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1
Content available remote Application of difference equations to certain tridiagonal matrices
100%
Borowska J. , Łacińska L. , Rychlewska J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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tom Vol. 11, nr 3
15-20
EN
In this paper we present an application of second order homogeneous linear difference equations with constant coefficients to evaluate the determinant of tridiagonal matrices. Comparing the obtained results with a certain alternative approach [1] some formulae for the finite sum are derived.
2
Content available On oscillatory solutions of certain difference equations
100%
Grzegorczyk G. , Werbowski J.
Opuscula Mathematica
|
2006
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tom Vol. 26, no. 2
317-326
EN
Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
3
Content available On the global attractivity and the periodic character of a recursive sequence
80%
Elsayed E. M.
Opuscula Mathematica
|
2010
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tom Vol. 30, no. 4
431-446
EN
In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence [formula], where the parameters a, b, c, d and e are positive real numbers and the initial conditions x-2, x-1 and x0 are positive real numbers.
4
Content available New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments
80%
Attia E. R. , El-Matary B. M. , Chatzarakis G. E.
Opuscula Mathematica
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2022
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tom Vol. 42, no. 6
769--791
EN
In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving lim sup, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.
5
Content available New aspects for the oscillation of first-order difference equations with deviating arguments
80%
Attia E. R. , El-Matary B. M.
Opuscula Mathematica
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2022
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tom Vol. 42, no. 3
393--413
EN
We study the oscillation of first-order linear difference equations with non-monotone deviating arguments. Iterative oscillation criteria are obtained which essentially improve, extend, and simplify some known conditions. These results will be applied to some numerical examples.
6
Content available Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian
80%
Candito P. , D'Agui G.
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2014
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tom Vol. 34, no. 4
683--690
EN
In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete p-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.
7
Content available Oscillation conditions for difference equations with several variable delays
80%
El-Matary B. M. , El-Morshedy H. A. , Benekas V. , Stavroulakis I. P.
Opuscula Mathematica
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2023
|
tom Vol. 43, no. 6
789--801
EN
A technique is developed to establish a new oscillation criterion for a first-order linear difference equation with several delays and non-negative coefficients. Our result improves recent oscillation criteria and covers the cases of monotone and non-monotone delays. Moreover, the paper is concluded with an illustrative example to show the applicability and strength of our result.
8
An explicit formula for solutions of some system of linear delay difference equations
80%
Kwapisz M. , Łachacz M.
Journal of Applied Analysis
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2002
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tom Vol. 8, nr 1
23-32
EN
The aim of this paper is to provide an explicit formula for solutions of the following system of delay difference equations (wzór) where (wzór) ;αn= [n/k] (the symbol [x] stands for entire part of the real number x and k is a fixed positive integer). (An), (Bn), n∈ N, are sequences of square matrices of order m, (fn) is a sequence of vectors from Rm. From this formula conditions for the stability and asymptotic stability of solutions are derived.
9
Content available Solution of infinite slab static problem using the finite strip method by difference equations
80%
Pawlak Z. , Rakowski J.
Journal of Theoretical and Applied Mechanics
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2009
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tom Vol. 47 nr 3
629-643
EN
An analytical approach to the solution of an infinite slab static problem using the finite strip method is presented. The structure simply supported on its opposite edges is treated as a discrete one. A regular mesh of identical finite strips approximates the continuous structure. This regular slab discretization enables one to derive a fundamental solution for the two-dimensional discrete strip structure in an analytical, closed form. Equilibrium conditions are derived from the finite element method formulation. The set of the infinite number of equilibrium conditions is replaced by one equivalent difference equation. The solution to this equation is the fundamental function, i.e. Green's function for considered slab strip.
PL
W pracy zaprezentowano analityczne rozwiązanie problemu statyki nieograniczonej tarczy metodą pasm skończonych. Tarcza swobodnie podparta na przeciwległych krawędziach jest rozwiązywana jako układ dyskretny. Ciągła struktura jest aproksymowana regularną siatką składającą się z identycznych pasm skończonych. Regularny podział pozwala na wyprowadzenie funkcji fundamentalnych dla dwuwymiarowego układu dyskretnego w analitycznej, zamkniętej formie. Warunki równowagi zostały wyprowadzone zgodnie ze sformułowaniem metody elementów skończonych. Układ równań równowagi składający się z nieskończonej liczby równań został zastąpiony jednym, równoważnym równaniem różnicowym. Rozwiązanie tego równania jest funkcją fundamentalną dla rozpatrywanej tarczy.
10
Content available remote On some difference-delay equations arising in a problem of capital deposits
80%
Kwapisz M. , Bartoszewski Z.
