A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things
Abstract
:1. Introduction
- To develop efficient technique for the approximate solution of nonlinear FVIDEs arising in WSN and IIoT
- To design algorithm for proposed technique
- To examine the efficiency of the developed technique on some test problems and compare the results of our technique with results [1] available in the literature
2. Literature Review
3. Haar Wavelet
- To find solutions of different nonlinear FVIDEs arising in WSN and IIoT
- To check the efficiency and accuracy of the developed technique, the proposed method is applied on some test problems
4. Numerical Method for Nonlinear Delay IDEs Arising in WSN and IIoT
4.1. Nonlinear Delay Fredholm IDEs
4.2. Nonlinear Delay Volterra IDEs
4.3. Nonlinear Delay Volterra–Fredholm IDEs
5. Numerical Assessments
6. Results and Discussion
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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J | Results [1] | |||
---|---|---|---|---|
1 | 4 | 2.1194 | 1.5933 | 4.84 |
2 | 8 | 6.3911 | 4.0412 | 1.36 |
3 | 16 | 1.7632 | 1.0141 | 2.01 |
4 | 32 | 4.6373 | 2.5447 | 3.54 |
5 | 64 | 1.1898 | 6.4159 | 3.85 |
6 | 128 | 3.0129 | 1.6638 | — |
7 | 256 | 7.5791 | 4.9327 | — |
J | Results [1] | |||
---|---|---|---|---|
1 | 4 | 5.4262 | 4.6432 | 1.1 |
2 | 8 | 1.5086 | 3.1776 | 1.1 |
3 | 16 | 3.9748 | 2.9549 | 1.9 |
4 | 32 | 1.0203 | 7.3941 | 2.8 |
5 | 64 | 2.5847 | 1.8489 | 9.5 |
6 | 128 | 6.5045 | 4.6226 | — |
7 | 256 | 1.6315 | 1.1556 | — |
8 | 512 | 4.0855 | 2.8892 | — |
9 | 1024 | 1.0222 | 7.2230 | — |
10 | 2048 | 2.5566 | 1.8057 | — |
J | |||
---|---|---|---|
1 | 4 | 4.71362 | 2.89263 |
2 | 8 | 1.02141 | 1.00189 |
3 | 16 | 3.72674 | 3.60812 |
4 | 32 | 2.61325 | 1.46973 |
5 | 64 | 4.58470 | 2.25831 |
6 | 128 | 1.84356 | 3.96374 |
7 | 256 | 4.01407 | 1.32281 |
8 | 512 | 1.37851 | 2.13459 |
9 | 1024 | 3.93057 | 4.53722 |
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Amin, R.; Nazir, S.; García-Magariño, I. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things. Sensors 2020, 20, 1962. https://doi.org/10.3390/s20071962
Amin R, Nazir S, García-Magariño I. A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things. Sensors. 2020; 20(7):1962. https://doi.org/10.3390/s20071962
Chicago/Turabian StyleAmin, Rohul, Shah Nazir, and Iván García-Magariño. 2020. "A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things" Sensors 20, no. 7: 1962. https://doi.org/10.3390/s20071962
APA StyleAmin, R., Nazir, S., & García-Magariño, I. (2020). A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things. Sensors, 20(7), 1962. https://doi.org/10.3390/s20071962