equations difference equations and linear systems

... 34 Chapter Linear equations 41 §3.1 Preliminaries from linear algebra 41 §3.2 Linear autonomous first order systems 47 §3.3 General linear first order systems 50 §3.4 Periodic linear systems 54 ... Furthermore we consider linear equations, the Floquet theorem, and the autonomous linear flow Then we establish the Frobenius method for linear equations in the complex domain and investigates Sturm–Liouville ... interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits Keywords and phrases Ordinary differential equations, dynamical systems, Sturm-Liouville equations...

Ngày tải lên: 31/03/2014, 15:56

Ngày tải lên: 01/02/2015, 23:46

... of linear difference equations, Trans Amer Math Soc 12 (1911), 243–284 [Bi2] ——— , The generalized Riemann problem for linear differential equations and the allied problems for linear difference equations, ... [Bor, §6] and [BB, §9] e for dPIV and dPV, and [BB, §10] for q-PVI This subject still remains to be thoroughly studied As was mentioned before, the difference and q-difference Schlesinger equations ... equal to ±1 with all other κ’s and δ’s being zero; cf [JM] Assume κi = −1 and κj = Denote by v and w the solutions of A(ai ) v = and At (aj ) w = Then R exists if and only if (v, w) := v t w =...

Ngày tải lên: 14/02/2014, 17:20

... Difference Equations and Inequalities Theory, Methods, and Applications, Monographs and Textbooks in Pure and Applied Mathematics, vol 155, Marcel Dekker, New York, 1992 R D Driver, G Ladas, and P ... delay-difference equations, Nonlinear Anal (1984), no 6, 645–654 J E Franke and A A Yakubu, Global attractors in competitive systems, Nonlinear Anal 16 (1991), no 2, 111–129 K Gopalsamy, Stability and Oscillations ... the systems (1.4), (1.5), and (1.6), un and represent the densities of the two population species at time nk(≡ n∆t), k is a small time increment, and for each l = 1,2,α(l) ,a(l) , b(l) , and...

Ngày tải lên: 23/06/2014, 00:20

... solusa sy tion for half -linear equations, in preparation M Cecchi, Z Doˇl´ , and M Marini, On recessive and dominant solutions for half -linear differsa ence equations, J Differ Equations Appl 10 (2004), ... D Ahlbrandt, Dominant and recessive solutions of symmetric three term recurrences, J Differential Equations 107 (1994), no 2, 238–258 C D Ahlbrandt and A C Peterson, Discrete Hamiltonian Systems ... 797–808 , Half -linear equations and characteristic properties of the principal solution, J Differential Equations 208 (2005), no 2, 494–507 S S Cheng, H J Li, and W T Patula, Bounded and zero convergent...

Ngày tải lên: 23/06/2014, 00:20

... Multistep Initial and Boundary Value Methods, Stability and Control: Theory, Methods and Applications, vol 6, Gordon and Breach, Amsterdam, 1998 [3] G Dahlquist, Convergence and stability in the ... Difference equations and the stability problem Corollary 3.9 Suppose that the polynomials ρk (z) and σk (z), defined in (2.11), admit roots on the unit circle Then, all of them are real and simple ... (z) and σk (z) be the polynomials defined in (2.11) and ν ≥ given by (2.18) Then, (1) ρk (z) and σk (z) are both of type (ν − 1,1,ν − 1), for k = 2ν − 1; (2) ρk (z) is of type (ν − 1,2,ν − 1) and...

Ngày tải lên: 23/06/2014, 00:20

... solutions for semilinear equations and systems in cylindrical domains Comm Appl Nonlinear Anal (2000), 19-30 10 W NI & J Serrin, Nonexistence thms for quasilinear partial differential equations Red ... many authors, comprise results of nonexistence of nontrivial solutions of the semilinear elliptic equations and systems, under various situations, see [1-8] The Pohozaˇv identity e [1] published ... Nonexistence of nontrivial solutions for the p (x) −Laplacian equations and systems in unbounded domains of Rn AKROUT Kamel∗1 Department of mathematics and informatics.Tebessa university Algeria Email: AKROUT...

