Lucas Polynomial Approach for Second Order Nonlinear Differential Equations
This paper presents the Lucas polynomial solution of second-order nonlinear ordinary differential equations with mixed conditions. Lucas matrix method is based on collocation points together with truncated Lucas series. The main advantage of the method is that it has a simple structure to deal with...
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Suleyman Demirel University
2020-04-01
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doaj-af2396d80f9146798c7eec4fbb3115882020-11-25T02:52:27ZengSuleyman Demirel UniversitySüleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi1300-76881308-65292020-04-0124123023610.19113/sdufenbed.546847546847Lucas Polynomial Approach for Second Order Nonlinear Differential EquationsSevin GumgumNurcan Baykus-SavasanerilOmur Kivanc KurkcuMehmet SezerThis paper presents the Lucas polynomial solution of second-order nonlinear ordinary differential equations with mixed conditions. Lucas matrix method is based on collocation points together with truncated Lucas series. The main advantage of the method is that it has a simple structure to deal with the nonlinear algebraic system obtained from matrix relations. The method is applied to four problems. In the first two problems, exact solutions are obtained. The last two problems, Bratu and Duffing equations are solved numerically; the results are compared with the exact solutions and some other numerical solutions. It is observed that the application of the method results in either the exact or accurate numerical solutions.http://dergipark.org.tr/tr/download/article-file/1050893lucas polynomialoperational matricescollocation points |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sevin Gumgum Nurcan Baykus-Savasaneril Omur Kivanc Kurkcu Mehmet Sezer |
spellingShingle |
Sevin Gumgum Nurcan Baykus-Savasaneril Omur Kivanc Kurkcu Mehmet Sezer Lucas Polynomial Approach for Second Order Nonlinear Differential Equations Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi lucas polynomial operational matrices collocation points |
author_facet |
Sevin Gumgum Nurcan Baykus-Savasaneril Omur Kivanc Kurkcu Mehmet Sezer |
author_sort |
Sevin Gumgum |
title |
Lucas Polynomial Approach for Second Order Nonlinear Differential Equations |
title_short |
Lucas Polynomial Approach for Second Order Nonlinear Differential Equations |
title_full |
Lucas Polynomial Approach for Second Order Nonlinear Differential Equations |
title_fullStr |
Lucas Polynomial Approach for Second Order Nonlinear Differential Equations |
title_full_unstemmed |
Lucas Polynomial Approach for Second Order Nonlinear Differential Equations |
title_sort |
lucas polynomial approach for second order nonlinear differential equations |
publisher |
Suleyman Demirel University |
series |
Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
issn |
1300-7688 1308-6529 |
publishDate |
2020-04-01 |
description |
This paper presents the Lucas polynomial solution of second-order nonlinear ordinary differential equations with mixed conditions. Lucas matrix method is based on collocation points together with truncated Lucas series. The main advantage of the method is that it has a simple structure to deal with the nonlinear algebraic system obtained from matrix relations. The method is applied to four problems. In the first two problems, exact solutions are obtained. The last two problems, Bratu and Duffing equations are solved numerically; the results are compared with the exact solutions and some other numerical solutions. It is observed that the application of the method results in either the exact or accurate numerical solutions. |
topic |
lucas polynomial operational matrices collocation points |
url |
http://dergipark.org.tr/tr/download/article-file/1050893 |
work_keys_str_mv |
AT sevingumgum lucaspolynomialapproachforsecondordernonlineardifferentialequations AT nurcanbaykussavasaneril lucaspolynomialapproachforsecondordernonlineardifferentialequations AT omurkivanckurkcu lucaspolynomialapproachforsecondordernonlineardifferentialequations AT mehmetsezer lucaspolynomialapproachforsecondordernonlineardifferentialequations |
_version_ |
1724729900756107264 |