In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.

People localization is a key building block in many applications. In this paper, we propose a deep learning based approach that significantly improves the localization accuracy and reduces the runtime of Wi-Fi based localization systems. Three variants of the deep learning approach are proposed, a sub-task architecture, an end-to-end architecture, and an architecture that incorporates prior knowledge. The performance of the three architectures under different conditions is evaluated and the significant improvement of the three architectures over existing approaches is demonstrated.

A single mode waveguide grating coupler based on multiple Si-SiO₂ pairs onto Si substrate has been designed. Numerical analysis has been carried out to calculate optimum thickness of the layers of Si-SiO₂ that ensures the constructive interference between reflected waves and actual guided wave for high coupling efficiency. Based on the results, an optimal design is developed and modeled by using a 2-D finite difference time domain (2-D FDTD) simulator that dictates a coupling efficiency of as much as 78% (-1.07 dB) at the wavelength of 1550 nm, and a 1-dB bandwidth of 77 nm. The numerical method will be useful to calculate the optimum thicknesses of the layers for any reflector based grating coupler of different materials.