An initial value problem for a Fractional Differential Equation (FDE) can be reformulated as a Volterra integral equation of the second kind with weakly singular kernel. Its solution can be approximated by applying suitable convolution quadratures. Methods of this type currently available in the literature are, for example, Adams product quadrature rules or Fractional Linear Multistep Methods, ...

In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre- and post-buckled rectangular plates for the first time. This is an answer to an existing need to develope a fast and precise numerical model which can handle the nonlinear vibrations of buckled plates under different boundary conditions and plate shapes. The method uses the differential quadrature element...

Abstract. We present a new tunably accurate Laguerre Petrov–Galerkin spectral method for solving linear multiterm fractional initial value problems with derivative orders at most one and constant coefficients on the half line. Our method results in a matrix equation of special structure which can be solved in O(N logN) operations. We also take advantage of recurrence relations for the generaliz...

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...

In this article, using generalized differential quadrature (GDQ) methods, free vibration of a thin annular plate coupled with two open circuit piezoelectric layers, is numerically studied based on the classical plate theory. The governing differential equations with respective boundary conditions are derived and transformed into a set of algebraic equations by implementing the GDQ rule, then so...

this paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. finally an example is given to illustrate the performance of the methods.

This paper presents a simple and systematic way for imposing boundary conditions in the differential quadrature free and forced vibration analysis of beams and rectangular plates. First, the Dirichlet- and Neumann-type boundary conditions of the beam (or plate) are expressed as differential quadrature analog equations at the grid points on or near the boundaries. Then, similar to CBCGE (direct ...

The unsteady pulsatile flow of blood through porous medium in an artery has been studied under the influence of periodic body acceleration and slip condition by considering blood as incompressible Newtonian electrically conducting fluid in the presence of magnetic field. In this paper, a new technique of differential quadrature method is introduced to find numerical solution of nonlinear partia...

Abstract Using a set of modified cubic trigonometric B-splines as test functions, a new differential quadrature technique is proposed for the 1D and 2D transient advection-diffusion equations of order α ∈ (0, 1]. The weighted coefficients are determined via solving the system of algebraic equations with a strictly diagonally dominant tri-diagonal matrix. Then, the original equation is converted...