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...

In this paper, we introduce the concept of interval pseudo-homegeneous uninorms. We extend the concept of pseudo-homogeneity of specific functions for interval pseudo-homogeneous functions. It is studied two cases of interval pseudo-homogeneous uninorms, that is, interval pseudo-homogeneous tnorms and interval pseudo-homogeneous t-conorms. It is proved a form of interval pseudo-homogeneous t-no...

presents a modiied Chebyshev pseudospec-tral method, involving mapping of the Chebyshev points, for solving rst-order hyperbolic initial boundary value problems. It is conjectured that the time step restriction for the modiied method is O(N ?1) compared to O(N ?2) for the standard Chebyshev pseudospectral method, where N is the number of discretization points in space. In the present paper we s...

This paper proposes a new technique to speed up the computation of the matrix of spectral collocation discretizations of surface single and double layer operators over a spheroid. The layer densities are approximated by a spectral expansion of spherical harmonics and the spectral collocation method is then used to solve surface integral equations of potential problems in a spheroid. With the pr...

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differen...

A spectral solution of the RLW equation based on collocation method using Chebyshev polynomials as a basis for the approximate solution is proposed. Test problems, including the motion of a single solitary wave with different amplitudes are used to validate this algorithm which is found to be more accurate than previous ones. The interaction of solitary waves is used to discuss the effect of th...

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [27] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to ‘enlarge the region of analyticity’ in the solution: an idea which can be extended to other numeri...