Comparison of Multiple Scales Method and Finite Difference Method for Solving Singularly Perturbed Convection Diffusion Problem

Baransel Güneş; Afshin Barati Chianeh; Mutlu Demirbaş

doi:10.17714/gumusfenbil.697534

EN TR

Comparison of Multiple Scales Method and Finite Difference Method for Solving Singularly Perturbed Convection Diffusion Problem

This article was retracted on October 15, 2020. https://dergipark.org.tr/tr/pub/gumusfenbil/article/1195843

Abstract

In this study, multiple scale method is introduced for singularly perturbed convection-diffusion equation. In this context, the mentioned problem is transformed into partial differential equation. Besides exponentially fitted difference scheme is established by the method of integral identities with using linear basis functions and interpolating quadrature rules with weight functions and remainder term in integral form. Some numerical experiments have been carried out to validate the theoretical results. The main objective of this article is to compare the multiple scale method and finite difference method for singularly perturbed convection-diffusion problems.

Keywords

Boundary Layer , Difference Scheme , Multiple Scales Method , Singular Perturbation , Uniform Convergent

Singüler Pertürbe Özellikli Konveksiyon Difüzyon Problemleri İçin Çoklu Ölçekler Metodu ve Sonlu Fark Metodunun Karşılaştırılması

Bu makale 15 Ekim 2020 tarihinde geri çekildi. https://dergipark.org.tr/tr/pub/gumusfenbil/article/1195843

Öz

Bu çalışmada singüler pertürbe özellikli konveksiyon difüzyon problemi için çoklu ölçekler metodu tanıtılmıştır. Bu bağlamda, söz konusu problem kısmi diferansiyel denklemlere dönüştürülmüştür. Ayrıca ağırlık fonksiyonu içeren ve kalan terimi integral biçiminde olan interpolasyon kuadratür kuralları ve lineer baz fonksiyonlarının kullanımı ile üstel katsayılı fark şeması kurulmuştur. Teorik sonuçları doğrulamak için bazı nümerik çalışmalara yer verilmiştir. Bu makalenin temel amacı, singüler pertürbe özellikli konveksiyon-difüzyon problemleri için çoklu ölçekler metodu ile sonlu fark metodunu karşılaştırmaktır.

Anahtar Kelimeler

Sınır Katmanı , Fark Şeması , Çoklu Ölçekler Metodu , Singüler Pertürbasyon , Düzgün Yakınsaklık

Kaynakça

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yazarlar

Baransel Güneş ^*
0000-0002-3265-8881
Türkiye

Afshin Barati Chianeh Bu kişi benim
0000-0002-9958-7117
Türkiye

Mutlu Demirbaş Bu kişi benim
0000-0001-8187-3919
Türkiye

Yayımlanma Tarihi

15 Ekim 2020

Gönderilme Tarihi

3 Mart 2020

Kabul Tarihi

28 Eylül 2020

Yayımlandığı Sayı

Yıl 2020 Cilt: 10 Sayı: 4

DOI

https://doi.org/10.17714/gumusfenbil.697534

IZ

https://izlik.org/JA22GZ87ZX

APA

Güneş, B., Barati Chianeh, A., & Demirbaş, M. (2020). Comparison of Multiple Scales Method and Finite Difference Method for Solving Singularly Perturbed Convection Diffusion Problem. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(4), 1169-1181. https://doi.org/10.17714/gumusfenbil.697534

e-ISSN: 2146-538X Yayın Modeli: Sürekli Yayın Atıf Dizinleri: TR Dizin , SCOPUS

Comparison of Multiple Scales Method and Finite Difference Method for Solving Singularly Perturbed Convection Diffusion Problem

Abstract

Keywords

Singüler Pertürbe Özellikli Konveksiyon Difüzyon Problemleri İçin Çoklu Ölçekler Metodu ve Sonlu Fark Metodunun Karşılaştırılması

Öz

Anahtar Kelimeler

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

DOI

IZ

Kaynak Göster