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A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor
Rohul Amin1, Shah Nazir2, Iván García-Magariño3,4
1Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25120, Pakistan.
Sensors (Basel, Switzerland)
|April 5, 2020
Summary
A new Haar wavelet method effectively solves complex nonlinear delay integro-differential equations for wireless sensor networks and the Industrial Internet of Things (IIoT). This approach offers a precise and efficient solution for large-scale IIoT applications.
Area of Science:
- Applied Mathematics
- Computer Science
Background:
- Wireless Sensor Networks (WSN) and the Industrial Internet of Things (IIoT) are expanding research areas with broad applications.
- Solving nonlinear delay integro-differential equations is crucial for large-scale IIoT systems.
Purpose of the Study:
- To develop and present the Haar wavelet collocation technique for nonlinear delay integro-differential equations.
- To address the computational challenges in WSN and IIoT applications.
Main Methods:
- The Haar wavelet collocation technique is applied to nonlinear delay Volterra, Fredholm, and Volterra-Fredholm integro-differential equations.
- The method utilizes Haar wavelets for approximating solutions.
Main Results:
- The Haar wavelet method demonstrates computational efficiency for solving these complex equations.
- Approximate solutions were compared with exact solutions, showing high accuracy.
- Maximum absolute and mean square root errors were calculated for various collocation points.
Conclusions:
- The Haar wavelet method is a simple, precise, and efficient technique for solving nonlinear delay integro-differential equations in IIoT.
- The proposed method shows superior performance compared to existing techniques in the literature.
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