Results 261 to 270 of about 17,758,657 (325)

Linear integral equations and nonlinear difference-difference equations

Physica D: Nonlinear Phenomena, 1984
We present a systematic method to obtain various integrable nonlinear difference-difference equations and the associated linear integral equations from which their solutions can be inferred. It is argued that these difference-difference equations can be regarded as arising from Bianchi identities expressing the commutativity of Bäcklund transformations.
Quispel, G. R. W., Nijhoff, F. W., Capel, H. W., van der Linden, J.   +3 more
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Partial Differential Equations and Difference Equations

Proceedings of the American Mathematical Society, 1965
(1. 1) Pi(alax)y = ? (1 _ i _ m) where x = (x1, * , xn), a/ax = (a/ax1, *, O/0xn). The Pi's are assumed to be homogeneous polynomials with real coefficients. The term solution is used to include the generalized solutions. A generalized solution is any function continuous on R which is a uniform limit on compact subsets of CX solutions (see [2, p. 65]).
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A Variational Complex for Difference Equations

Foundations of Computational Mathematics, 2004
The authors state and prove an analogue of the Poincaré lemma for exact forms on a lattice. From the results, a variational complex for difference equations is constructed and, furthermore, it is proved to be locally exact. In order to calculate the Lagrangians for discrete Euler-Lagrange systems, homotopy maps are applied.
Peter E. Hydon, Elizabeth L. Mansfield
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On the system of rational difference equations

AIP Conference Proceedings, 2018
In this paper, we investigate solutions of the system of difference equations xn+1=xn−1ynxn−1, yn+1=yn−1xnyn−1−1, zn+1=xnynzn−1, where x0,x−1,y0,y−1,z0,z−1 real numbers such that y0 x−1 ≠1 and x0y−1 ≠ 1In this paper, we investigate solutions of the system of difference equations xn+1=xn−1ynxn−1, yn+1=yn−1xnyn−1−1, zn+1=xnynzn−1, where x0,x−1,y0,y−1 ...
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Language Equations with Symmetric Difference

Fundamenta Informaticae, 2006
The paper investigates the expressive power of language equations with the operations of concatenation and symmetric difference. For equations over every finite alphabet Σ with |Σ| ≥ 1, it is demonstrated that the sets representable by unique solutions of such equations are exactly the recursive sets over Σ, and the sets representable by their least ...
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Difference schemes for the dispersive equation

Computing, 1983
In this paper a table of difference schemes for the dispersive equationui=auxxx is presented. A collection of criterions for deriving stability conditions of difference schemes is given and applied to these difference schemes.
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Difference Equations and Differential Equations

2012
In this chapter we focus on the Markov model in continuous time. The differential equations are the continuous counter part to the difference equations of the discrete model.
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On the Partial Difference Equations, of Mathematical Physics

, 2015
R. Courant, K. Friedrichs, H. Lewy
semanticscholar   +1 more source

Some differences between difference equations and differential equations

Journal of Difference Equations and Applications, 1996
In this expository paper we discuss some instances in which analogues which might be expected between the behavior of solutions of differential equations and difference equations fail to hold, focussing particularly on questions related to boundedness and oscillation.
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Difference Equations and Inequalities: Theory, Methods, and Applications

, 2019
R. Agarwal
semanticscholar   +1 more source