In this paper, a hybrid technique of differential quadrature method and Runge-Kutta fourth order method is employed to analyze reaction-diffusion problems. The obtained results are compared with the available analytical ones. Further, a parametric study is introduced to investigate the influence of reaction and diffusion characteristics on behavior of the obtained results. Index Term-Reaction-d...

The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the aspect ratio of the element is large or (2) the field point is closed to the element boundary; thus a large number of quadrature points are needed to achieve a...

The nonlinear analysis of nanoelectromechanical systems using the differential quadrature model is investigated. The differential quadrature method is applied to overcome the difficulty of determining the nonlinear equation of motion. The characteristics of various combinations of curved electrodes and cantilever beams are considered to optimize the design. Various nano-actuators, such as the c...

this paper presents a method for diagnosis of eccentricity fault in a switched-reluctance motor (srm) during offline and standstill modes. in this method, the fault signature is differential induced voltage (div) achieved by injecting diagnostic pulses to the motor windings. it will be demonstrated by means of results that there is a correlation between differential induced voltage and eccentri...

V-shaped and triangular cantilevers are widely employed in atomic force microscope (AFM) imaging techniques due to their stability. For the design of vibration control systems of AFM cantilevers which utilize patched piezo actuators, obtaining an accurate system model is indispensable prior to acquiring the information related to natural modes. A general differential quadrature element method (...

A general adaptive element subdivision technique is presented for the numerical evaluation of weakly singular integrals, which often appear in three-dimensional boundary element analysis equations. In this algorithm, the weakly singular boundary element is broken up into a few sub-elements through a sphere of decreasing radius. The sub-elements involving the singular point are evaluated numeric...

A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three-points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved f...

A new differential quadrature method based on quartic B-spline functions is introduced. The weighting coefficients are determined via a semi-explicit algorithm containing an algebraic equation system with four-band coefficient matrix. In order to validate the proposed method, the Burgers’ Equation is selected as test problem. The shock wave and the sinusoidal disturbance solutions of the Burger...