Results 21 to 30 of about 4,153,672 (273)
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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Spectral equivalences, Bethe ansatz equations, and reality properties in PT-symmetric quantum mechanics [PDF]
, 2001 The one-dimensional Schrodinger equation for the potential x(6)+alphax(2)+l (l+1)/x(2) has many interesting properties. For certain values of the parameters I and a the equation is in turn supersymmetric (Witten) and quasi-exactly solvable (Turbiner ...
Dunning, Clare +2 more
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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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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
A discrete linearizability test based on multiscale analysis [PDF]
, 2010 In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution.
C Scimiterna +6 more
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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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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
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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
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Numerical solution of the Falkner-Skan equation using third-order and high-order-compact finite difference schemes [PDF]
, 2011 We present a computational study of the solution of the Falkner-Skan equation (a third-order boundary value problem arising in boundary-layer theory) using high-order and high-order-compact finite differences schemes.
Galeano, Carlos +5 more
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