An energy-stable pseudospectral scheme for Swift-Hohenberg equation with its Lyapunov functional

We analyze a first order in time Fourier pseudospectral scheme for Swift-Hohenberg equation. One major challenge for the higher order diffusion non-linear systems is how to ensure the unconditional energy stability and we propose an efficient scheme for the equation based on the convex splitting of the energy. The?oretically, the energy stability of the scheme is proved. Moreover, following the derived aliasing error estimate, the convergence analysis in the discrete l2-norm for the proposed scheme is given.

MIXED PSEUDOSPECTRAL METHOD FOR HEAT TRANSFER

In this paper, we propose a mixed generalized Laguerre-Legendre pseudospectral method for non-isotropic heat transfer with inhomogeneous boundary conditions on an infinite strip. Some properties about the mixed generalized LaguerreLegendre approximation are established. By reformulating the equation with suitable functional transform defined on an infinite strip, a mixed Laguerre-Legendre pseudospectral scheme is constructed. Its convergence is proved. Numerical results are presented to demonstrate the efficiency of this new approach and to validate our theoretical analysis.