摘要:

Olver has given an elegant construction of recessive solutions of nonhomogeneous scalar three term recurrence relations. We investigate the feasibility of applying his methods to block tridiagonal nonhomogeneous systemswhere the coefficient matricesABCaren × nmatrices andYandDaren×m. Such systems withm= 1 arise in numerical methods for solving partial differential equations [7,11]. Of course, the results obtained are also applicable to the symmetric case withand symmetricBk. The homogeneous case withm =narises in matrix continued fractions [4] and the well-studied symmetric homogeneous case is closely realted to discrete Hamiltonian systems and, form=n, to discrete Riccati equations [2,1,3,5].

ISSN:1023-6198    

DOI:10.1080/10236199508808003

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

摘要:

In this paper we obtain sufficient conditions for the existence of solutions of the difference equationwhich converge monotonically to unstable equilibria. We also obtain sufficient conditions for all solutions to be bounded and sufficient conditions for the existence of unbounded solutions.

ISSN:1023-6198    

DOI:10.1080/10236199508808004

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

摘要:

we review some recent approaches to the numerical solution of ODE. They are based on the solution of IVP (Initial Value Problem) by means of suitable BVM (Boundary Value Methods). A discussion of their properties of stability and covergence is presented along with their practical construction. The advantages of such methods with respect to IVP methods consist in a higher accuracy in the case of stiff problems and in a more covenient implementation on parallel computers.

ISSN:1023-6198    

DOI:10.1080/10236199508808005

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

摘要:

J.C.P's Miller ‘symbolic exponentiation’ algorithm is exposited and aq-analog is given. It is pointed out that these simple method, that usesdifference equations in an essential way, are superior to the Fast FourierTransform.

ISSN:1023-6198    

DOI:10.1080/10236199508808006

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

摘要:

The paper investigates the properties of the stabilizing and antistabilizing solutions to a special couple of discrete-time Riccati equations which arise in the context of the contractiveness of the input-output operator defined by an exponentially stable time-varying discrete linear system. Lower and upper bounds as well as duality and attractiveness properties are established for these solutions.

ISSN:1023-6198    

DOI:10.1080/10236199508808007

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

摘要:

Consider the following two-term analog of the Collatz 3n+1 iteration:Start with two positive integers. If the sum is even, take the average. If the sum is odd, multiply the difference by 3/2 and add 1/2. Iterate on the last two terms of the sequence. More generally, forb≥1 an odd integer and :1,x2εIN, we study the second order difference equationsfor their asymptotic properties, sensitivity to initial conditions, and predictability of the limit of {Xn}, which is shown necessarily to exist only whenb= 1,3 or 5.

ISSN:1023-6198    

DOI:10.1080/10236199508808008

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

摘要:

Let a fourth order linear difference operatorLbe defined byfortin a discrete interval [a+ 2,b+ 2] whereb-ais a nonegative integer. Solutions ofLy= 0 are then determined on the discrete interval [a,b+ 4]. Defining generalized zeros appropriately, the equationLy= 0 is (2,2)-disconjugate on [a,b+ 4] provided no nontrivial solution ofLy= 0 has two distinct generalized zeros, each of order two or more, in [a,b+ 4]. Lettingq–(t) = max{−q(t),0}, the main theorem gives a condition onq(t), in the form of a strict inequality thatq–(t) summed over the interval [a+ 2b+ 2] satisfies, which guarantees thatLy= 0 is (2,2)-disconjugate on [a,b+ 4]. An example is given showing that the inequality is sharp. The proof of the main result utilizes an appropriately defined quadratic form.

ISSN:1023-6198    

DOI:10.1080/10236199508808009

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

摘要:

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.

ISSN:1023-6198    

DOI:10.1080/10236199508808010

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor

ISSN:1023-6198    

DOI:10.1080/10236199508808002

出版商:Gordon and Breach Science Publishers SA    

年代:1995

数据来源: Taylor