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The journal was established in 2004 and publishes articles on theory, methodology, and application of difference and differential equations. Originally published by Hindawi Publishing Corporation, the journal was acquired by Springer Science+Business Media in early 2011. [1] The editors-in-chief are Ravi Agarwal, Martin Bohner, and Elena Braverman.
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
Differential Equations is a peer-reviewed mathematics journal published by Springer. Founded in 1965, the journal publishes English translations of papers from the journal Differentsial'nye Uravneniya ( ISSN 0374-0641 ), which publishes in Russian and focuses on work by scholars in states of the former USSR.
When ,,, and the initial condition are real numbers, this difference equation is called a Riccati difference equation. [ 3 ] Such an equation can be solved by writing w t {\displaystyle w_{t}} as a nonlinear transformation of another variable x t {\displaystyle x_{t}} which itself evolves linearly.
Other books on similar topics include A Treatise on the Calculus of Finite Differences by George Boole, Introduction to Difference Equations by S. Goldberg, [5] Difference Equations: An Introduction with Applications by W. G. Kelley and A. C. Peterson, An Introduction to Difference Equations by S. Elaydi, Theory of Difference Equations: An Introduction by V. Lakshmikantham and D. Trigiante ...
For many sensory modalities, over a wide range of stimulus magnitudes sufficiently far from the upper and lower limits of perception, the 'JND' is a fixed proportion of the reference sensory level, and so the ratio of the JND/reference is roughly constant (that is the JND is a constant proportion/percentage of the reference level).
A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. [1] [2] The order of the equation is the maximum time gap between any two indicated values of the variable vector. For ...
For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).