β Scribed by H. Herrero; A.M. Mancho
No coin nor oath required. For personal study only.
An example of a high order method (Chebyshev collocation) applied to the study of a bifurcation problem in three dimensions is presented. The non-linear basic equations are solved by an iterative technique. The first contribution to the solution is obtained using a low-order finite difference scheme while corrective terms are obtained through collocation. The bifurcation thresholds are calculated through the perturbation equations. We study the convergence of the collocation method comparing different expansions. The polynomials and their derivatives have been evaluated a priori at the collocation points instead of using the differentiation operators on those points. This procedure simplifies the implementation.
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A research code has been written to solve an elliptic system of coupled non-linear partial differential equations of conservation form on a rectangularly shaped three-dimensional domain. The code uses the method of collocation of Gauss points with tricubic Hermite piecewise continuous polynomial bas
This paper concerns a numerical study of convergence properties of the boundary knot method (BKM) applied to the solution of 2D and 3D homogeneous Helmholtz, modified Helmholtz, and convection-diffusion problems. The BKM is a new boundary-type, meshfree radial function basis collocation technique. T
The aim of this chapter is to provide some mathematical tools for the modeling of degradation processes that arise in structures operating under unstable environmental conditions. These uncertainties may come from a lack of scientific knowledge or from the intrinsic random nature of the observed phy