Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2006
Volume
Vol. 26
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 26 (2006)
Projects
Pages
Articles
Further properties of the rational recursive sequence xn + 1 = axn - 1 / (b + cxnxn - 1)
(2006) Andruch-Sobiło, Anna; Migda, Małgorzata
In this paper we consider the difference equation $x_{n+1}=\frac{ax_{n-1}}{b+cx_{n}x_{n-1}}, \quad n=0,1,...(E)$ with positive parameters $a$ and $c$, negative parameter $b$ and nonnegative initial conditions. We investigate the asymptotic behavior of solutions of equation $\text{(E)}$.
Initial data generating bounded solutions of linear discrete equations
(2006) Baštinec, Jaromír; Diblík, Josef; Růžičková, Miroslava
A lot of papers are devoted to the investigation of the problem of prescribed behavior of solutions of discrete equations and in numerous results sufficient conditions for existence of at least one solution of discrete equations having prescribed asymptotic behavior are indicated. Not so much attention has been paid to the problem of determining corresponding initial data generating such solutions. We fill this gap for the case of linear equations in this paper. The initial data mentioned are constructed with use of two convergent monotone sequences. An illustrative example is considered, too.
New efficient time integrators for non-linear parabolic problems
(2006) Bujanda, Blanka; Jorge, Juan Carlos
In this work a new numerical method is constructed for time-integrating multidimensional parabolic semilinear problems in a very efficient way. The method reaches the fourth order in time and it can be combined with standard spatial discretizations of any order to obtain unconditinally convergent numerical algorithms. The main theoretical results which guarantee this property are explained here, as well as the method characteristics which guarantee a very strong reduction of computational cost in comparison with classical discretization methods.
The asymptotic properties of the dynamic equation with a delayed argument
(2006) Čermák, Jan; Urbánek, Miroslav
In this paper, we present some asymptotic results related to the scalar dynamic equation with a delayed argument. Using the time scale calculus we generalize some results known in the differential and difference case to the more general dynamic case.
Polynomial quasisolutions of linear differential-difference equations
(2006) Cherepennikov, Valery B.; Ermolaeva, Polina G.
The paper discusses a linear differential-difference equation of neutral type with linear coefficients, when at the initial time moment $t=0$ the value of the desired function $x(t)$ is known. The authors are not familiar with any results which would state the solvability conditions for the given problem in the class of analytical functions. A polynomial of some degree $N$ is introduced into the investigation. Then the term »polynomial quasisolution« (PQ-solution) is understood in the sense of appearance of the residual $\Delta (t)=O(t^N)$, when this polynomial is substituted into the initial problem. The paper is devoted to finding PQ-solutions for the initial-value problem under analysis.