Matematyka Stosowana : matematyka dla społeczeństwa
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1996
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tom Nr 39
75--82
EN
Introduction. We consider a real life problem: a. person has made a deposit of D0 dollars in bank B, which calculates interest on this deposit at in=100•in% after each n+l-st quarter and the interest is compounded at the end of each consecutive year since the deposit date, which means that the interest is capitalised yearly. In the case discussed the basic time unit is a quarter but the conversion period - the time interval at the end of which the interest is compounded - is four quarters (for the terminology see [3]). We ask the following question: what is the balance of the person after n time units, i.e. after n quarters? Such a question is important to people planning various sorts of investments or making arrangements with life insurance institutions. We cannot find an answer to this question in available literature. In particular, it is not to be found in recent books devoted to the subject [see 1-6]. We want to find general formulas that would allow us to express this balance by the other given quantities. Such formulas allow us to solve inverse problems consisting in finding the initial deposit Z)q , the interest rate i or the length of the period after which a capital reaches a given level. In this paper we give explicit formulas for the above-mentioned balance. They can be applied to the problems with any number of payments. At the end of this paper we give some examples of application of these formulas to solving the mentioned inverse problems. The obtained formulas make solving such problems easy. A straightforward application of backward recurrence formulas derived from formula (2), although possible, is quite troublesome.ct
11
Content available Oscillation criteria for linear difference equations with several variable delays
70%
Benekas V. , Garab A. , Kashkynbayev A. , Stavroulakis I. P.
Opuscula Mathematica
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2021
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tom Vol. 41, no. 5
613--627
EN
We obtain new sufficient criteria for the oscillation of all solutions of linear delay difference equations with several (variable) finite delays. Our results relax numerous well-known limes inferior-type oscillation criteria from the literature by letting the limes inferior be replaced by the limes superior under some additional assumptions related to slow variation. On the other hand, our findings generalize an oscillation criterion recently given for the case of a constant, single delay.
12
Content available Difference equations with impulses
70%
Danca M. , Feckan M. , Pospisil M.
Opuscula Mathematica
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2019
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tom Vol. 39, no. 1
5--22
EN
Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.
13
Content available remote About oscillatory behavior of solutions when passing from difference to differential equations
70%
Komashynska I. , Ateiwi A.
Demonstratio Mathematica
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2005
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tom Vol. 38, nr 4
867--874
EN
We study a second order difference equations. We obtain conditions of preservation of solutions when passmg from difference to differential equations.
14
Content available remote Reconstruction of potential and boundary conditions for second order difference equations
70%
Currie S. , Love A.
Commentationes Mathematicae
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2018
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tom Vol. 58, No. 1/2
1--9
EN
Assume the eigenvalues and the weights are given for a difference boundary value problem and that the form of the boundary conditions at the endpoints is known. In particular, it is known whether the endpoints are fixed (i.e. Dirichlet or non-Dirichlet boundary conditions) or whether the endpoints are free to move (i.e. boundary conditions with affine dependence on the eigenparameter). This work illustrates how the potential as well as the exact boundary conditions can be uniquely reconstructed. The procedure is inductive on the number of unit intervals. This paper follows along the lines of S. Currie and A. Love, Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions, Quaestiones Mathematicae, 40 (2017), no. 7, 861-877. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in the above reference, an additional spectrum is required more often than was the case in the unique reconstruction of the potential alone.
15
Content available On the stability of some systems of exponential difference equations
70%
Psarros N. , Papaschinopoulos G. , Schinas C. J.
Opuscula Mathematica
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2018
|
tom Vol. 38, no. 1
95--115
EN
In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
16
Oscillation criteria of comparison type for second order deifference equations
60%
Grace S. R. , El-Morshedy H. A.
Journal of Applied Analysis
|
2000
|
tom Vol. 6, nr 1
87-103
EN
In this paper we investigate the oscillatory character of the second order nonlinear difference equations of the forms (wzór) n = 1,2, ... and the corresponding nonhomogeneous equation (wzór) n= 1,2,... via comparison with certain second order linear difference equations where the function f is not necessarily monotonic. The results of this paper are essentially new and can be extended to more general equations.
17
Content available remote Euler approximations can destroy unbounded solutions
60%
Guy R. T. , Misiurewicz M.
Fasciculi Mathematici
|
2010
|
tom Nr 44
43-52
EN
We show that there are ordinary differential equations in Rd with unbounded solutions, for which the difference equations obtained by using the forward Euler method have all solutions bounded.
18
Content available remote On the dynamics of the recursive sequence ...[wzór]
60%
Erdogan M. E. , Cinar C.
Fasciculi Mathematici
|
2013
|
tom Nr 50
59--66
EN
In this paper, we investigate the global behavior of the difference equation ...[wzór] where β is a positive parameter and α, γ are non-negative parameters and non-negative initial conditions.
19
Content available remote On the qualitative study of the nonlinear difference equation ...[wzór]
60%
Zayed E. M. E. , El-Moneam M. A.
Fasciculi Mathematici
|
2013
|
tom Nr 50
137--147
EN
In this paper, we investigate the global behavior of the following non-linear difference equation ...[wzór] where the coefficients α, β, y, p Є (0,∞) and σ, τ Є N and the initial conditions x-x, x0 x-ω are arbitrary positive real numbers, where ω = max {σ, τ}.
20
Content available remote Generalized Euler method for nonlinear first order partial differential functional equations
60%
Kamont Z. , Nadolski A.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 4
976-996
EN
Classical solutions of the local Cauchy problem on the Haar pyramid are approximated in the paper by solutions of suitable quasilinear systems of difference equations. The proof of the stability of the difference problem is based on a comparison technique with nonlinear estimates of the Perron type. This new approach to the numerical solving of nonlinear functional differential equations is generated by a quasilinearization method for initial problems. Numerical examples are given.
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