A new implicit-explicit local differential method for boundary value problems

Hüseyin Tunç; Murat Sari

doi:10.3906/mat-2009-68

A new implicit-explicit local differential method for boundary value problems

Hüseyin Tunç
, Murat Sari^*

^*Bu çalışma için yazışmadan sorumlu yazar

Yildiz Technical University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

2 Atıf (Scopus)

Özet

In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM is investigated by following the analysis of approximation matrices. To illustrate efficiency of the method, qualitative and quantitative results are presented for various challenging BVPs. It is tested that the current method is reliable and accurate for a broad range of problems even for strongly nonlinear and singularly perturbed BVPs. The produced results have revealed that the IELDTM is more accurate than the existing ones in literature.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	742-766
Sayfa sayısı	25
Dergi	Turkish Journal of Mathematics
Hacim	45
Basın numarası	2
DOI'lar	https://doi.org/10.3906/mat-2009-68
Yayın durumu	Yayınlandı - 2021
Harici olarak yayınlandı	Evet

Bibliyografik not

Publisher Copyright:
© 2021. TÜBİTAK.

Finansman

The authors thank the anonymous referees of the Turkish Journal of Mathematics for their valuable comments and suggestions to improve the article. The first author would like to thank the Science Fellowships and Grant Programmes Department of TÜBİTAK (BİDEB) for their financial support to his academic research. The second author thanks Dr. Aniela Balacescu (Constantin Brâncuşi University of Târgu Jiu, Romania) for the great hospitality during the conference. The authors thank the anonymous referees of the Turkish Journal of Mathematics for their valuable comments and suggestions to improve the article. The first author would like to thank the Science Fellowships and Grant Programmes Department of T?B?TAK (B?DEB) for their financial support to his academic research. The second author thanks Dr. Aniela Balacescu (Constantin Br?ncu?i University of T?rgu Jiu, Romania) for the great hospitality during the conference.

Finansörler
Programmes Department of T?B?TAK
Programmes Department of TÜBİTAK

Belgeye Erişim

10.3906/mat-2009-68

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "A new implicit-explicit local differential method for boundary value problems",

abstract = "In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM is investigated by following the analysis of approximation matrices. To illustrate efficiency of the method, qualitative and quantitative results are presented for various challenging BVPs. It is tested that the current method is reliable and accurate for a broad range of problems even for strongly nonlinear and singularly perturbed BVPs. The produced results have revealed that the IELDTM is more accurate than the existing ones in literature.",

keywords = "Implicit-explicit methods, Taylor series, boundary value problem, numerical algorithms, stiff problems",

author = "H{\"u}seyin Tun{\c c} and Murat Sari",

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year = "2021",

doi = "10.3906/mat-2009-68",

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TY - JOUR

T1 - A new implicit-explicit local differential method for boundary value problems

AU - Tunç, Hüseyin

AU - Sari, Murat

PY - 2021

Y1 - 2021

N2 - In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM is investigated by following the analysis of approximation matrices. To illustrate efficiency of the method, qualitative and quantitative results are presented for various challenging BVPs. It is tested that the current method is reliable and accurate for a broad range of problems even for strongly nonlinear and singularly perturbed BVPs. The produced results have revealed that the IELDTM is more accurate than the existing ones in literature.

AB - In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM is investigated by following the analysis of approximation matrices. To illustrate efficiency of the method, qualitative and quantitative results are presented for various challenging BVPs. It is tested that the current method is reliable and accurate for a broad range of problems even for strongly nonlinear and singularly perturbed BVPs. The produced results have revealed that the IELDTM is more accurate than the existing ones in literature.

KW - Implicit-explicit methods

KW - Taylor series

KW - boundary value problem

KW - numerical algorithms

KW - stiff problems

UR - https://www.scopus.com/pages/publications/85103730259

U2 - 10.3906/mat-2009-68

DO - 10.3906/mat-2009-68

M3 - Article

AN - SCOPUS:85103730259

SN - 1300-0098

VL - 45

SP - 742

EP - 766

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 2

ER -

A new implicit-explicit local differential method for boundary value problems

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

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