Curve Fitting Initial Guess for Iterative Differential Quadrature Solution of Burgers Equation

Year 2022, , 699 - 709, 01.06.2022

Zekeriya Girgin , Faruk Emre Aysal , Hüseyin Bayrakçeken

https://doi.org/10.2339/politeknik.821806

Abstract

According to presented numerical studies in the literature, the solution of Burgers Equation (BE) performed for dt=0.001 and dt=0.0001 commonly. In this study, numerical solution of BE carried out by using the Iterative Differential Quadrature Method (I-DQM), as dt=0.01. Convergence speed and accuracy of iterative methods depends on the initial guess. Every Partial Differential Equation (PDE) describes one or more than one physical problems from the perspective of the engineering view. Unlike the previous iterative studies, in this work, an initial guess value is used in accordance with the physical nature of the discussed problem by using curve fitting. Absolute error analysis of obtained results performed for comparison with some previous studies. The consequence of comparisons shows that more accurate results and faster solution than other studies could be obtained by using I-DQM with curve fitting initial guess.

Keywords

Burgers equation, iterative differential quadrature method, initial guess, newton-raphson method

Supporting Institution

Afyon Kocatepe University Scientific Research Projects Commission

Project Number

17.FEN.BIL.76

Thanks

This study is supported by Afyon Kocatepe University Scientific Research Projects Commission with 17.FEN.BIL.76 numbered project.

Bugers Denkleminin İterarif Diferansiyel Quadrature Çözümü için Eğri Uydurmalı Başlangıç Tahmini

Abstract

Literatürde sunulan sayısal çalışmalara göre, Burgers Denkleminin (BE) çözümü yaygın olarak dt = 0.001 ve dt = 0.0001 için yapılmıştır. Bu çalışmada BE'nin sayısal çözümü, İteratif Diferansiyel Quadrature Yöntemi (I-DQM) kullanılarak dt = 0.01 olarak gerçekleştirilmiştir. İteratif yöntemlerin yakınsama hızı ve doğruluğu başlangıç tahmini değerine bağlıdır. Her Kısmi Diferansiyel Denklem (PDE), mühendislik bakış açısından bir veya daha fazla fiziksel problemi tanımlar. Önceki iteratif çalışmalardan farklı olarak, bu çalışmada, eğri uydurma kullanılarak tartışılan problemin fiziksel doğasına uygun bir başlangıç tahmini değeri kullanılmıştır. Elde edilen sonuçların mutlak hata analizi, önceki bazı çalışmalarla karşılaştırılmak üzere yapılmıştır. Karşılaştırmaların sonucu, eğri uydurmalı başlangıç tahmini ile I-DQM kullanılarak diğer çalışmalardan daha doğru sonuçların ve daha hızlı çözümün elde edilebileceğini göstermektedir.

Keywords

Burgers denklemi, iteratif diferansiyel quadrature metodu, başlangıç tahmini, newton-raphson metodu

Project Number

17.FEN.BIL.76

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