linear difference equations wikipedia

... pagesdoi:10.1155/2009/521058 Research Article Summation Characterization of the Recessive Solution for Half-Linear Difference Equations Ondˇrej Do ˇsl ´y1 and Simona Fi ˇsnarov ´a2 1 Department of Mathematics and ... certain nonlinear function which appears in the Picone-type identity for1.1 The recessive solution of1.1 is a discrete counterpart of the concept of the principal solution of the half-linear ... medium, provided the original work is properly cited 1 Introduction We consider the second-order half-linear difference equation Δr k ΦΔx k   c k Φx k1   0, Φx : |x| p−2 x, p > 1, 1.1

Ngày tải lên: 21/06/2014, 20:20

... Trang 1EQUATIONS WITH SMALL PARAMETERSTAHIA ZERIZER Received 14 December 2005; Revised 5 April 2006; Accepted 26 April 2006 We consider a boundary value problem for a linear difference ... equating the coefficients at the same powers ofε, a set of equations is obtained For the zeroth-order asymptotic approximation, the resulting equations are given by y(0) k = α k, k =0, 1, ,n −1, a ... multi-time-scale digital systems Such systems are Hindawi Publishing Corporation Advances in Di fference Equations Volume 2006, Article ID 19214, Pages 1 12 DOI 10.1155/ADE/2006/19214 Trang 2prevalent

Ngày tải lên: 22/06/2014, 22:20

... 1fference EquationsVolume 2008, Article ID 438130, 18 pages doi:10.1155/2008/438130 Research Article Linearized Riccati Technique and (Non-)Oscillation Criteria for Half-Linear Difference Equations ... i Let p ≥ 2 and let linear equation 1.6 be nonoscillatory Then 1.4 is also nonoscillatory. 1.4 be nonoscillatory Then linear equation 1.6 is also nonoscillatory. The linearization technique ... deeply developed linear oscillation theory when investi-gating oscillations of half-linear equation1.1 As we will see in the next sections, compared to the continuous case, the linearization technique

Ngày tải lên: 22/06/2014, 22:20

... of infinity,” like in the linear case Other asymptotic properties of recessive and dominant solutions are treated too 1 Introduction Consider the second-order half-linear difference equation ∆
a ... Another concept recently extended to the half-linear case is the concept of a reces-sive solution (see [11]) We recall (see, e.g., [1,8,14]) that in the linear case, if (1.2) is nonoscillatory, then ... (1.2), linearly independent of u Solution u is called a recessive solution and x a dominant solution Both solutions play Copyright©2005 Hindawi Publishing Corporation Advances in Di fference Equations

Ngày tải lên: 23/06/2014, 00:20

... permits to transform the nonlinear problem into a linear one Regarding the class of linear multistep meth-ods (LMMs), the propagation of the errors can be studied by means of a linear difference equation ... mentioned in the Introduction, the study of the stability for dissipative nonlinear problems is made by linearizing the nonlinearity around the asymptotically stable critical point This is equivalent ... October 2004 The study of the stability properties of numerical methods leads to considering linear dif-ference equations depending on a complex parameterq Essentially, the associated char-acteristic

Ngày tải lên: 23/06/2014, 00:20

... these equations are not adjoint equations and are referred to as quasi-adjoint equations. Equation (E) is a special case of linearnth-order difference equations with quasi-differ-ences Such equations ... above-quoted results for third-order differential equations Moreover, the oscillation of (E) and (EA) is characterized by means of second-order linear difference equations and the problem of the number ... Trang 1INVOLVING QUASI-DIFFERENCESZUZANA DOˇSL ´A AND ALEˇS KOBZA Received 30 June 2004; Revised 20 September 2004; Accepted 12 October 2004 We study the third-order linear difference equation

Ngày tải lên: 23/06/2014, 00:20

... SCIENCE Ngô Thi Thanh Nga STABILITY AND ROBUST STABILITY OF SINGULAR LINEAR DIFFERENCE EQUATIONS Speciality: Dierential and Integral Equations Speciality Code: 62 46 01 03 THESIS FOR THE DEGREE OFDOCTOR ... some fundamental notions on singular lineardierence equations and other auxiliary results which will be used in nextchapters 1.1 Linear singular dierence equations by tractability-index approach ... 10Chapter 2 Singular systems of rst-order dierence equations 282.1 Stability notions for singular dierence equations 28 2.2 Stability of perturbed equations 32 2.2.1 The case of one-sided perturbation