Ngày tải lên: 20/06/2014, 21:20

... linear non-autonom ous implicit difference equations, which is sim ilar to that of linear differential-algebraic equations Then we extend this index notion to a class o f nonlinear implicit difference ... radii o f linear systems Systems C ontrol Letl ( I9 ) 4- I0 [1 ] D Hinrichsen A.J Priichard, S ta b ility radii for structured pcnuibiitions and I lie algcbruic Kiccali equations, Systems Control ... 32(4) (2004) 467-473 P K A n il and H T N Yen , On (lie s o lv a b ility (>r iiiilia l-v n h ic problem s loi nonlinear im p licit difference equations, Advances ill Difference I'.f/Itaiioiis 2004:3...

Ngày tải lên: 18/03/2015, 11:46

... INDEFINITE LINEAR SYSTEMS 43 3.1 Introduction 43 3.2 Linear Systems Discretized from Biot’s Consolidation Equations 45 3.2.1 Biot’s Consolidation Equations ... (c) Total runtime ratio between Pc and GJ, and (d) Total/iteration time ratio between Pc and GJ (“Material 1” and “Material 2” refers to soft clays and dense sands, respectively) 4.4 88 Rate ... solution of linear equations is essential in engineering problems and scientific computing Traditionally, direct solution methods are preferred to linear system of equations A general form of linear...

Ngày tải lên: 16/09/2015, 08:31

... corresponds to integrands in Eqs (26) and (27), and f (T1 , T ' , t ) corresponds to the right term of Eq (25) Then HJB control equations corresponding to objectives of Eqs (26) and (27) are, respectively, ... heat flux rates absorbed and released by the working fluid in the heat engine be q1 and q2 , respectively T1 and T2 are the reservoir temperatures corresponding to the high- and low-temperature sides, ... values of Eqs (32) and (33) subject to the constraints of discrete Eqs (34) and (35) From Eqs (32)-(35), the Bellman’s backward recurrence equations corresponding to Eqs (32) and (33) are, respectively,...

Ngày tải lên: 05/09/2013, 15:28

... to solve for some y the linear system (W(x) + λS) · y = R, and then substitute y into both the numerators and denominators of 18.6.12 or 18.6.13.) Equations (18.6.12) and (18.6.13) have a completely ... set of linear equations for each desired value of x By contrast, in (18.5.8), one solves an M × M linear set, but only once In general, the computational burden of repeatedly solving linear systems ... have unit area at every x, giving 818 Chapter 18 Integral Equations and Inverse Theory CITED REFERENCES AND FURTHER READING: Backus, G.E., and Gilbert, F 1968, Geophysical Journal of the Royal Astronomical...

Ngày tải lên: 17/10/2013, 22:15

... Nonlinear equations are harder to solve than linear equations For image processing, however, the large number of equations usually dictates an iterative solution procedure, even for linear equations, ... 1985, Astronomy and Astrophysics, vol 144, 381–387 [4] Narayan, R., and Nityananda, R 1986, Annual Review of Astronomy and Astrophysics, vol 24, pp 127–170 [5] Skilling, J., and Bryan, R.K 1984, ... Skilling, J., and Gull, S.F 1985, in Maximum-Entropy and Bayesian Methods in Inverse Problems, C.R Smith and W.T Grandy, Jr., eds (Dordrecht: Reidel) [10] Skilling, J 1986, in Maximum Entropy and Bayesian...

Ngày tải lên: 24/10/2013, 15:15

... integrand K(t, s, f(t), f(s)) Nonlinear Fredholm equations are considerably more complicated than their linear counterparts Fortunately, they not occur as frequently in practice and we shall by and ... with well-conditioned systems of equations We then return to Volterra equations (§18.2), and find that simple and straightforward methods are generally satisfactory for these equations In §18.3 we ... contrast, solving nonlinear Volterra equations usually involves only a slight modification of the algorithm for linear equations, as we shall see Almost all methods for solving integral equations numerically...

Ngày tải lên: 21/01/2014, 18:20

... routines for use with linear Fredholm equations of the second kind The routine fred2 sets up equation (18.1.6) and then solves it by LU decomposition with calls to the routines ludcmp and lubksb The ... input, a and b are the limits of integration, and n is the number of points used in the Gaussian quadrature g and ak are user-supplied external functions that respectively return g(t) and λK(t, ... float)) Solves a linear Fredholm equation of the second kind On input, a and b are the limits of integration, and n is the number of points to use in the Gaussian quadrature g and ak are user-supplied...

