Efficient sustainable algorithm for numerical solution of nonlinear delay Fredholm-Volterra integral equations via Haar wavelet for dense sensor networks in emerging telecommunications

Emerging technologies such as cloud computing, integration of Internet of Things, data science, self-powered data centers, dense sensor network, artificial intelligence convergence, machine learning and deep learning, self-service IT for business users and others play an important role in daily life. Dense sensor networks (DSNs) can be useful in fields such as structured health monitoring and turbine blades monitoring. Given the high number of sensors and the required small size, these sensors usually have very low processing capabilities for fitting to the size restrictions and limiting the production costs of the whole DSN. In this context, algorithms need to be really efficient so the algorithms can be achieved. This article focuses on providing an efficient algorithm for solving integral equations that can be useful in common problems in for emerging telecommunications. More concretely, this article presents an efficient numerical scheme for solution of nonlinear delay Fredholm integral equations, nonlinear delay Volterra integral equations and nonlinear delay Fredholm Volterra integral equations which are based on the use of Haar wavelets. Maximum absolute errors and experimental rates of convergence are computed using different numbers of collocation points.Numerical examples are given to show the computational efficiency of the proposed method. The numerical results exhibit that the technique is efficient and effective. The proposed research work can be used in wireless sensor network, emerging technologies, hereditary's phenomena in physics and heat transfer problems, electron emission and X-rays radiography.