The Convergence of the Spectral Scheme for Solving Two-Dimensional Vorticity Equations

Abstract

Much work has been done for the spectral scheme of the P.D.E. The author proposed a technique to prove the strict error estimation of the spectral scheme for the K.D.V.-Burgers equation. In this paper, the technique is generalized to two-dimensional vorticity equations. Under some conditions, the error estimation implies the convergence. The more smooth the solution of the vorticity equations, the more accurate the approximate solution.