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Algorithms for Solving Linear Differ...

Imamoglu, Erdal.

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Algorithms for Solving Linear Differential Equations with Rational Function Coefficients.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Algorithms for Solving Linear Differential Equations with Rational Function Coefficients./
作者:	Imamoglu, Erdal.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
面頁冊數:	70 p.
附註:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10280381
ISBN:	9780355326604

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

Algorithms for Solving Linear Differential Equations with Rational Function Coefficients. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 70 p.

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

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

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.

ISBN: 9780355326604Subjects--Topical Terms:

515831
Mathematics.

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.
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300 $a 70 p.
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.
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.
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