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

被引:24
作者
Amin, Rohul [1 ]
Nazir, Shah [2 ]
Garcia-Magarino, Ivan [3 ,4 ]
机构
[1] Univ Peshawar, Dept Math, Khyber Pakhtunkhwa 25120, Pakistan
[2] Univ Swabi, Dept Comp Sci, Khyber Pakhtunkhwa 23430, Pakistan
[3] Complutense Madrid Univ, Dept Software Engn & Artificial Intelligence, Madrid 28040, Spain
[4] UCM, Inst Tecnol Conocimiento, Madrid 28040, Spain
关键词
integro-differential equations; nonlinear delay integro-differential equations; Haar wavelet; internet of things; wireless sensor network; HAAR WAVELET; DIFFERENTIAL-EQUATIONS; SYSTEM;
D O I
10.3390/s20071962
中图分类号
O65 [分析化学];
学科分类号
070302 ; 081704 ;
摘要
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.
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页数:11
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