Baransel GÜNEŞ, Afshin B. CHIANEH, Mutlu DEMİRBAŞ

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

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.

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

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

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