Application of HAM for Nonlinear Integro-Differential Equations of Order Two

In this work, we consider the second order nonlinear integro-differential Equation (IDEs) of the Volterra-Fredholm type. One of the popular methods for solving Volterra or Fredholm type IDEs is the method of quadrature while the problem of consideration is a linear problem. If IDEs are nonlinear or integral kernel is complicated, then quadrature rule is not most suitable;therefore, other types of methods are needed to develop. One of the suitable and effective method is homotopy analysis method (HAM) developed by Liao in 1992. To apply HAM, we firstly reduced the IDEs into nonlinear integral Equation (IEs) of Volterra-Fredholm type;then the standard HAM was applied. Gauss-Legendre quadrature formula was used for kernel integrations. Obtained system of algebraic equations was solved numerically. Moreover, numerical examples demonstrate the high accuracy of the proposed method. Comparisons with other methods are also provided. The results show that the proposed method is simple, effective and dominated other methods.

An optical method for wavelength fine-selection in optical spectrum analysers

This letter describes a novel optical method for wavelength fine-selection in the optical spectrum analysers (OSAs) for dense wavelength division multiplexing (DWDM) applications. The proposed new method employs a 'refractive optical lever' system consisting of a rotating optical wedge prism. A new OSA system based on Littman-type monochromator is proposed and the wavelength selection accuracy and resolution of OSA that has included such an optical lever system have been improved by a factor of 20 to 100 depending on the wedge angle and offset orientation angle of the optical wedge prism. This proposed 'refractive optical lever' may also simplify the rotation mechanism of the mirror in the commercially available OSAs.

Aerodynamic design of tractor propeller for high-performance distributed electric propulsion aircraft

Aiming to maximize the aerodynamic performance of the Distributed Electric Propulsion(DEP)aircraft,a hybrid design framework which focuses on the aerodynamic performance of the propeller/wing integration has been developed and validated numerically.Variable-fidelity modelling for propeller aerodynamics has been used to achieve computational efficiency with reasonable accuracy.By optimizing the aerodynamic loading distributions on the tractor propeller disk,the induced slipstream is redistributed into a form that is beneficial for the wing downstream,based on which the propeller blade geometry is generated through a rapid inversed design procedure.As compared with the Minimum Induced Loss(MIL)propeller at a specified thrust level,significant improvements of both the lift-to-drag ratio of the wing and the propeller/wing integrated aerodynamic efficiency is achieved,which shows great promise to deliver aerodynamic benefits for the wing within the propeller slipstream without any additional devices.