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

Emre Kırlı

Article Details

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

Authors:

Emre Kırlı

Publisher:

Eskişehir Osmangazi University

Main Topics:

Bilgisayar Yazılımı

Journal:

Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.10-15

Document Type:

Article

Publication Date:

6/2023

Document Language:

English

Document ID (Org No.):

2001287657

pISSN:

2687-606X

Keywords:

Abstract:

 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 Adams 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.

 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 Adams 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.

 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 Adams 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.

 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, Adams 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.

Article Details

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

Authors:

Emre Kırlı

Publisher:

Eskişehir Osmangazi University

Main Topics:

Bilgisayar Yazılımı

Journal:

Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.10-15

Document Type:

Article

Publication Date:

6/2023

Document Language:

English

Document ID (Org No.):

2001287657

pISSN:

2687-606X

Quintic Trigonometric B-spline

Modified Regularized Long Wave Equation

Collocation MethodKuintik B-spline

Kolokasyon Metodu

Modified Regularized Long Wave Denklemi

Issues

Article Details

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

Authors: Emre Kırlı

Publisher: Eskişehir Osmangazi University

Main Topics: Bilgisayar Yazılımı

Journal: Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.10-15

Document Type: Article

Publication Date: 6/2023

Document Language: English

Document ID (Org No.): 2001287657

pISSN: 2687-606X

Quintic Trigonometric B-spline

Modified Regularized Long Wave Equation

Collocation MethodKuintik B-spline

Kolokasyon Metodu

Modified Regularized Long Wave Denklemi

Issues

Authors:

Emre Kırlı

Publisher:

Eskişehir Osmangazi University

Main Topics:

Bilgisayar Yazılımı

Journal:

Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.10-15

Document Type:

Article

Publication Date:

6/2023

Document Language:

English

Document ID (Org No.):

2001287657

pISSN:

2687-606X