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Algorithms for Solving Linear Differential Equations with Rational Function Coefficients.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Algorithms for Solving Linear Differential Equations with Rational Function Coefficients./
Author:	Imamoglu, Erdal.
Description:	1 online resource (70 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355326604

Algorithms for Solving Linear Differential Equations with Rational Function Coefficients.
Imamoglu, Erdal.

Algorithms for Solving Linear Differential Equations with Rational Function Coefficients. - 1 online resource (70 pages)

Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.

Thesis (Ph.D.)--The Florida State University, 2017.

Includes bibliographical references

This thesis introduces two new algorithms to find hypergeometric solutions of second order regular singular differential operators with rational function or polynomial coefficients. Algorithm 3.2.1 searches for solutions of type exp(∫ r dx) • 2F1( a1,a2;b 1;f) and Algorithm 5.2.1 searches for solutions of type exp(∫ r dx) (r0 • 2F1(a1,a 2;b1;f) + r1 • 2F'1(a 1,a2;b1; f) where f, r, r0, r 1 Q¯(x¯) and a 1,a2,b1 ∈ Q. The algorithms use modular reduction, Hensel lifting, rational function reconstruction, and rational number reconstruction to do so. Numerous examples from different branches of science (mostly from combinatorics and physics) showed that the algorithms presented in this thesis are very effective. Presently, Algorithm 5.2.1 is the most general algorithm in the literature to find hypergeometric solutions of such operators.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355326604Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Algorithms for Solving Linear Differential Equations with Rational Function Coefficients.
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245 1 0 $a Algorithms for Solving Linear Differential Equations with Rational Function Coefficients.
264 0 $c 2017
300 $a 1 online resource (70 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Adviser: Mark van Hoeij.
502 $a Thesis (Ph.D.)--The Florida State University, 2017.
504 $a Includes bibliographical references
520 $a This thesis introduces two new algorithms to find hypergeometric solutions of second order regular singular differential operators with rational function or polynomial coefficients. Algorithm 3.2.1 searches for solutions of type exp(∫ r dx) • 2F1( a1,a2;b 1;f) and Algorithm 5.2.1 searches for solutions of type exp(∫ r dx) (r0 • 2F1(a1,a 2;b1;f) + r1 • 2F'1(a 1,a2;b1; f) where f, r, r0, r 1 Q¯(x¯) and a 1,a2,b1 ∈ Q. The algorithms use modular reduction, Hensel lifting, rational function reconstruction, and rational number reconstruction to do so. Numerous examples from different branches of science (mostly from combinatorics and physics) showed that the algorithms presented in this thesis are very effective. Presently, Algorithm 5.2.1 is the most general algorithm in the literature to find hypergeometric solutions of such operators.
520 $a This thesis also introduces a fast algorithm (Algorithm 4.2.3) to find integral bases for arbitrary order regular singular differential operators with rational function or polynomial coefficients. A normalized (Algorithm 4.3.1) integral basis for a differential operator provides us transformations that convert the differential operator to its standard forms (Algorithm 5.1.1) which are easier to solve.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The Florida State University. $b Mathematics. $3 1180541
773 0 $t Dissertation Abstracts International $g 79-02B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10280381 $z click for full text (PQDT)