An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation
Yıl: 2022 Cilt: 12 Sayı: 2 Sayfa Aralığı: 269 - 282 Metin Dili: İngilizce DOI: 10.37094/adyujsci.1156498 İndeks Tarihi: 11-01-2023
An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation
Öz: In this paper, we deal with the numerical solution of Sawada-Kotera (SK) equation classified as the type of fifth order Korteweg-de Vries (gfKdV) equation. In the first step of our study consisting of several steps, nonlinear model problem is split into the system with the coupled new equations by using the transformation w_xxx=v. In the second step, to get rid of the nonlinearity of the problem, Rubin-Graves type linearization is used. After these applications, the approximate solutions are obtained by using the trigonometric quintic B-Spline collocation method. The efficiency and accuracy of the present method is demonstrated with the tables and graphs. As it is seen in the tables given with the error norms L_2 and L_∞ for different time and space steps, the present method is more accurate for the larger element numbers and smaller time steps.
Anahtar Kelime: Sawada-Kotera Denklemi için Trigonometrik Beşli Baz Fonksiyonları Kollokasyon Yönteminin Bir Uygulaması
Öz: Bu çalışmada, beşinci dereceden Korteweg-de Vries (gfKdV) denklemlerinin türü olarak sınıflandırılan Sawada-Kotera (SK) denkleminin nümerik çözümü ele alınmaktadır. Birkaç adımdan oluşan çalışmamızın ilk adımında, lineer olmayan model problem w_xxx=v dönüşümü kullanılarak iki yeni denklem sistemine ayrıştırılmıştır. İkinci adımda, problemin lineer olmama durumundan kurtulmak için Rubin-Graves tipi lineerleştirme kullanılmıştır. Bu uygulamalardan sonra trigonometrik beşli B-Spline kollokasyon yöntemi kullanılarak yaklaşık çözümler elde edilmiştir. Mevcut yöntemin etkinliği ve doğruluğu tablolar ve grafiklerle gösterilmiştir. Farklı zaman ve konum adımı için L_2 ve L_∞ hata normları ile verilen tablolardan görüldüğü üzere, mevcut yöntem daha büyük eleman sayıları ve daha küçük zaman adımları için yüksek doğruluktadır.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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| APA | karabenli h, Esen A, YAGMURLU N (2022). An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. , 269 - 282. 10.37094/adyujsci.1156498 |
| Chicago | karabenli hatice,Esen Alaattin,YAGMURLU Nuri Murat An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. (2022): 269 - 282. 10.37094/adyujsci.1156498 |
| MLA | karabenli hatice,Esen Alaattin,YAGMURLU Nuri Murat An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. , 2022, ss.269 - 282. 10.37094/adyujsci.1156498 |
| AMA | karabenli h,Esen A,YAGMURLU N An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. . 2022; 269 - 282. 10.37094/adyujsci.1156498 |
| Vancouver | karabenli h,Esen A,YAGMURLU N An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. . 2022; 269 - 282. 10.37094/adyujsci.1156498 |
| IEEE | karabenli h,Esen A,YAGMURLU N "An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation." , ss.269 - 282, 2022. 10.37094/adyujsci.1156498 |
| ISNAD | karabenli, hatice vd. "An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation". (2022), 269-282. https://doi.org/10.37094/adyujsci.1156498 |
| APA | karabenli h, Esen A, YAGMURLU N (2022). An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. Adıyaman Üniversitesi Fen Bilimleri Dergisi, 12(2), 269 - 282. 10.37094/adyujsci.1156498 |
| Chicago | karabenli hatice,Esen Alaattin,YAGMURLU Nuri Murat An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. Adıyaman Üniversitesi Fen Bilimleri Dergisi 12, no.2 (2022): 269 - 282. 10.37094/adyujsci.1156498 |
| MLA | karabenli hatice,Esen Alaattin,YAGMURLU Nuri Murat An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. Adıyaman Üniversitesi Fen Bilimleri Dergisi, vol.12, no.2, 2022, ss.269 - 282. 10.37094/adyujsci.1156498 |
| AMA | karabenli h,Esen A,YAGMURLU N An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. Adıyaman Üniversitesi Fen Bilimleri Dergisi. 2022; 12(2): 269 - 282. 10.37094/adyujsci.1156498 |
| Vancouver | karabenli h,Esen A,YAGMURLU N An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation. Adıyaman Üniversitesi Fen Bilimleri Dergisi. 2022; 12(2): 269 - 282. 10.37094/adyujsci.1156498 |
| IEEE | karabenli h,Esen A,YAGMURLU N "An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation." Adıyaman Üniversitesi Fen Bilimleri Dergisi, 12, ss.269 - 282, 2022. 10.37094/adyujsci.1156498 |
| ISNAD | karabenli, hatice vd. "An Application of Trigonometric Quintic B-Spline Collocation Method for Sawada-Kotera Equation". Adıyaman Üniversitesi Fen Bilimleri Dergisi 12/2 (2022), 269-282. https://doi.org/10.37094/adyujsci.1156498 |
