COLLOCATION METHOD APPLIED TO NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS

Birkan Durak; Aziz Sezgin; Hasan Ömür Özer; Lütfi Emir Sakman; Şule Kapkın

doi:10.17780/ksujes.1346489

EN TR

COLLOCATION METHOD APPLIED TO NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

Integro-differential equations are encountered in such fields of study as mechanics, physics, chemistry, biophysics, astronomy, economic theory, and population dynamics. In rare cases the solution methods for differential and/or integral equations can be generalized to integro-differential equations; but in general, numerical methods have to be applied. Recent years have seen the development of a large number of methods applicable to integro-differential equations. The present study aims to compare these newer methods with the classical method of point collocation, which is one of the weighted residual methods. The method was applied to test problems chosen from the literature, both linear and nonlinear integro-differential equations, and was seen to give good results.

Keywords

İNTEGRO-DİFERANSİYEL DENKLEMLERİN SAYISAL ÇÖZÜMÜNE UYGULANAN KOLLOKASYON YÖNTEMİ

Öz

İntegro-diferansiyel denklemler mekanik, fizik, kimya, biyofizik, astronomi, ekonomi teorisi ve nüfus dinamiği gibi çalışma alanlarında karşımıza çıkmaktadır. Nadir durumlarda diferansiyel ve/veya integral denklemlerin çözüm yöntemleri integro-diferansiyel denklemlere genelleştirilebilir; ancak genel olarak sayısal yöntemlerin uygulanması gerekir. Son yıllarda integro-diferansiyel denklemlere uygulanabilen çok sayıda yöntem geliştirilmiştir. Bu çalışma, bu yeni yöntemleri, ağırlıklı kalıntı yöntemlerinden biri olan klasik nokta kollokasyon yöntemi ile karşılaştırmayı amaçlamaktadır. Yöntem, literatürden seçilen doğrusal ve doğrusal olmayan integro-diferansiyel denklemlerden oluşan test problemlerine uygulanmış ve iyi sonuçlar verdiği görülmüştür.

Anahtar Kelimeler

Thanks

The authors would like to thank Prof.Dr. Erol Uzal for his suggestions and contributions to the study.

References

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Details

Primary Language

English

Subjects

Numerical Methods in Mechanical Engineering

Journal Section

Research Article

Authors

Birkan Durak ^*
0000-0002-8196-5407
Türkiye

Aziz Sezgin
0000-0001-6861-5309
Türkiye

Hasan Ömür Özer
0000-0002-6388-4638
Türkiye

Lütfi Emir Sakman
0000-0002-9599-8875
Türkiye

Şule Kapkın
0000-0003-4951-7089
Türkiye

Publication Date

December 3, 2023

Submission Date

August 21, 2023

Acceptance Date

October 24, 2023

Published in Issue

Year 2023 Volume: 26 Number: 4

DOI

https://doi.org/10.17780/ksujes.1346489

IZ

https://izlik.org/JA93BY43JA

Cite

RIS / Bibtex

APA

Durak, B., Sezgin, A., Özer, H. Ö., Sakman, L. E., & Kapkın, Ş. (2023). COLLOCATION METHOD APPLIED TO NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 26(4), 1010-1020. https://doi.org/10.17780/ksujes.1346489

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