Ngày tải lên: 15/09/2020, 06:59

... SCIENCE Ngô Thi Thanh Nga STABILITY AND ROBUST STABILITY OF SINGULAR LINEAR DIFFERENCE EQUATIONS Speciality: Dierential and Integral Equations Speciality Code: 62 46 01 03 THESIS FOR THE DEGREE OFDOCTOR ... some fundamental notions on singular lineardierence equations and other auxiliary results which will be used in nextchapters 1.1 Linear singular dierence equations by tractability-index approach ... 10Chapter 2 Singular systems of rst-order dierence equations 282.1 Stability notions for singular dierence equations 28 2.2 Stability of perturbed equations 32 2.2.1 The case of one-sided perturbation

Ngày tải lên: 03/07/2021, 10:36

... Issue-6; Jun, 2022INVERSE OF THE GENERALIZED VANDERMONDE MATRIX VIA THE FUNDAMENTAL SYSTEM OF LINEAR DIFFERENCE EQUATIONS CLAUDEMIR ANIZ AND MUSTAPHA RACHIDI Instituto de Matem´atica INMA, UFMS, Av Costa ... Van-dermonde matrix, using the analytic properties of a fundamental system related to a specific linear difference equations We establish two approaches allowing us to provide explicit formulas for the ... Words: Generalized Vandermonde matrix; Inverse of the generalized Vander-monde matrix; Linear difference equations; Analytic formulas; Fibonacci funda-mental system. 2010 Mathematical Subject

Ngày tải lên: 11/10/2022, 16:50

... time is usually deseribed by differential and difference equations In discrete-time scale, mathematical modcls lead to difference equations Difference equations play imporlani roles in many areas ... definitions 21 1.2.3 Linear time-invariant singular difference equations af sec- 1.3 Further auxiliary resulis cuc ee 28 Trang 10Chapter 2 Singular systems of first-order difference equations 28 ... Ngô Thị Thanh Nga STABILITY AND ROBUST STABILITY OF SINGULAR LINEAR DIFFERENCE EQUATIONS Speciality: Differential and Integral Equations Speciality Code: 62 46 01 03 THESIS FOR THE DEGREE

Ngày tải lên: 15/05/2025, 21:50

... Trang 1fference EquationsVolume 2008, Article ID 932831, 22 pages doi:10.1155/2008/932831 Research Article Asymptotic Representation of the Solutions of Linear Volterra Difference Equations Istv ... the asymptotic behaviour of solutions of linear Volterra difference equations Some sufficient conditions are presented under which the solutions to a general linear equation converge to limits, which ... solutions of Volterra difference equations isextensive, and application of this theory is rapidly increasing to various fields For the basictheory of difference equations, we choose to refer to

Ngày tải lên: 22/06/2014, 11:20

... two dimensional linear fractional c c system of difference equations,... and J F Selgrade, On a system of rational difference equations, c Journal of Difference Equations and Applications ... ASYMPTOTIC BEHAVIOR OF A COMPETITIVE SYSTEM OF LINEAR FRACTIONAL DIFFERENCE EQUATIONS M. R. S. KULENOVI ´ C AND M. NURKANOVI ´ C Received 18 July 2005; Revised ... Perron’s theorems for difference equations, Journal of Difference e Equations and... Clark and M R S Kulenovi´ , A coupled system of rational difference equations, Computers & c Mathematics

Ngày tải lên: 22/06/2014, 22:20

... difference equations, for the behavior investiga-of the solutions investiga-of certain linear delay difference equations with continuous variable aswell as for the behavior of solutions of a linear ... study the behavior of solutions of linear neutral Volterra difference equationswith infinite delay, and, especially, of linear (non-neutral) Volterra difference equationswith infinite delay Our results ... of solutions of linear neutral integrodifferential equations with unbounded de-lay, and, especially, of linear (non-neutral) integrodifferential equations with unboundeddelay Our purpose in this

