first order difference equation
Existence of a unique bounded solution to a linear second order difference equation and the linear first order difference equation
... difference equation and present an elegant proof based on a combination of theory of linear difference equations and the Banach fixed point ...the equation by using theory of solvability of difference ...
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Bounded and periodic solutions to the linear first order difference equation on the integer domain
... Periodic solutions to () on N were studied in [], which was another motivation for this paper. Our main result on periodicity is a nice complement to that in []. Namely, for the case when the coefficients of ...
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Qualitative Research of First Order Linear Difference Equations
... of difference equations; see, for example papers [1 -11] and references cited there ...of difference equation with deviating argument and nonnegative ...
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Second order integrability conditions for difference equations. An integrable equation.
... erence equation. With the term integrability of a di ff erence equation, we understand the existence of an infinite hierarchy of ...a first order recursion operator were given in [10] and we ...
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Oscillation criteria for first order forced nonlinear difference equations
... respectively. These conditions are also sufficient for the oscillation of (1.1) and (1.2) with p ( n ) ≡ 0 provided that there exists an oscillatory sequence { η ( n ) } such that Δη ( n ) = e ( n ) . In this paper, we are ...
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High-accuracy Alternating Difference Scheme for the Fourth-order Diffusion Equation
... Abdullah first developed the alternating group ex- plicit (AGE) scheme [1, 2] for parabolic ...dispersive equation [6, 7, 8, 10, 11, 13, 16], non- linear three-order KdV equation [9], ...
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Positive periodic solution of higher order functional difference equation
... The existence of positive periodic solutions of discrete mathematical models such as the discrete model of blood cell production and the single-species discrete periodic popula- tion model has been studied extensively in ...
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High Order Finite Difference Method for Helmholtz Equation in Polar Coordinates
... Helmholtz equation has attracted much attention in many fields such as elec- tromagnetic cavity scattering problems [1], wave propagation [2] and acoustic problems ...finite difference method [4], finite ...
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Hyers Ulam stability of the first order matrix difference equations
... 10. Czerwik, S: Functional Equations and Inequalities in Several Variables. World Scientific, Singapore (2002) 11. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, ...
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Application of First Order Differential Equation in Temperature Problems
... For these type of problem we will be assuming that the question involves the temperature (T) of a certain body placed in a medium of constant temperature (M) and as time (t) varies so does T. (So T has a rate of change ...
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A method for solving first order fuzzy differential equation
... Definition 2.3 Let x, y ∈ E. If there exists z ∈ E such that x = y + z, then z is called the H-difference of x and y and it is denoted by x ⊖ y. In this paper we consider the following defini- tion of ...
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Regarding the dynamics of a third order nonlinear difference equation
... First we study the relation of attractivity and stability of equilibrium point of this equation and some related equations. Further more we prove the existence of Neimark-Sacker and period doubling (flip) ...
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Global dynamics of cubic second order difference equation in the first quadrant
... Equation () shows that () can have at most three period-two ...of equation () in some special cases. Equation () can be solved but its solutions are very complicated and would depend on ...
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On the convergence of a finite difference scheme for a second order differential equation containing nonlinearly a first derivative
... finite difference scheme to the solu- tion of a second order ordinary differential equation with the right-hand-side nonlinearly dependent on the first ...
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Results and Conjectures about Order Lyness' Difference Equation in , with a Particular Study of the Case
... the first invariant function for order q Lyness’ equation, and prove that the invariant manifolds associated to it are homeomorphic to the sphere S q−1 ...
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Compact difference scheme for two dimensional fourth order hyperbolic equation
... in order to design a high-order scheme for the problem, the spatial derivatives are discretized by applying the compact finite difference method or compact volume ...
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On bounds for solutions of monotonic first order difference differential systems
... The condition d(x)e(x) > 0 generally holds in the whole maximal interval of continu- ity of the functions because the coefficients d(x) and e(x) do not change sign under very general conditions (see, for instance, ...
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On the Difference Equation
... But “a question ” of mathematics and biology is whether stable and sustained oscillation possible for 1.1, when αβ > 1, increases. In the present paper, we provide a detailed analysis of these questions. Regarding β ...
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Positive solutions of second order linear difference equation with variable delays
... 33. Lei, C: Remarks on oscillation of second-order linear difference equation. Appl. Math. Comput. 215, 2855-2857 (2009) 34. Li, X, Jiang, J: Oscillation of second-order linear difference equations. ...
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A classification scheme for nonoscillatory solutions of a higher order neutral difference equation
... Nonoscillatory solutions of a nonlinear neutral type higher order difference equations are classified by means of their asymptotic behaviors. By means of the Kranoselskii’s fixed point theorem, existence criteria ...
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