Results 31 to 40 of about 2,765 (249)
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 ...
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source
Representations of general solutions to some classes of nonlinear difference equations
Advances in Difference Equations, 2019 Representations of general solutions to three related classes of nonlinear difference equations in terms of specially chosen solutions to linear difference equations with constant coefficients are given.
Stevo Stević +2 more
doaj +1 more source
Solution of a Solvable System of Difference Equation
Ikonion Journal of Mathematics, 2022 In this study we give solutions for the following difference equation sytem x_{n+1}= (a.x_{n}y_{n-3}/y_{n-2}-\alpha)+\beta y_{n+1}=(b.x_{n-3}y_{n}/x_{n-2}-\beta) +\alpha n ∈N0 where the parameters a,b,, and initial values x_{-i}, y_{-i}, i=0,1,2,3 are non-zero real numbers. We show the asymptotic behavior of the system of equation.
GELİŞKEN, Ali, ARI, Murat
openaire +2 more sources
Representation of solutions of a solvable nonlinear difference equation of second order
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We present a representation of well-defined solutions to the following nonlinear second-order difference equation $$x_{n+1}=a+\frac{b}{x_n}+\frac{c}{x_nx_{n-1}},\quad n\in\mathbb{N}_0,$$ where parameters $a, b, c$, and initial values $x_{-1}$ and $x_0 ...
Stevo Stevic +3 more
doaj +1 more source
Journal of Inequalities and Applications, 2021 There has been some recent interest in investigating the hyperbolic-cotangent types of difference equations and systems of difference equations. Among other things their solvability has been studied.
Stevo Stević +3 more
doaj +1 more source
Mathematics, 2022 In this work, we study the bifurcation and the numerical analysis of the nonlinear Benjamin-Bona-Mahony-KdV equation. According to the bifurcation theory of a dynamic system, the various kinds of traveling wave profiles are obtained including the ...
Teeranush Suebcharoen +2 more
doaj +1 more source
Two ways for solving a class of rational second-order difference equations
Advances in Difference Equations, 2019 We consider a class of second-order rational difference equations with two parameters, and we show, in two ways, that the class of equations is solvable in closed form. One way is based on using an invariant for the class of equations, whereas the second
Stevo Stević
doaj +1 more source
Energy Reports, 2020 We propose a simple but non-trivial mathematical model of a dam–reservoir system balancing between the downstream environmental management and hydropower production.
Hidekazu Yoshioka
doaj +1 more source