One-sided invertibility of discrete operators with bounded coefficients

2021 ◽  
Author(s):  
Luis Eduardo Flores-Zapotitla ◽  
Yuri I. Karlovich
Keyword(s):  
Discrete Operators

On invariant subspaces for nonlinear finite-difference operators

1998 ◽  
Vol 128 (6) ◽  
pp. 1293-1308 ◽  
Author(s):  
Victor A. Galaktionov
Keyword(s):  
Finite Difference ◽  
Differential Operators ◽  
Invariant Subspaces ◽  
Reaction Diffusion ◽  
Difference Operators ◽  
Diffusion Type ◽  
Nonlinear Differential Operators ◽  
Discrete Operators ◽  
Spatial Discretisation ◽  
Lower Dimensional

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.

q-Discrete Operators and Their Results

2013 ◽  
pp. 15-72
Author(s):  
Ali Aral ◽  
Vijay Gupta ◽  
Ravi P. Agarwal
Keyword(s):  
Discrete Operators

Discrete differential operators for periodic and two-periodic time functions

2019 ◽  
Vol 38 (1) ◽  
pp. 325-347 ◽  
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.

scholarly journals TWO-SCALE ESTIMATES FOR SPECIAL FINITE DISCRETE OPERATORS

2017 ◽  
Vol 22 (3) ◽  
pp. 300-310 ◽  
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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