Item Details

abstract

This thesis provides explicit, applicable bounds for solutions of a wide class of second-order difference equations with nonconstant coefficients. Among the applications is an affirmative answer to a question of Stevi´c. We also present bounds for second-order difference equations with positive restricted (nonconstant) coefficients. It is determined that whenever the coefficients of the associated monic equation are less than the constant (1/3)^(1/3), all solutions tend to zero at an exponential rate. This constant is optimal. Some further asymptotic results and optimal explicit inequalities are also given. We then extend our results to give explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher order equations.

subject

growth rates

linear recurrences

partitions

restricted coefficients

contributor

Goedhart, Eva (author)

Fredric T. Howard (committee chair)

Edward E. Allen (committee member)

Kenneth S. Berenhaut (committee member)

creator

Goedhart, Eva

date

2008-09-28T10:50:46Z (accessioned)

2010-06-18T18:59:57Z (accessioned)

2006-05-24 (available)

2008-09-28T10:50:46Z (available)

2010-06-18T18:59:57Z (available)

2005-04-26 (issued)

degree

null (defenseDate)

Mathematics (discipline)

Wake Forest University (grantor)

MA (level)

identifier

FinalThesis.pdf

http://hdl.handle.net/10339/14907 (uri)

migration

etd-05102005-222845 (oldETDId)

rights

Release the entire work immediately for access worldwide. (accessRights)

I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Wake Forest University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. (license)

title

Explicit Bounds for Linear Difference Equations