A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things

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Amin, Rohul and Nazir, Shah and García-Magariño García, Iván (2020) A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things. Sensors, 20 (7). p. 1962. ISSN 1424-8220

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Official URL: https://doi.org/10.3390/s20071962




Abstract

Wireless sensor network and industrial internet of things have been a growing area of research which is exploited in various fields such as smart home, smart industries, smart transportation, and so on. There is a need of a mechanism which can easily tackle the problems of nonlinear delay integro-differential equations for large-scale applications of Internet of Things. In this paper, Haar wavelet collocation technique is developed for the solution of nonlinear delay integro-differential equations for wireless sensor network and industrial Internet of Things. The method is applied to nonlinear delay Volterra, delay Fredholm and delay Volterra–Fredholm integro-differential equations which are based on the use of Haar wavelets. Some examples are given to show the computational efficiency of the proposed technique. The approximate solutions are compared with the exact solution. The maximum absolute and mean square roots errors for distant number of collocation points are also calculated. The results show that Haar method is efficient for solving these equations for industrial Internet of Things. The results are compared with existing methods from the literature. The results exhibit that the method is simple, precise and efficient.


Item Type:Article
Uncontrolled Keywords:integro-differential equations; nonlinear delay integro-differential equations; Haar wavelet; internet of things; wireless sensor network
Subjects:Sciences > Computer science > Internet
Sciences > Mathematics > Differential equations
ID Code:67657
Deposited On:06 Sep 2021 14:42
Last Modified:06 Sep 2021 14:46

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