A High-Order Accurate Numerical Algorithm for the Numerical Solution of Burgers’ Equation

Öz

In this study, a high accurate numerical solution of the Burgers’ equation is obtained. For this, the collocation method based on quintic B-spline functions for space discretization and the fourth-order single step method for time discretization are used. In order to see the efficiency of the algorithm, a test problem with an analytical solution is discussed and compared with the numerical solution obtained.

Anahtar Kelimeler

• Burgers' equation,Collocation method,fourth order single step method,quintic B-spline functions

Burgers Denkleminin Nümerik Çözümü için Yüksek Dereceden Doğruluklu Nümerik Algoritma

Öz

Bu çalışmada, Burgers denkleminin yüksek doğruluklu bir sayısal çözümü elde edilmiştir. Bunun için, konum ayrıştırmasında quintic B-spline fonksiyonlarını temel alan kolokasyon yöntemi ve zaman ayrıştırmasında dördüncü dereceden tek adımlı yöntem kullanılmıştır. Algoritmanın etkinliğini görmek için, analitik çözüme sahip bir test problemi ele alınmış ve elde edilen sayısal çözümler ile karşılaştırılmıştır.

Anahtar Kelimeler

• Burgers denklemi,Dördüncü dereceden tek adımlı yöntem,Kolokasyon metodu,Kuintik B-spline fonksiyonları

Kaynakça

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