Results 11 to 20 of about 2,673 (255)
Solvability of a class of hyperbolic-cosine-type difference equations
Advances in Difference Equations, 2020 We describe a method for constructing one of the basic classes of solvable hyperbolic-cosine-type difference equations, generalizing a known difference equation by Laplace in a natural way.
Stevo Stević +3 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 We introduce notion of a generalized invariant for difference equations, which naturally generalizes notion of an invariant for the equations. Some motivations, basic examples and methods for application of invariants in the theory of solvability of ...
Stevo Stevic
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Quasiexactly solvable difference equations [PDF]
Journal of Mathematical Physics, 2007 Several explicit examples of quasiexactly solvable “discrete” quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogs of the well-known quasiexactly solvable systems, the harmonic oscillator (with∕without the centrifugal potential) deformed by a sextic ...
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Solvability of a one-parameter class of nonlinear second-order difference equations by invariants
Advances in Difference Equations, 2019 By using an invariant we show in an original and quite unexpected way that a one-parameter class of nonlinear second-order difference equations is solvable in closed form, improving and theoretically explaining a recent result in the literature.
Stevo Stević
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New Quasi-Exactly Solvable Difference Equation [PDF]
Journal of Nonlinear Mathematical Physics, 2008 Exact solvability of two typical examples of the discrete quantum mechanics, i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials with full parameters, is newly demonstrated both at the Schroedinger and Heisenberg picture levels.
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Electronic Journal of Qualitative Theory of Differential Equations, 2014 Well-defined solutions of the bilinear difference equation are represented in terms of generalized Fibonacci sequences and the initial value. Our results extend and give natural explanations of some recent results in the literature.
Stevo Stevic
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On some classes of solvable difference equations related to iteration processes
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We present several classes of nonlinear difference equations solvable in closed form, which can be obtained from some known iteration processes, and for some of them we give some generalizations by presenting methods for constructing them.
Stevo Stevic
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 We present general solutions to four classes of nonlinear difference equations, as well as some representations of the general solutions for two of the classes in terms of specially chosen solutions to linear homogeneous difference equations with ...
Stevo Stevic
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Note on a discrete initial value problem from a competition
Advances in Difference Equations, 2021 The following discrete initial value problem x n + 1 = x n ( x n − 1 2 − 2 ) − x 1 , n ∈ N , $$ x_{n+1}=x_{n}\bigl(x_{n-1}^{2}-2 \bigr)-x_{1},\quad n\in {\mathbb{N}}, $$ x 0 = 2 $x_{0}=2$ and x 1 = 5 / 2 $x_{1}=5/2$ , appeared at an international ...
Stevo Stević
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Some representations of the general solution to a difference equation of additive type
Advances in Difference Equations, 2019 The general solution to the difference equation xn+1=axnxn−1xn−2+bxn−1xn−2+cxn−2+dxnxn−1xn−2,n∈N0, $$x_{n+1}=\frac {ax_{n}x_{n-1}x_{n-2}+bx_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n}x_{n-1}x_{n-2}},\quad n\in\mathbb{N}_{0}, $$ where a,b,c∈C $a, b, c\in\mathbb{C}$, d∈
Stevo Stević
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