One-sided invertibility of discrete operators with bounded coefficients

We study linear subspaces invariant under discrete operators corresponding to finitedifference approximations of differential operators with polynomial nonlinearities. In several cases, we establish a certain structural stability of invariant subspaces and sets of nonlinear differential operators of reaction–diffusion type with respect to their spatial discretisation. The corresponding lower-dimensional reductions of the finite-difference solutions on the invariant subspaces are constructed.

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q-Discrete Operators and Their Results

Applications of q-Calculus in Operator Theory ◽

10.1007/978-1-4614-6946-9_2 ◽

2013 ◽

pp. 15-72

Author(s):

Ali Aral ◽

Vijay Gupta ◽

Ravi P. Agarwal

Keyword(s):

Discrete Operators

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Discrete differential operators for periodic and two-periodic time functions

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/compel-03-2018-0123 ◽

2019 ◽

Vol 38 (1) ◽

pp. 325-347 ◽

Cited By ~ 2

Author(s):

Tadeusz Sobczyk ◽

Michał Radzik ◽

Natalia Radwan-Pragłowska

Keyword(s):

Differential Operators ◽

High Accuracy ◽

Large Set ◽

Periodic Functions ◽

Content Type ◽

Second Derivatives ◽

Non Linear ◽

Discrete Operators ◽

Linear Differential ◽

Very High

Purpose To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions. Design/methodology/approach The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions. Findings Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic. Research limitations/implications Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist. Practical implications Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time. Originality/value Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.

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TWO-SCALE ESTIMATES FOR SPECIAL FINITE DISCRETE OPERATORS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2017.1307790 ◽

2017 ◽

Vol 22 (3) ◽

pp. 300-310 ◽

Cited By ~ 4

Author(s):

Alexander V. Vasilyev ◽

Vladimir B. Vasilyev

Keyword(s):

Integral Operator ◽

Discrete Approximation ◽

Discrete Operators ◽

Discrete Functions

We consider a certain finite discrete approximation for multidimensional Calderon–Zygmund integral operator and give a comparison between solutions of corresponding equations in some spaces of discrete functions.

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