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

Year 2020, Volume: 10 Issue: 4, 1169 - 1181, 15.10.2020

Baransel Güneş , Afshin Barati Chianeh Mutlu Demirbaş

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

This article was retracted on October 15, 2020. https://dergipark.org.tr/en/pub/gumusfenbil/issue/57242/1195843

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

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

This article was retracted on October 15, 2020. https://dergipark.org.tr/en/pub/gumusfenbil/issue/57242/1195843

Abstract

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.

Keywords

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

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