Modified Regularized Long Wave Denkleminin Nümerik Çözümü İçin Kuintik Trigonometrik B-spline Algoritması

Yıl 2023, Cilt: 4 Sayı: 2, 10 - 15, 30.06.2023

Emre Kırlı

https://doi.org/10.53608/estudambilisim.1288254

Cited By: 1

Öz

Bu çalışma, modified regularized long-wave (MRLW) denklemini çözmek için yeni bir sayısal algoritma sunmaktadır. Konumsal değişkenleri ve türevlerini ayrıklaştırmak için kuintik trigonometrik B-spline kolokasyon tekniği kullanılır ve zamansal türev için, Adam's Moulton şeması uygulanır. Sayısal algoritmanın performans ve verimliliği, tek solitary dalganın hareketini içeren örnek problem üzerinde test edilmiştir. Hata normu ve ve üç korunum sabitleri hesaplanır ve literatürde mevcut olanlardan bazıları ile karşılaştırılır. Hesaplanan sonuçlar, önerilen algoritmanın, mevcut yöntemlere kıyasla MRLW denkleminin yüksek derecede doğru yaklaşık çözümünü elde etmede avantaja sahip olduğunu doğrulamaktadır. Yöntemin avantajı, uygulanmasının kolay olması ve düşük hesaplama maliyeti gerektirmesidir.

Anahtar Kelimeler

Kuintik B-spline, Kolokasyon Metodu, Modified Regularized Long Wave Denklemi

Quintic Trigonometric B-spline Algorithm for Numerical Solution of the Modified Regularized Long Wave Equation

Öz

This study introduces a new numerical algorithm for solving the modified regularized long-wave (MRLW) equation. To discretize the spatial variables and their derivatives, the collocation technique with quintic trigonometric B-spline functions is utilized and for the temporal derivative, the Adam's Moulton scheme is implemented. The performance and efficiency of the computational algorithm is tested on sample problem including the motion of single solitary wave. The error norm and three conservation constants are computed and compared with some of those available in the literature. The computed results verify that the suggested algorithm has the advantage in obtaining a highly accurate approximate solution of the MRLW equation as compared to the existing methods. The advantage of the method is that it is easy to implement and requires the low computational cost.

Anahtar Kelimeler

Quintic Trigonometric B-spline, Modified Regularized Long Wave Equation, Collocation Method

Kaynakça

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