We are concerned with linear and nonlinear multi-term fractional differential equations (FDEs). The shifted Chebyshev operationalmatrix (COM) of fractional derivatives is derived and used together with spectral methods for solving FDEs. Our approach was based on the shifted Chebyshev tau and collocation methods. The proposed algorithms are applied to solve two types of FDEs, linear and nonlinea...

We study uniform bounds associated with the Allen–Cahn equation and its numerical discretization schemes. These uniform bounds are different from, and weaker than, the conventional energy dissipation and the maximum principle, but they can be helpful in the analysis of numerical methods. In particular, we show that finite difference spatial discretization, like the original continuum model, sha...

— The conservation and convergence properties o f spectral Fourier methods for the numerical approximation o f the Korteweg-de Vries équation are analyzed. It is proven thaï the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point ofview. This resuit provides a précise mathematica...

In this paper, we mainly study the superconvergence properties in approximation of second- and third-order BVPs by spectral collocation methods. The theoretical analyses identify points interpolation function. Ample numerical experiments are carried out which perfectly match results. addition, results show that also hold solving PDEs.

The famous de Boor conjecture states that the condition of the polynomial B-spline collocation matrix at the knot averages is bounded independently of the knot sequence, i.e., it depends only on the spline degree. For highly nonuniform knot meshes, like geometric meshes, the conjecture is known to be false. As an effort towards finding an answer for uniform meshes, we investigate the spectral c...

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of nonlinear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of deri...