1D and 2D finite-difference operators for periodic functions on arbitrary mesh

This paper presents novel discrete differential operators for periodic functions of one- and two-variables, which relate the values of the derivatives to the values of the function itself for a set of arbitrarily chosen points over the function’s area. It is very characteristic, that the values of t...

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Bibliographic Details
Published in:Archives of Electrical Engineering (Online) Vol. 71; no. 1; pp. 265 - 275
Main Author: Sobczyk, Tadeusz Jan
Format: Journal Article
Language:English
Published: Warsaw Polish Academy of Sciences 01.01.2022
Subjects:
arbitrary meshes
Boundary value problems
Computer engineering
Derivatives
Design optimization
Difference equations
Electrical engineering
Finite difference method
Finite differences
finite-difference operators
Magnetic fields
Mathematical analysis
Nonlinear differential equations
Operators (mathematics)
Ordinary differential equations
Partial differential equations
partial finite difference operators
Periodic functions
two-variable periodic functions
ISSN:2300-2506, 1427-4221, 2300-2506
Online Access:Get full text
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Summary:This paper presents novel discrete differential operators for periodic functions of one- and two-variables, which relate the values of the derivatives to the values of the function itself for a set of arbitrarily chosen points over the function’s area. It is very characteristic, that the values of the derivatives at each point depend on the function values at all points in that area. Such operators allow one to easily create finite-difference equations for boundaryvalue problems. The operators are addressed especially to nonlinear differential equations.
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content type line 14
ISSN:2300-2506
1427-4221
2300-2506
DOI:10.24425/aee.2022.140209