In this note, convex Homotopy perturbation method (HPM) is presented for the approximate solution of the linear Fredholm-Volterra integral and integro-differential equation. Convergence and rate of convergence of the HPM are proved for both equations. Five numerical examples are provided to verify the validity and accuracy of the proposed method. Example reveals that HPM is very accurate and simple to implement for integral and integrodifferential equations.

Simple and efficient convex homotopy perturbation method (HPM) is presented to obtain an approximate solution of hyper-singular integral equations of the first kind. Convergence and error estimate of HPM are obtained. Three numerical examples were provided to verify the effectiveness of the HPM. Comparisons with reproducing kernel method (Chen et al., 2011) for the same number of iteration is also presented. Numerical examples reveal that the convergence of HPM can still be achieved for some problems even if the condition of convergence of HPM is not satisfied.

Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [?1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707?1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265�274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636�641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points. � 2016, The Author(s).

Nowadays, Wi-Fi fingerprinting-based positioning systems provide enterprises the ability to track their various resources more efficiently and effectively. The main idea behind fingerprinting is to build signal strength database of target area prior to location estimation. This process is called calibration and the positioning accuracy highly depends on calibration intensity. Unfortunately, calibration procedure requires huge amount of time and effort, and makes large scale deployments of Wi-Fi based indoor positioning systems non-trivial. In this research we present a novel location estimation algorithm for Wi-Fi based indoor positioning systems. The proposed algorithm combines signal sampling and hyperbolic location estimation techniques to estimate the location of mobile users. The algorithm achieves cost-efficiency by reducing the number of fingerprint measurements while providing reliable location accuracy. Moreover, it does not require any additional hardware upgrades to the existing network infrastructure. Experimental results show that the proposed algorithm with easy-to-build signal strength database performs more accurate than conventional signal strength-based methods. � 2019 Inderscience Enterprises Ltd.

Nowadays fast and accurate positioning of assets and people is as a crucial part of many businesses, such as, warehousing, manufacturing and logistics. Applications that offer different services based on mobile user location gaining more and more attention. Some of the most common applications include location-based advertising, directory assistance, point-to-point navigation, asset tracking, emergency and fleet management. While outdoors mostly covered by the Global Positioning System, there is no one versatile solution for indoor positioning. For the past decade Wi-Fi fingerprinting based indoor positioning systems gained a lot of attention by enterprises as an affordable and flexible solution to track their assets and resources more effectively. The concept behind Wi-Fi fingerprinting is to create signal strength database of the area prior to the actual positioning. This process is known as a calibration carried out manually and the indoor positioning system accuracy highly depends on a calibration intensity. Unfortunately, this procedure requires huge amount of time, manpower and effort, which makes extensive deployment of indoor positioning system a challenging task. approach of constructing signal strength database from a minimal number of measurements using Chebyshev wavelets approximation. The main objective of the research is to minimize the calibration workload while providing high positioning accuracy. The field tests as well as computer simulation results showed significant improvement in signal strength prediction accuracy compared to existing approximation algorithms. Furhtermore, the proposed algorithm can recover missing signal values with much smaller number of on-site measurements compared to conventional calibration algorithm.