Ngày tải lên: 21/01/2014, 18:20

... operations Unlike Fredholm equations, it is not necessary to solve a system of linear equations Volterra equations thus usually involve less work than the corresponding Fredholm equations which, as ... the inversion of, sometimes large, linear systems The efficiency of solving Volterra equations is somewhat counterbalanced by the fact that systems of these equations occur more frequently in ... Integral Equations with Singular Kernels 797 CITED REFERENCES AND FURTHER READING: Linz, P 1985, Analytical and Numerical Methods for Volterra Equations (Philadelphia: S.I.A.M.) [1] Delves, L.M., and...

Ngày tải lên: 21/01/2014, 18:20

... CITED REFERENCES AND FURTHER READING: Abramowitz, M., and Stegun, I.A 1964, Handbook of Mathematical Functions, Applied Mathematics Series, Volume 55 (Washington: National Bureau of Standards; reprinted ... rules is to write down the n linear equations that must be satisfied if the quadrature rule is to be exact for the n functions f (x) = const, x, x2 , , xn−1 , and then solve these for the coefficients ... square brackets equation (18.3.5) each become independent of k, and (18.3.5) in fact reduces to Wn = 800 Chapter 18 Integral Equations and Inverse Theory hh=h; hi=1.0/hh; for (j=1;j

Ngày tải lên: 26/01/2014, 15:20

... as to their choices of A and B, as to whether the prescription (18.4.12) yields linear or nonlinear equations, as to their recommended method for selecting a final λ, and as to their practicality ... Regularization 806 Chapter 18 Integral Equations and Inverse Theory (or any other simple quadrature — it rarely matters which) We will view equations (18.4.5) and (18.4.7) as being equivalent for ... 1985, Astronomy and Astrophysics, vol 144, pp 381–387 Jeffrey, W., and Rosner, R 1986, Astrophysical Journal, vol 310, pp 463–472 18.5 Linear Regularization Methods What we will call linear regularization...

Ngày tải lên: 26/01/2014, 15:20

... 809 18.5 Linear Regularization Methods M −1 [u (x)] dx ∝ B∝ [uµ − uµ+1 ]2 (18.5.1) µ=1 since it is nonnegative and equal to zero only when u(x) is constant Here uµ ≡ u(xµ ), and the second ... u (18.5.6) This can readily be reduced to a linear set of normal equations, just as in §15.4: The components uµ of the solution satisfy the set of M equations in M unknowns, Aiµ Aiρ ρ i + λHµρ ... trade@cup.cam.ac.uk (outside North America) Equations (18.5.7) or (18.5.8) can be solved by the standard techniques of Chapter 2, e.g., LU decomposition The usual warnings about normal equations being ill-conditioned...

Ngày tải lên: 26/01/2014, 15:20

... January 2004, and in SISSA (Trieste) in June 2006 Their scope was to present problems and techniques of some of the most promising and fascinating areas of research related to nonlinear hyperbolic ... dimensional problems and control problems for hyperbolic systems ; from CIRAM (Research Center of Applied Mathematics) and the Fund for International Programs of University of Bologna; and from Seminario ... Bologna and the Department of Mathematics of Bologna for their kind hospitality and for all the help and support they have provided throughout the school Bologna, Trieste, Brescia, Z¨ rich, u and...

Ngày tải lên: 17/02/2014, 17:20

... Translated by R SANDLING 273 Spectral theory and geometry, E.B DAVIES & Y SAFAROV (eds) 274 The Mandelbrot set, theme and variations, T LEI (ed) 275 Descriptive set theory and dynamical systems, M ... JOHNSON Discrete and continuous nonlinear Schr¨dinger systems, M.J ABLOWITZ, B PRINARI & A.D o TRUBATCH Number theory and algebraic geometry, M REID & A SKOROBOGATOV (eds) Groups St Andrews 2001 ... (u, v) = Ω and |v| = (v, v)1/2 , M Boukrouche & G Lukaszewicz and in V the scalar product and norm are (∇u, ∇v) and |∇v|2 = (∇v, ∇v) We use the notation ·, · for the pairing between V and its dual...

Ngày tải lên: 14/03/2014, 10:20