On the computation of high order pseudospectral derivatives

A study is presented on the computation of pseudospectral differentiation m atrices for higher derivatives using the general Lagrangian polynomial inte rpolation formulation. The diagonal elements of the differentiation matrice s are computed as the negative row sum of the off-diagonal elements and we show why this technique should be used instead of the explicit formula that is usually given in the literature. An efficient recursive algorithm for c omputing the higher order differentiation matrices are derived. For the Eve n-Odd Decomposition algorithm a similar efficient recursive algorithm is al so provided. The Chebyshev and Legendre collocation methods commonly used i n applications are one of the special case, (C) 2000 IMACS. Published by El sevier Science B.V. All rights reserved.