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...

A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate th...

Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods. The derived difference schemes enjoy the same stability and accuracy properties with correspondent differential quadrature methods but have a simpler form of c...

Abstract In this paper, we study the numerical solutions of Fisher’s equation and to a nonlinear diffusion equation of the Fisher type by differential quadrature method. Fisher's equation combines diffusion with logistic nonlinearity. The equation occurs in logistic population growth models, neurophysiology and nuclear reactions. Therefore, numerical study of these types of equations is very im...

Purpose – The purpose of this paper is to use the polynomial differential quadrature method (PDQM) to find the numerical solutions of some Burgers’-type nonlinear partial differential equations. Design/methodology/approach – The PDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The obtained system of ODEs is solved by Ru...

in this article we have considered a non-standard finite difference method for the solution of second order  fredholm integro differential equation type initial value problems. the non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the fredholm integro-differential equation into a system of equations. we have also developed a numerical met...

This paper extends the application of the differential quadrature method (DQM) to high order (2 3rd) ordinary differential equations with the boundary conditions specified at multiple points (2 three different points). Explicit weighting coefficients for higher order derivatives have been derived using interpolating trigonometric polynomials. A three-point, linear third-order differential equat...

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...

Piezoelectric materials, due to their electromechanical coupling properties, are widely used as actuators and sensors in intelligent structures control vibrations bends of multilayer sheets with piezoelectric layers. In this paper, the response free a composite shell new Generalized Differential Quadrature Method (GDQM) for different boundary conditions is investigated. The governing equations ...