In this paper, we have presented the Differential Quadrature Method (DQM) for finding the numerical solution of boundary-value problems for a singularly perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having a positive shift. Such problems are associated with expected first exit time problems of the membrane potential in mo...

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, vibration analysis of thick functionally graded beam with simply supported boundary condition under constant axial load is studied. The beam has a uniform cross-sectional area and the mechanical properties of the fungtionally graded beam are assumed to be vary through the thickness of the beam. Fundamental relations, the equilibrium and stability equations based on the displaceme...

Differential quadrature method DQM is proposed for the numerical solution of oneand twospace dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature PDQ and Fourier-based differential quadrature FDQ are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by usi...

A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtai...

In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear strain-displacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlineariti...

where y(x) denotes the solution of the differential equation. The idea is to use a quadrature formula to estimate the integral of (1). This requires knowledge of the integrand at specified arguments x¿ in (xo, -To + h)—hence we require the values of y(x) at these arguments. A numerical integration method may be used to estimate y(x) for the required arguments. In this way a numerical integratio...