The pseudo-differential approach to finite differences revisited

Peter A. Markowich; Frederic Poupaud

doi:10.1007/s100920050029

The pseudo-differential approach to finite differences revisited

Peter A. Markowich^*, Frederic Poupaud

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We systematically derive arbitrary-order finite difference discretizations of linear (pseudo-) differential problems by appropriately approximating the symbols of the (pseudo) differential operators in frequency space. The convergence (i.e., stability and consistency) analysis of the difference schemes is based directly on micro-local properties of the exact and approximating symbols. The analytical approach presented here sheds new light on the general philosophy of finite differences.

Original language	English (US)
Pages (from-to)	161-186
Number of pages	26
Journal	Calcolo
Volume	36
Issue number	3
DOIs	https://doi.org/10.1007/s100920050029
State	Published - 1999
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics

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10.1007/s100920050029

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title = "The pseudo-differential approach to finite differences revisited",

abstract = "We systematically derive arbitrary-order finite difference discretizations of linear (pseudo-) differential problems by appropriately approximating the symbols of the (pseudo) differential operators in frequency space. The convergence (i.e., stability and consistency) analysis of the difference schemes is based directly on micro-local properties of the exact and approximating symbols. The analytical approach presented here sheds new light on the general philosophy of finite differences.",

author = "Markowich, {Peter A.} and Frederic Poupaud",

year = "1999",

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T1 - The pseudo-differential approach to finite differences revisited

AU - Markowich, Peter A.

AU - Poupaud, Frederic

PY - 1999

Y1 - 1999

N2 - We systematically derive arbitrary-order finite difference discretizations of linear (pseudo-) differential problems by appropriately approximating the symbols of the (pseudo) differential operators in frequency space. The convergence (i.e., stability and consistency) analysis of the difference schemes is based directly on micro-local properties of the exact and approximating symbols. The analytical approach presented here sheds new light on the general philosophy of finite differences.

AB - We systematically derive arbitrary-order finite difference discretizations of linear (pseudo-) differential problems by appropriately approximating the symbols of the (pseudo) differential operators in frequency space. The convergence (i.e., stability and consistency) analysis of the difference schemes is based directly on micro-local properties of the exact and approximating symbols. The analytical approach presented here sheds new light on the general philosophy of finite differences.

UR - http://www.scopus.com/inward/record.url?scp=0011569744&partnerID=8YFLogxK

U2 - 10.1007/s100920050029

DO - 10.1007/s100920050029

M3 - Article

AN - SCOPUS:0011569744

SN - 0008-0624

VL - 36

SP - 161

EP - 186

JO - Calcolo

JF - Calcolo

IS - 3

ER -

The pseudo-differential approach to finite differences revisited

Abstract

ASJC Scopus subject areas

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