Finite difference formulas in the complex plane

Among general functions of two variables f ( x , y ), analytic functions f ( z ) with z = x + i y form a very important special case. One consequence of analyticity turns out to be that 2-D finite difference (FD) formulas can be made remarkably accurate already for small stencil sizes. This article...

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Bibliographic Details
Published in:Numerical algorithms Vol. 90; no. 3; pp. 1305 - 1326
Main Author: Fornberg, Bengt
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2022
Springer Nature B.V
Subjects:
Algebra
Algorithms
Analytic functions
Approximation
Computer Science
Finite difference method
Interpolation
Numeric Computing
Numerical Analysis
Numerical differentiation
Original Paper
Stencils
Theory of Computation
30E20
Analytic functions
65E99
Euler-Maclaurin
30-E10
Finite differences
Contour integration
Analytic continuation
Secondary: 30B40
Complex variables
Primary: 30-08
65D25
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:Among general functions of two variables f ( x , y ), analytic functions f ( z ) with z = x + i y form a very important special case. One consequence of analyticity turns out to be that 2-D finite difference (FD) formulas can be made remarkably accurate already for small stencil sizes. This article discusses some key properties of such complex plane FD formulas. Application areas include numerical differentiation, interpolation, contour integration, and analytic continuation.
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content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-021-01231-5