Spectral collocation method and Darvishi’s preconditionings for Tchebychev-Gauss-Lobatto points

In this paper, we present central, left and right Darvishi’s preconditionings to reduce roundoff error in matrix vector multiplication method. This method is applied to compute derivative(s) of an unknown function in spectral collocation method. We show mentioned preconditionings reduce roundoff error in computing derivatives of functions as well, because errors of derivatives are very small.

Darvishi’s preconditionings; Differentiation matrix; Spectral methods; Tchebychev points