We are concerned with the numerical exact controllability of semilinear wave equation on interval (0, 1). introduce a Picard iterative scheme yielding sequence approximated solutions which converges towards solution null problem, provided that initial data small enough. The boundary control, is applied at endpoint $$x=1$$ , taken in space $$H^1_0(0,T)$$ for $$T=2$$ . For linear part, control in...

This work focuses on the extension of the recently introduced Spectral Difference Method to viscous flow. The spectral difference method is a conservative pseudo-spectral scheme based on a local collocation on unstructured elements. Recently results for scalar transport equations and the Euler equations have been presented. For the extension to viscous flow several techniques are investigated, ...

on the interval [0, 2π]. Spectral discretizations of this equation have been in use ever since the work of Camassa and Holm [2] and Camassa, Holm and Hyman [3]. However, to the knowledge of the authors, no proof that such a discretization actually converges has appeared heretofore. Therefore, this issue is taken up here. Our method of proof is related to the work of Maday and Quarteroni on the ...

In the present work, the effect of fluid’s elasticity was investigated on the hydrodynamic instability of Blasius flow. To determine the critical Reynolds number as a function of the elasticity number, a two-dimensional linear temporal stability analysis was invoked. The viscoelastic fluid is assumed to obey the Walters’ B fluid model for which base flow velocity profiles were fortunately avail...

We develop in this paper a numerical method to simulate three-dimensional incompressible flows based on a decomposition of the flow into an axisymmetric part, in terms of the stream function and the circulation, and a non-axisymmetric part in terms of a potential vector function. The method is specially suited for the study of nonlinear stability of axially symmetric flows because one may follo...

The present work proposes a collocation spectral method for solving the three-dimensional Navier-Stokes equations using cylindrical coordinates. The whole diameter −R ≤ r ≤ R is discretized with an even number of radial Gauss-Lobatto collocation points and an angular shift is introduced in the Fourier transform that avoid pole and parity conditions usually required. The method keeps the spectra...