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Classification of nonoscillatory solutions of higher order neutral type difference equations

Ethiraju Thandapani, P. Sundaram, John R. Graef, A. Miciano, Paul W. Spikes (1995)

Archivum Mathematicum

The authors consider the difference equation Δ m [ y n - p n y n - k ] + δ q n y σ ( n + m - 1 ) = 0 ( * ) where m ≥ 2 , δ = ± 1 , k ∈ N 0 = { 0 , 1 , 2 , ⋯ } , Δ y n = y n + 1 - y n , q n > 0 , and { σ ( n ) } is a sequence of integers with σ ( n ) ≤ n and lim n → ∞ σ ( n ) = ∞ . They obtain results on the classification of the set of nonoscillatory solutions of ( * ) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included.

Classification rationnelle et confluence des systèmes aux différences singuliers réguliers

Julien Roques (2006)

Annales de l’institut Fourier

En choisissant des “caractères” et des “logarithmes”, méromorphes sur ℂ , construits à l’aide de la fonction Gamma d’Euler, et en utilisant des séries de factorielles convergentes, nous sommes en mesure, dans une première partie, de donner une “forme normale” pour les solutions d’un système aux différences singulier régulier. Nous pouvons alors définir une matrice de connexion d’un tel système. Nous étudions ensuite, suivant une idée de G.D. Birkhoff, le lien de celles-ci avec le problème de la classification...

Conjugacy criteria for second order linear difference equations

Ondřej Došlý, Pavel Řehák (1998)

Archivum Mathematicum

We establish conditions which guarantee that the second order difference equation Δ 2 x k + p k x k + 1 = 0 possesses a nontrivial solution with at least two generalized zero points in a given discrete interval

Continuous dependence on parameters for second order discrete BVP’s

Marek Galewski, Szymon Głąb (2012)

Open Mathematics

Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.

Criterion of p -criticality for one term 2 n -order difference operators

Petr Hasil (2011)

Archivum Mathematicum

We investigate the criticality of the one term 2 n -order difference operators l ( y ) k = Δ n ( r k Δ n y k ) . We explicitly determine the recessive and the dominant system of solutions of the equation l ( y ) k = 0 . Using their structure we prove a criticality criterion.

Difference operators from interpolating moving least squares and their deviation from optimality

Thomas Sonar (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp. 37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.

Difference operators from interpolating moving least squares and their deviation from optimality

Thomas Sonar (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.

Currently displaying 61 – 80 of 395