Two Reliable Computational Techniques for Solving the MRLW Equation
In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using the Sinc-collocation method. This approach approximates the space dimension of the solution with a cardinal expansion of Sinc functions. First, discretizing the time derivative of the MRLW equ...
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MDPI AG
2023-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/2/174 |
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| author | Kamel Al-Khaled Haneen Jafer |
| author_facet | Kamel Al-Khaled Haneen Jafer |
| author_sort | Kamel Al-Khaled |
| collection | DOAJ |
| description | In this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using the Sinc-collocation method. This approach approximates the space dimension of the solution with a cardinal expansion of Sinc functions. First, discretizing the time derivative of the MRLW equation by a classic finite difference formula, while the space derivatives are approximated by a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><mo>—</mo></mrow></semantics></math></inline-formula>weighted scheme. For comparison purposes, we also find a soliton solution using the Adomian decomposition method (ADM). The Sinc-collocation method was were found to be more accurate and efficient than the ADM schemes. Furthermore, we show that the number of solitons generated can be approximated using the Maxwellian initial condition. The proposed methods’ results, analytical solutions, and numerical methods are compared. Finally, a variety of graphical representations for the obtained solutions makes the dynamics of the MRLW equation visible and provides the mathematical foundation for physical and engineering applications. |
| first_indexed | 2024-03-11T09:10:35Z |
| format | Article |
| id | doaj.art-f6b194939d384219bce7aa5f809e15a4 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:10:35Z |
| publishDate | 2023-02-01 |
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| series | Axioms |
| spelling | doaj.art-f6b194939d384219bce7aa5f809e15a42023-11-16T19:06:19ZengMDPI AGAxioms2075-16802023-02-0112217410.3390/axioms12020174Two Reliable Computational Techniques for Solving the MRLW EquationKamel Al-Khaled0Haneen Jafer1Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, JordanDepartment of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, JordanIn this paper, a numerical solution of the modified regularized long wave (MRLW) equation is obtained using the Sinc-collocation method. This approach approximates the space dimension of the solution with a cardinal expansion of Sinc functions. First, discretizing the time derivative of the MRLW equation by a classic finite difference formula, while the space derivatives are approximated by a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><mo>—</mo></mrow></semantics></math></inline-formula>weighted scheme. For comparison purposes, we also find a soliton solution using the Adomian decomposition method (ADM). The Sinc-collocation method was were found to be more accurate and efficient than the ADM schemes. Furthermore, we show that the number of solitons generated can be approximated using the Maxwellian initial condition. The proposed methods’ results, analytical solutions, and numerical methods are compared. Finally, a variety of graphical representations for the obtained solutions makes the dynamics of the MRLW equation visible and provides the mathematical foundation for physical and engineering applications.https://www.mdpi.com/2075-1680/12/2/174MRLW equationsoliton solutionssinc-collocation methodAdomian decomposition method |
| spellingShingle | Kamel Al-Khaled Haneen Jafer Two Reliable Computational Techniques for Solving the MRLW Equation Axioms MRLW equation soliton solutions sinc-collocation method Adomian decomposition method |
| title | Two Reliable Computational Techniques for Solving the MRLW Equation |
| title_full | Two Reliable Computational Techniques for Solving the MRLW Equation |
| title_fullStr | Two Reliable Computational Techniques for Solving the MRLW Equation |
| title_full_unstemmed | Two Reliable Computational Techniques for Solving the MRLW Equation |
| title_short | Two Reliable Computational Techniques for Solving the MRLW Equation |
| title_sort | two reliable computational techniques for solving the mrlw equation |
| topic | MRLW equation soliton solutions sinc-collocation method Adomian decomposition method |
| url | https://www.mdpi.com/2075-1680/12/2/174 |
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