kernel method for solving the system of the linear volterra integral equations with variable coefficients in this paper we apply the reproducing kernel method to give the exact solution and approximate solution for the system of the linear volterra integral equations with variable coefficients some examples are given showing its effectiveness and convenience finally the numerical results obtained by the reproducing kernel method are superior to those obtained by other methods in farshid mirzaee 2010 4 tahmasbi and fard 2008 5 saeed and ahmed 2008 8

solving the generalized regularized long wave equation on the basis of a reproducing kernel space on the basis of a reproducing kernel space an iterative algorithm for solving the generalized regularized long wave equation is presented the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution u n is constructed by truncating the series to n terms the convergence of u n to the analytical solution is also proved results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations

new algorithm for a class of nonlinear integro differential equations in the reproducing kernel space this paper is concerned with the new algorithm for giving the approximate solution of a class of nonlinear integro differential equations in the reproducing kernel space two integro differential equations are solved using the algorithm it turns out that this algorithm is valid

on a model connected with the kirchhoff equation abstract we prove a global existence result in suitable sobolev spaces for the solution of the nonlinear cauchy problem tt u t x 1 r n dy k x y y u t y 2 x u t x 0 u 0 x u 0 x t u 0 x u 1 x 0 where n 3 is the space dimension the initial data are c with compact support in rn and k z is a positive smooth function rapidly decreasing as z our approach is based on the energy estimates combined with the classical von wahl inequalities

a class of non analytic functions for the global solvability of kirchhoff equation abstract we consider the global solvability to the cauchy problem of kirchhoff equation with generalized classes of manfrin s class manfrin s class is a subclass of sobolev space but we shall extend this class as a subclass of the ultradifferentiable class and we succeed to prove the global solvability of kirchhoff equation with large data in wider classes from the previous works

an approximate algorithm for a kirchhoff wave equation the initial boundary value problem for a hyperbolic type quasilinear equation w tt varphi int 0 pi w x 2dx w xx is considered its solution is derived by means of a numerical algorithm consisting of the projection method and the difference method for approximation with respect to spatial and time variables while the resulting discrete system is solved by an iteration process the accuracy of the proposed algorithm is estimated

a numerical algorithm for the nonlinear kirchhoff string equation the initial boundary value problem is considered for the dynamic string equation its solution is found by means of an algorithm the constituent parts of which are the galerkin method the modified crank nicolson difference scheme used to perform approximation with respect to spatial and time variables and also a picard type iteration process for solving the system of nonlinear equations obtained by discretization errors of the three parts of the algorithm are estimated and as a result its total error estimate is obtained

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

paper uniformly optimal control of linear feedback systems the problem of uniformly optimal control is posed in the context of linear time varying discrete time systems the controller is optimal uniformly over a pre specified set of exogenous signals existence of an optimal controller is proved and a formula for the minimum cost is derived the time invariant case is treated in the frequency domain it is shown that for time invariant systems an optimal time varying controller is no better than an optimal time invariant controller

new algorithm for second order boundary value problems of integro differential equation this paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of boundary value problems in the reproducing kernel space the analytical solution u x and approximate solution u n x are represented in terms of series for any initial function u 1 x w 2 3 0 1 we prove u n x u x u n x u x u n x u x n two numerical examples are studied to demonstrate the accuracy of the present method results obtained by the method indicate the method is simple and effective

logarithmic integrals and system dynamics an analogue of bode s sensitivity integral for continuous time time varying systems a new time domain interpretation of bode s integral is presented this allows for a generalization to the class of time varying systems which possess an exponential dichotomy it is shown that the sensitivity function is constrained on average by the spectral values in the dichotomy spectrum of the antistable component of the open loop dynamics

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

a relationship between sensitivity and stability of multivariable feedback systems both comparison sensitivity and robust stability analysis attempt to extend concepts which are well understood in scalar feedback systems to multivariable control system design although the two bodies of work have developed about a decade apart the basic philosophies are similar both attempt to maintain a system property sensitivity reduction versus stability in the presence of plant modeling errors this paper demonstrates how the similarity in philosophy translates into a similarity in results and interpretations

simplified reproducing kernel method and convergence order for linear volterra integral equations with variable coefficients abstract this paper proposes a simplified reproducing kernel method to solve the linear volterra integral equations with variable coefficients the main idea of the method is to establish a reproducing kernel direct space that can be used in volterra integral equations and in the first time this paper analyzes the convergence order and stability of the approximate solution then the uniform convergence of the numerical solution is proved and the time consuming schmidt orthogonalization process is avoided the proposed method is proved to be stable and is not less than the second order convergence the algorithm is proved to be feasible and stable through some numerical examples

sensitivity improvement by a stable controller in siso digital control systems abstract lower bounds which are simple functions of the sampling period are developed for h norm sensitivity functions in digital control systems with and without computational time delay it is shown that the sensitivity property can be improved by a stable controller using a new simple scheme called 2 delay digital control in which we use the inter sample information of the output as well as the data at each sampling instant

existence theorems of global solutions of initial value problems for nonlinear integrodifferential equations of mixed type in banach spaces and applications abstract this paper investigates the existence of global solutions for initial value problems of the nonlinear integrodifferential equations in banach spaces we obtain the existence of global solutions by schauder s fixed point theorem our results are the generalizations and improvements of recent results as applications of our results the existence of global solutions of two classes of third order mixed boundary value problem is obtained and an example of infinite system for nonlinear integrodifferential equations is worked out to illustrate our main results