Numerical approximation with the splitting algorithm to a solution of the modified regularized long wave equation

Melike Karta

Article Details

Numerical approximation with the splitting algorithm to a solution of the modified regularized long wave equation

Authors:

Melike Karta

Publisher:

Ankara University

Main Topics:

Applied Mathematics

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.1034-1054

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001303622

pISSN:

1303-5991

Keywords:

Abstract:

 In this article, a Lie-Totter splitting algorithm, which is highly reliable, flexible and convenient, is proposed along with the collocation finite element method to approximate solutions of the modified regular long wave equation. For this article, quintic B-spline approximation functions are used in the implementation of collocation methods. Four numerical examples including a single solitary wave, the interaction of two- three solitary waves, and a Maxwellian initial condition are presented to test the closeness of the solutions obtained by the proposed algorithm to the exact solutions. The solutions produced are compared with those in some studies with the same parameters that exist in the literature. The fact that the present algorithm produces results as intended is a proof of how useful, accurate and reliable it is. It can be stated that this fact will be very useful the application of the presented technique for other partial differential equations, with the thought that it may lead the reader to obtain superior results from this study.

 In this article, a Lie-Totter splitting algorithm, which is highly reliable, flexible and convenient, is proposed along with the collocation finite element method to approximate solutions of the modified regular long wave equation. For this article, quintic B-spline approximation functions are used in the implementation of collocation methods. Four numerical examples including a single solitary wave, the interaction of two- three solitary waves, and a Maxwellian initial condition are presented to test the closeness of the solutions obtained by the proposed algorithm to the exact solutions. The solutions produced are compared with those in some studies with the same parameters that exist in the literature. The fact that the present algorithm produces results as intended is a proof of how useful, accurate and reliable it is. It can be stated that this fact will be very useful the application of the presented technique for other partial differential equations, with the thought that it may lead the reader to obtain superior results from this study.

 In this article, a Lie-Totter splitting algorithm, which is highly reliable, flexible and convenient, is proposed along with the collocation finite element method to approximate solutions of the modified regular long wave equation. For this article, quintic B-spline approximation functions are used in the implementation of collocation methods. Four numerical examples including a single solitary wave, the interaction of two- three solitary waves, and a Maxwellian initial condition are presented to test the closeness of the solutions obtained by the proposed algorithm to the exact solutions. The solutions produced are compared with those in some studies with the same parameters that exist in the literature. The fact that the present algorithm produces results as intended is a proof of how useful, accurate and reliable it is. It can be stated that this fact will be very useful the application of the presented technique for other partial differential equations, with the thought that it may lead the reader to obtain superior results from this study.

 In this article, a Lie-Totter splitting algorithm, which is highly reliable, flexible and convenient, is proposed along with the collocation finite element method to approximate solutions of the modified regular long wave equation. For this article, quintic B-spline approximation functions are used in the implementation of collocation methods. Four numerical examples including a single solitary wave, the interaction of two- three solitary waves, and a Maxwellian initial condition are presented to test the closeness of the solutions obtained by the proposed algorithm to the exact solutions. The solutions produced are compared with those in some studies with the same parameters that exist in the literature. The fact that the present algorithm produces results as intended is a proof of how useful, accurate and reliable it is. It can be stated that this fact will be very useful the application of the presented technique for other partial differential equations, with the thought that it may lead the reader to obtain superior results from this study.

Article Details

Numerical approximation with the splitting algorithm to a solution of the modified regularized long wave equation

Authors:

Melike Karta

Publisher:

Ankara University

Main Topics:

Applied Mathematics

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.1034-1054

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001303622

pISSN:

1303-5991

The modified regularized long wave equation

B-splines

collocation method

Lie- Trotter splitting

Issues

Article Details

Numerical approximation with the splitting algorithm to a solution of the modified regularized long wave equation

Authors: Melike Karta

Publisher: Ankara University

Main Topics: Applied Mathematics

Journal: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.1034-1054

Document Type: Article

Publication Date: 12/2023

Document Language: English

Document ID (Org No.): 2001303622

pISSN: 1303-5991

The modified regularized long wave equation

B-splines

collocation method

Lie- Trotter splitting

Issues

Authors:

Melike Karta

Publisher:

Ankara University

Main Topics:

Applied Mathematics

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.72 Issue 4, pp.1034-1054

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001303622

pISSN:

1303-5991