Bounds for fourth-order [0, 1] difference equations

Kenneth S. Berenhaut; Benjamin G. Gibson; Jonathan H. Newman; Jacob F. Anderson

doi:10.1016/j.camwa.2006.10.039

Bounds for fourth-order [0, 1] difference equations

Kenneth S. Berenhaut
, Benjamin G. Gibson
, Jonathan H. Newman
, Jacob F. Anderson

Geosciences Department

Wake Forest University

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

Abstract

This note examines bounds for fourth-order linear difference equations with coefficients restricted to the unit interval. It is shown that all solutions are of order strictly less than (3 / 2)ⁿ. The bound is shown to be nearly best possible. Applications to zero-one banded matrices are also discussed.

Original language	English
Pages (from-to)	1250-1259
Number of pages	10
Journal	Computers and Mathematics with Applications
Volume	54
Issue number	9-10
DOIs	https://doi.org/10.1016/j.camwa.2006.10.039
State	Published - Nov 2007

Keywords

Explicit bounds
Fourth-order difference equations
Growth rates
Nonconstant coefficients
Restricted coefficients

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10.1016/j.camwa.2006.10.039

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@article{400f9ad1e36f450d8836aa58c05d7544,

title = "Bounds for fourth-order [0, 1] difference equations",

abstract = "This note examines bounds for fourth-order linear difference equations with coefficients restricted to the unit interval. It is shown that all solutions are of order strictly less than (3 / 2)n. The bound is shown to be nearly best possible. Applications to zero-one banded matrices are also discussed.",

keywords = "Explicit bounds, Fourth-order difference equations, Growth rates, Nonconstant coefficients, Restricted coefficients",

author = "Berenhaut, \{Kenneth S.\} and Gibson, \{Benjamin G.\} and Newman, \{Jonathan H.\} and Anderson, \{Jacob F.\}",

year = "2007",

month = nov,

doi = "10.1016/j.camwa.2006.10.039",

language = "English",

volume = "54",

pages = "1250--1259",

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TY - JOUR

T1 - Bounds for fourth-order [0, 1] difference equations

AU - Berenhaut, Kenneth S.

AU - Gibson, Benjamin G.

AU - Newman, Jonathan H.

AU - Anderson, Jacob F.

PY - 2007/11

Y1 - 2007/11

N2 - This note examines bounds for fourth-order linear difference equations with coefficients restricted to the unit interval. It is shown that all solutions are of order strictly less than (3 / 2)n. The bound is shown to be nearly best possible. Applications to zero-one banded matrices are also discussed.

AB - This note examines bounds for fourth-order linear difference equations with coefficients restricted to the unit interval. It is shown that all solutions are of order strictly less than (3 / 2)n. The bound is shown to be nearly best possible. Applications to zero-one banded matrices are also discussed.

KW - Explicit bounds

KW - Fourth-order difference equations

KW - Growth rates

KW - Nonconstant coefficients

KW - Restricted coefficients

UR - https://www.scopus.com/pages/publications/35348916056

U2 - 10.1016/j.camwa.2006.10.039

DO - 10.1016/j.camwa.2006.10.039

M3 - Article

AN - SCOPUS:35348916056

SN - 0898-1221

VL - 54

SP - 1250

EP - 1259

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 9-10

ER -

Bounds for fourth-order [0, 1] difference equations

Abstract

Keywords

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