On the use of spectral methods for stiff problems

This paper describes some aspects of the use of spectral methods for the numerical solution of systems of stiff partial differential equations. It is shown that despite the high spatial precision of these methods, a reasonable accuracy can only be attained with a large number of number and therefore, some kind of adaptive 'gridding' is necessary. A way to implement this adaptation based on the computation of a norm of the solution is proposed. Numerical examples concerning flame propagation problems and Burges' equation are presented and discussed.