Solution of third-order nonlinear integro-differential equations with parallel computing for intelligent IoT and wireless networks using the Haar wavelet method

We investigate a class of third-order nonlinear integro-differential equations (IDEs) with parallel computing of intelligent Internet of Things and wireless networks for numerical solutions. A numerical scheme based on the Haar wavelet has been established to compute the approximate solution for the problem under our consideration. By utilizing the mentioned tool, we discretize the involved derivatives and integrals. In this way, a sophisticated scheme is derived. Formulations for maximum root mean square and absolute errors have been given. Also, the convergent method has been discussed. In engineering, such as structural dynamics and control systems, third-order IDEs can improve modelling precision and solution effectiveness. Various examples have been testified by the aforementioned method. Additionally, by using different Gauss and collocation points (CPs), the aforementioned error terms were recorded. The convergence rate using distinct numbers of CPs has also been calculated, which is nearly equal to 2.