Results 241 to 250 of about 4,949,896 (284)

Nonsymmetric Difference Equations

Journal of the Society for Industrial and Applied Mathematics, 1965
The purpose of this paper is to discuss several nonsymmetric difference equations. By this we mean that not all points are calculated by the same equation. Proofs of convergence will attempt to follow the methods of Richtmyer [4]. Nonsymmetric difference equations are well known at the present time. The Peaceman-Rachford alternating implicit scheme [3]
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Difference Equations as Difference Analogues of Differential Equations

2011
Functional differential equations arise in the modeling of hereditary systems such as ecological and biological systems, chemical and mechanical systems and many-many other. The long-term behavior and stability of such systems is an important area for investigation. For example, will a population decline to dangerously low levels?
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DIFFERENCE EQUATIONS FOR CELLULAR AUTOMATA

International Journal of Bifurcation and Chaos, 2009
In this paper, we propose new difference equations which can generate the evolution rules of cellular automata.
Makoto Itoh, Leon O. Chua
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What is a Difference Equation ?

1986
The theory of difference equations, despite its absence from the undergraduate curriculum, is an old and beautiful part of mathematics, one with diverse applications to many subjects: biology, economics, numerical analysis, etc. In a difference equation, change takes place in discrete time intervals.
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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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