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In this paper, Chebyshev polynomial derivative-based spectral schemes are constricted for solving linear and non-linear ordinary differential equations. Linearization relation and some essential integrated formulae concerning the basis functions are provided to deal with the spectral tau method. Unlike the regular weight function, another modified weight is introduced. Also, different patterns and results have been obtained regarding the relation between the Jacobi polynomials, ultraspherical polynomials, Chebyshev polynomials, and their derivatives. Moreover, the algebraic systems of the spectral expansion for solving the Riccati, Lane-Emden equations, and water contamination model are discussed. Error bounds are introduced, studied, and proven. Finally, several real applications are numerically solved using 2ndDCh polynomial-based spectral tau method. The obtained results are compared with different methods to confirm the accuracy and efficiency of the schemes. [ABSTRACT FROM AUTHOR]

Visible Light Communication (VLC) can be utilized for Indoor Positioning Systems (IPSs). Most of VLC IPSs work when LED lights are ON. This causes energy less when lighting system is off, at least when sleeping. We face a fundamental challenge in VLC systems that require the light ON all time. Then how to communicate when the lights appears "OFF"? In this paper, we propose a positioning system of receiver that is used in dark light VLC based on the Received Signal Strength (RSS) positioning technique, showing its possibility to use in dark environment. Because of its simplicity, the RSS technique is used in indoor positioning. This proposition can ensure the IP even when light is "OFF", which can be actualized in VLC systems to save energy and give precise illumination control. The obtained results reveal that the average error in positioning with LED power of dark VLC is lower than that in the normal mode. The obtained simulation results reveal that the average positioning error is improved by 25% of traditional method when Dark VLC is used with 1.4 mW LED power without background noise. This ensures that the proposed system shows superiority when compared with other VLC IPS systems, in energy saving and high positioning accuracy. [ABSTRACT FROM AUTHOR]

Visible light communication (VLC) is a rising guaranteeing new innovation for optical wireless communication with taking part favorable circumstances not available on radio communication. Especially, as connectivity propagation, both across the world and via the Internet of Things. Any communication system is based on the LED light is luminous to verifying the connection. The major challenge in VLC is how to make a communication system to download data in the dark light when indoor lighting is not needed. This paper explains how visible light can be used to transmit data even when the light appears dark or off. We investigate VLC minimum illumination to receive power, to enable users to receive data when the light is “OFF”. This paper focuses on improving the system performance including signal to noise ratio, required power and bit error rate. VLC with different modulation schemes highlighting as the On–OFF Keying, Pulse Position Modulation, L-Pulse Position Modulation, and Inverse L-Pulse Position Modulation are investigated in the dark light for communication. A short part of Pulse Width Modulation is used for dimming illumination. The paper examines the selected parameters and essential requirements of VLC dark light system which are power, bandwidth efficiency and the dimming factor of light sources. We confirm that dark light is enough to keep up information paces of a few kbps. This looks good for the eventual fate of VLC for actualizing shrewd lighting systems. [ABSTRACT FROM AUTHOR]