Ngày tải lên: 22/06/2014, 22:20

... subadjoint equation are established Keywords Linear singular difference equations· Differential algebraic equations · Adjoint equations· Subadjoint equations · Discrete Lagrange identity Mathematics ... For index-1 linear singular difference equations, the concept of the subadjoint equation is analysed in full detail based on the Kronecker normal form and the inherent regular ordinary difference ... Trang 1DOI 10.1007/s10013-013-0003-9Subadjoint Equations of Index-1 Linear Singular Difference Equations Le Cong Loi Received: 12 December 2011 / Published online: 30

Ngày tải lên: 15/12/2017, 04:40

... HOANG, Stability of a class of singular difference equations, Inter J Difference Equ., 1, 181-193 (2006) [2] P K Anh, N H Du, L C Loi, Singular difference equations: an overview, Vietnam J Math ... difference equations and differential-algebraic equations, Acta Math Vietnam 29 (2004), pp 23-39 [4] P K Anh, H T N Yen, On the solvability of initial-value problems for nonlinear implicit difference ... two above results for the constant coefficient implicit difference equations with perturbations in both sides Consider the linear implicit difference equation with constant coefficient Ex n + =

Ngày tải lên: 15/12/2017, 05:35

... and the second is IIR Trang 9Solution of Difference Equation „ Just as differential equations for continuous-time systems, a linear constant-coefficient difference equation for discrete-time systems ... When a k = 0 for k = 1 … N, the difference equation degenerates to a FIR system „ The output consists of a linear combination of finite inputs. n y 0 Trang 4Difference equation: IIR System ... An important subclass of linear time-invariant systems consist of those system for which the input x[n] and output y[n] satisfy an Nth-order linear constant-coefficient difference equation „ A

Ngày tải lên: 17/08/2020, 08:38

... for More Equations than Unknowns This situation will occur in Chapter 15, when we wish to find the least-squares solution to an overdetermined set of linear equations In tableau, the equations ... throwing away one linear combination of the set of equations that we are trying to solve The resolution of the paradox is that we are throwing away precisely a combination of equations that is ... w[j]=0.0; svbksb(u,w,v,N,N,b,x); Now we can backsubstitute. SVD for Fewer Equations than Unknowns If you have fewer linear equations M than unknowns N , then you are not of solutions If you want

Ngày tải lên: 24/12/2013, 12:16

... dynamic equations with respect to linear dynamic perturbations on time scales A formula for the stability radius is given Keywords and phrases : time scales, exponential function, linear dynamic ... formula of the stability radius were extended to linear time-invariant differential-algebraic systems [6, 7]; and to linear time-varying differential and difference-algebraic systems [8, 9] On the ... exponential stability and given a formula for the stability radius of time-invarying linear dynamic equations with linear disturbance on time scales by giving the domain of exponential stability and

Ngày tải lên: 22/03/2014, 11:20

... functional difference equations Appl Math Comput 161, 441–462 (2005) [11] Padhi, S, Pati, S, Srivastava, S: Multiple positive periodic solutions for nonlinear first order functional difference equations ... below) For information about publishing your research in Advances in Difference Equations go to http://www.advancesindifferenceequations.com/authors/instructions/ For information about other SpringerOpen ... solutions for first-order functional difference equations [8–12] Only a few article have been published on the same problem for higher-order functional difference equations Recently, using coincidence

Ngày tải lên: 18/06/2014, 22:20

... made available soon. On the boundedness of the solutions in nonlinear discrete Volterra difference equations Advances in Difference Equations 2012, 2012:2 doi:10.1186/1687-1847-2012-2 Istvan Gyori ... publishing your research in Advances in Difference Equations go to Trang 2On the boundedness of the solutions in nonlinear discrete Volterra difference equationsIstv´an Gy˝ori∗1 and Essam Awwad1,2 ... non-convolution-type linear and nonlinear Volterra difference equations(see [1–17] and references therein) Appleby et al [2], under appropriate assumptions, have proved that thesolutions of the discrete linear

Ngày tải lên: 20/06/2014, 20:20