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

Yıl 2019, Cilt: 7 Sayı: 2, 653 - 656, 26.12.2019

Melis Zorsahin Gorgulu

https://doi.org/10.18586/msufbd.621498

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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