Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation
In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of the non-linear Hunter–Saxton equation. Firstly, the operational matrices of integration associated with the Fibonacci wavelets are constructed by following the strategy of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/12/15/7738 |
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| author | H. M. Srivastava Firdous A. Shah Naied A. Nayied |
| author_facet | H. M. Srivastava Firdous A. Shah Naied A. Nayied |
| author_sort | H. M. Srivastava |
| collection | DOAJ |
| description | In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of the non-linear Hunter–Saxton equation. Firstly, the operational matrices of integration associated with the Fibonacci wavelets are constructed by following the strategy of Chen and Hsiao. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that can be solved by any classical method, such as Newton’s method. Moreover, the non-linearity arising in the Hunter–Saxton equation is handled by invoking the quasi-linearization technique. To show the efficiency and accuracy of the Fibonacci-wavelet-based numerical technique, the approximate solutions of the non-linear Hunter–Saxton equation with other numerical methods including the Haar wavelet, trigonometric <i>B</i>-spline, and Laguerre wavelet methods are compared. The numerical outcomes demonstrate that the proposed method yields a much more stable solution and a better approximation than the existing ones. |
| first_indexed | 2024-03-09T05:35:17Z |
| format | Article |
| id | doaj.art-2260790fab4a4611929ef9b4cc5f28b8 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T05:35:17Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-2260790fab4a4611929ef9b4cc5f28b82023-12-03T12:29:04ZengMDPI AGApplied Sciences2076-34172022-08-011215773810.3390/app12157738Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton EquationH. M. Srivastava0Firdous A. Shah1Naied A. Nayied2Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, South Campus, University of Kashmir, Anantnag 192101, Jammu and Kashmir, IndiaDepartment of Mathematics, South Campus, University of Kashmir, Anantnag 192101, Jammu and Kashmir, IndiaIn this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of the non-linear Hunter–Saxton equation. Firstly, the operational matrices of integration associated with the Fibonacci wavelets are constructed by following the strategy of Chen and Hsiao. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that can be solved by any classical method, such as Newton’s method. Moreover, the non-linearity arising in the Hunter–Saxton equation is handled by invoking the quasi-linearization technique. To show the efficiency and accuracy of the Fibonacci-wavelet-based numerical technique, the approximate solutions of the non-linear Hunter–Saxton equation with other numerical methods including the Haar wavelet, trigonometric <i>B</i>-spline, and Laguerre wavelet methods are compared. The numerical outcomes demonstrate that the proposed method yields a much more stable solution and a better approximation than the existing ones.https://www.mdpi.com/2076-3417/12/15/7738Hunter–Saxton equationFibonacci waveletFibonacci polynomialoperational matricesquasi-linearizationconvergence |
| spellingShingle | H. M. Srivastava Firdous A. Shah Naied A. Nayied Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation Applied Sciences Hunter–Saxton equation Fibonacci wavelet Fibonacci polynomial operational matrices quasi-linearization convergence |
| title | Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation |
| title_full | Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation |
| title_fullStr | Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation |
| title_full_unstemmed | Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation |
| title_short | Fibonacci Wavelet Method for the Solution of the Non-Linear Hunter–Saxton Equation |
| title_sort | fibonacci wavelet method for the solution of the non linear hunter saxton equation |
| topic | Hunter–Saxton equation Fibonacci wavelet Fibonacci polynomial operational matrices quasi-linearization convergence |
| url | https://www.mdpi.com/2076-3417/12/15/7738 |
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