On the computation of high order pseudospectral derivatives

A study is presented on the computation of pseudospectral differentiation matrices for higher derivatives using the general Lagrangian polynomial interpolation formulation. The diagonal elements of the differentiation matrices 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 computing the higher order differentiation matrices are derived. For the Even–Odd Decomposition algorithm a similar efficient recursive algorithm is also provided. The Chebyshev and Legendre collocation methods commonly used in applications are one of the special case.