In this paper an accurate method to construct the bidiagonal factorization of collocation and Wronskian matrices Jacobi polynomials is obtained used compute with high relative accuracy their eigenvalues, singular values inverses. The particular cases Legendre polynomials, Gegenbauer Chebyshev first second kind rational are considered. Numerical examples included.

In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...

In this paper, a Chebyshev–Legendre spectral viscosity (CLSV) method is developed for nonlinear conservation laws with initial and boundary conditions. The boundary conditions are dealt with by a penalty method. The viscosity is put only on the high modes, so accuracy may be recovered by postprocessing the CLSV approximation. It is proved that the bounded solution of the CLSV method converges t...

and Applied Analysis 3 nonlinear term is treated with the Chebyshev collocation method. The time discretization is a classical Crank-Nicholson-leap-frog scheme. Yuan and Wu 43 extended the Legendre dual-Petrov-Galerkin method proposed by Shen 44 , further developed by Yuan et al. 45 to general fifth-order KdV-type equations with various nonlinear terms. The main aim of this paper is to propose ...

In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG) method on 3D curvilinear meshes for the GLM-MHD equations: single-fluid magneto-hydrodynamics (MHD) equations with a generalized Lagrange multiplier (GLM) divergence cleaning mechanism. For continuous entropy analysis to hold and ensure Galilean invariance in technique, system requires use of non-conservat...

In this paper, a numerical method is presented to obtain approximate solutions for the system of nonlinear delay integrodifferential equations derived from considering biological species living together. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Also, to illustrate the pertinent features of the method examples are pre...

The flux reconstruction approach to high-order methods is robust, efficient, simple to implement, and allows various high-order schemes, such as the nodal discontinuous Galerkin method and the spectral difference method, to be cast within a single unifying framework. Utilizing a flux reconstruction formulation, it has been proved (for onedimensional linear advection) that the spectral differenc...