Sabit Katsayılı İki Boyutlu Lineer Hiperbolik Denklemler İçin Cauchy Probleminin Süreksiz Fonksiyonlar Sınıfında Yüksek Mertebeden Hassas Sonlu Farklar Şeması

Year 2020, , 6 - 12, 30.06.2020

Öykü Yener Bahaddin Sinsoysal Mahir Resulov

https://doi.org/10.20854/bujse.736345

Abstract

Bu çalışmada, hidrodinamiğin çeşitli alanlarında karşılaşılan iki boyutlu skaler adveksiyon denklemi için yazılmış Cauchy probleminin pratik hesaplanması için bir sonlu fark şeması geliştirilmiştir. Bu amaçla, ana probleme göre bazı avantajları olan bir yardımcı problem sunulmuştur. Önerilen yardımcı problem, daha yüksek mertebeden hassas bir sonlu farklar şeması oluşturmaya imkan sağlar.

Keywords

Hidrodinamiğin model denklemleri, Süreksiz fonksiyonlar sınıfında zayıf çözüm

A Higher-Order Sensitive Finite Differences Scheme Of The Cauchy Problem For 2D Linear Hyperbolic Equations With Constant Coefficients In A Class Of Discontinuous Functions

Abstract

In this study we develop a finite difference schema for practical calculation of the Cauchy problem for the 2D scalar advection equation with a higher accuracy oder constant coefficient, encountered in different areas of hydrodynamics. For this aim to develop an auxiliary problem having some advantages over the main problem is introduced. The proposed auxiliary problem permits us construct a higher order sensitive finite differences schema.

Keywords

Modelling equations of hydrodynamics, Weak solution in a class of discontinuous functions

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