linear difference equations pdf

... in Difference Equations Volume 2008, Article ID 932831, 22 pages doi:10.1155/2008/932831 Research Article Asymptotic Representation of the Solutions of Linear Volterra Difference Equations Istv ´ an ... equivalence for difference equations with infinite delay,” Journal of Difference Equations and Applications, vol. 5, no. 1, pp. 1–23, 1999. 14 S. Elaydi, “Asymptotics for linear difference equations. II. ... j  c z h∞−hn. 5.31 22 Advances in Difference Equations 10 S. Bodine and D. A. Lutz, “Asymptotic solutions and error estimates for linear systems of difference and differential equations, ” Journal of Mathematical...

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... in Difference Equations Volume 2010, Article ID 594783, 19 pages doi:10.1155/2010/594783 Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The ... we consider a nonlinear first-order difference equation. 2 Advances in Difference Equations Unlike t he method used by Olver 4 to treat asymptotic solutions of second-order linear differential equations, ... second-order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions to the associated homogeneous linear difference...

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... Difference Equations 18 O. Do ˇ sl ´ y and S. Fi ˇ snarov ´ a, “Linearized Riccati technique and non-oscillation criteria for half -linear difference equations, ” Advances in Difference Equations, ... half -linear second order difference equations, ” Journal of Difference Equations and Applications, vol. 9, no. 1, pp. 49–61, 2003. 8 M. Cecchi, Z. Do ˇ sl ´ a, and M. Marini, “Nonoscillatory half -linear ... of solutions of half -linear difference equations, ” submitted. 10 M. Cecchi, Z. Do ˇ sl ´ a, M. Marini, and I. Vrko ˇ c, “Asymptotic properties for half -linear difference equations, ” Mathematica...

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... Difference Equations Volume 2007, Article ID 42530, 9 pages doi:10.1155/2007/42530 Research Article Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations Peng ... linking theorem. 2AdvancesinDifference Equations Equations similar in structure to (1.3) arise in the study of the existence of solitary waves of lattice differential equations, see [1] and the references ... JournalofDynamicsandDifferential Equations, vol.16,no.2,pp. 575–586, 2004. [8] P. H. Rabinowitz, Minimax Methods in Crit ical Point Theory with Applications to Di fferential Equations, vol. 65 of CBMS...

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... of nonlinear difference equations In this section, as an application of our previous results on Poincar ´ edifference equations, we establish an asymptotic expansion of the solutions of nonlinear ... Corporation Advances in Difference Equations Volume 2007, Article ID 67492, 12 pages doi:10.1155/2007/67492 Research Article Asymptotic Expansions for Higher-Order Scalar Difference Equations Ravi P. Agarwal ... behavior of the solutions of higher- order nonlinear difference equations in a neighborhood of an equilibrium. In the spe- cific case of rational difference equations, this problem has been studied in...

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... & Methods 3 (1982), no. 2, 121–131. [15] T. Sari and T. Zerizer, Perturbations for linear difference equations, Journal of Mathematical Anal- ysis and Applications 305 (2005), no. 1, 43–52. Tahia ... difference equations, The Rocky Moun- tain Journal of Mathematics 6 (1976), no. 4, 561–567. [2] P. W. Eloe, Maximum principles for a family of nonlocal boundary value problems,Advancesin Difference Equations ... equating the coefficients at thesamepowersofε, 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 n,k y (0) k+n +...

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... 42 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... Program B-2, p. 298. Westlake, J.R. 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley). Ralston, A., and Rabinowitz, P. 1978, A First Course in Numerical ... containing one subtraction and one multiplication, are executed N 3 and N 2 M times (where there are N equations and M unknowns). The corresponding loops in Gaussian elimination are executed only 1 3 N 3 times...

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... 104 Chapter 2. Solution of Linear Algebraic Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... inversion! This is fun, but let’s look at practicalities: If you estimate how large N has to be before the difference between exponent 3 and exponent log 2 7=2.807 is substantial enough to outweigh the bookkeeping ... 1987, Algorithms: Their Complexity and Efficiency , 2nd ed. (New York: Wiley). Winograd, S. 1971, Linear Algebra and Its Applications , vol. 4, pp. 381–388. Pan, V. Ya. 1980, SIAM Journal on Computing ,...

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... differential equations can be found in numerous texts on the subject [1]. 2.2 Difference Equations Thedevelopmentofdifferenceequationsisparalleltothatofdifferentialequations. Weconsiderhere only linear difference ... LLC 2 Ordinary Linear Differential and Difference Equations B.P. Lathi California State University, Sacramento 2.1 Differential Equations Classical Solution • MethodofConvolution 2.2 Difference Equations Initial ... concerning the classical method for solving differential equations also apply to difference equations. General discussion of difference equations can be found in texts on the subject [2]. References [1]...

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... transformations of linear systems of difference equations By Alexei Borodin ISOMONODROMY TRANSFORMATIONS 1147 probability can be expressed through a solution of the difference Schlesinger equations ... the difference Schlesinger equations (3.1)– (3.3) with the initial conditions {B i (0) = B i }, and let B i (x 1 , ,x n )bethe solution of the classical Schlesinger equations (5.4) with the initial ... of this conjecture, we explicitly show that the difference Schlesinger equations converge to the conventional Schlesinger equations in the limit ε → 0. Note that the monodromy representation of...

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... Conclusion In this paper, we consider a class of impulsive difference equations with distributed delays. By establishing an impulsive delay difference inequality and using the properties of “r-cone” ... vol. 157,American Mathematical Society, Providence, RI (1996) 2. Xu, DY: Asymptotic behavior of nonlinear difference equations with delays. Comput Math Appl. 42, 393–398 (2001). doi:10.1016/S0898-1221(01)00164-X Li ... impulsive delay difference equation. Appl Math Comput. 181, 65–72 (2006). doi:10.1016/j.amc.2006.01.015 9. Zhu, W: Invariant and attracting sets of impulsive delay difference equations with continuous...

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... 781750, 16 pages doi:10.1155/2010/781750 Research Article A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term Jinsong Hu, 1 Youcai Xu, 2 and ... initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence ... Benjamin-Bona-Mahony equations, ” Journal of Mathematical Analysis and Applications, vol. 141, no. 2, pp. 527–537, 1989. 3 C. J. Amick, J. L. Bona, and M. E. Schonbek, “Decay of solutions of some nonlinear...

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... stochastic linear difference equations, ” Applied Mathematics Letters, vol. 10, no. 3, pp. 111–115, 1997. 47 B. Paternoster and L. Shaikhet, “About stability of nonlinear stochastic difference equations, ” ... Corporation Advances in Difference Equations Volume 2008, Article ID 718408, 21 pages doi:10.1155/2008/718408 Research Article Stability of Equilibrium Points of Fractional Difference Equations with Stochastic ... very large interest in studying the behavior of solutions of nonlinear difference equations, in particular, fractional difference equations 1–38. This interest really is so large that a necessity...

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... solutions of nonlinear second-order difference equations, ” Advances in Difference Equations, vol. 2005, no. 2, pp. 173–192, 2005. 3 S. N. Elaydi, An Introduction to Difference Equations, Undergraduate ... Corporation Advances in Difference Equations Volume 2008, Article ID 867635, 6 pages doi:10.1155/2008/867635 Research Article Reducibility and Stability Results for Linear System of Difference Equations Aydin Tiryaki 1 and ... well. 3. Stability of linear systems It turns out that to obtain a stability result, one needs take Sn, a periodic matrix 2. Indeed, this allows using the Floquet theory for linear periodic system...

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