A fourth-order time-splitting Laguerre–Hermite pseudospectral method is introduced for Bose–Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The method is explicit, time reversible, and time transverse invariant. It conserves the position density and is spectral accurate in space and fourth-order accurate in time. Moreover, the new method has two other important advant...

In this paper, we develop a numerical method for the L\'evy-Fokker-Planck equation with fractional diffusive scaling. There are two main challenges. One comes from two-fold nonlocality, that is, need to apply Laplacian operator power law decay distribution. The other arises long-time/small mean-free-path scaling, which introduces stiffness equation. To resolve first difficulty, use change of va...

A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m2n) operations, where m is the number of Chebyshev points needed to resolve the coefficients of the differential operator and n is the number of Chebyshev coefficients ...

In this paper, we investigate the mixed Laguerre-Legendre interpolation approximation and its application. Some approximation results are established. A mixed Laguerre-Legendre pseudospectral scheme is constructed for incompressible fluid flow in an infinite strip. Its stability and convergence are proved. Numerical results show the efficiency of this new approach.

We aim at analyzing in detail the different heat transfer mechanisms involved a confined shallow cave embedded rock massif submitted to seasonal variations of ground temperature. Heat conduction massif, radiative between walls, and turbulent natural convection inside are considered. The problem is solved by large-eddy simulations (LES) using Chebyshev pseudo-spectral method associated with spec...

We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkinmethod while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and i...