Numerical Approach Based on the Haar Wavelet Collocation Method for Solving a Coupled System with the Caputo–Fabrizio Fractional Derivative
Abstract
:1. Introduction
2. Basic Knowledge
2.1. Caputo–Fabrizio Fractional Integral and Derivative
2.2. Haar Wavelet Basis
3. Haar Wavelet Approximation Method
3.1. Method of Solution
3.2. Analysis of Error Estimations
4. Numerical Examples
5. Conclusions
- It can decrease computational efforts and is suitable in terms of computation costs and the convergence rate.
- It is suitable for the analysis of the dynamical system with fractional derivatives.
- The convergence properties of this class of methods are very helpful.
- The error analysis of this method is characterized by a good convergence rate.
- Unlike the collocation method, other methods have several limitations in their applications to unlimited classes of singular problems.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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J | M | of Proposed Method | of ADM | ||
---|---|---|---|---|---|
0 | 1 | 2 | |||
1 | 2 | 4 | |||
2 | 4 | 8 | |||
3 | 8 | 16 | |||
4 | 16 | 32 |
J | M | of Proposed Method | of ADM | ||
---|---|---|---|---|---|
0 | 1 | 2 | |||
1 | 2 | 4 | |||
2 | 4 | 8 | |||
3 | 8 | 16 | |||
4 | 16 | 32 |
J | M | of Proposed Method | of ADM | ||
---|---|---|---|---|---|
0 | 1 | 2 | |||
1 | 2 | 4 | |||
2 | 4 | 8 | |||
3 | 8 | 16 | |||
4 | 16 | 32 |
J | M | of Proposed Method | of ADM | ||
---|---|---|---|---|---|
0 | 1 | 2 | |||
1 | 2 | 4 | |||
2 | 4 | 8 | |||
3 | 8 | 16 | |||
4 | 16 | 32 |
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Dehda, B.; Yazid, F.; Djeradi, F.S.; Zennir, K.; Bouhali, K.; Radwan, T. Numerical Approach Based on the Haar Wavelet Collocation Method for Solving a Coupled System with the Caputo–Fabrizio Fractional Derivative. Symmetry 2024, 16, 713. https://doi.org/10.3390/sym16060713
Dehda B, Yazid F, Djeradi FS, Zennir K, Bouhali K, Radwan T. Numerical Approach Based on the Haar Wavelet Collocation Method for Solving a Coupled System with the Caputo–Fabrizio Fractional Derivative. Symmetry. 2024; 16(6):713. https://doi.org/10.3390/sym16060713
Chicago/Turabian StyleDehda, Bachir, Fares Yazid, Fatima Siham Djeradi, Khaled Zennir, Keltoum Bouhali, and Taha Radwan. 2024. "Numerical Approach Based on the Haar Wavelet Collocation Method for Solving a Coupled System with the Caputo–Fabrizio Fractional Derivative" Symmetry 16, no. 6: 713. https://doi.org/10.3390/sym16060713
APA StyleDehda, B., Yazid, F., Djeradi, F. S., Zennir, K., Bouhali, K., & Radwan, T. (2024). Numerical Approach Based on the Haar Wavelet Collocation Method for Solving a Coupled System with the Caputo–Fabrizio Fractional Derivative. Symmetry, 16(6), 713. https://doi.org/10.3390/sym16060713