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Fourier spectral or pseudo-spectral methods are usually extremely efficient for periodic problems. However this efficiency is lost if the solutions have zones of rapid variations or internal layers. For these cases, a large number of Fourier modes are required and this makes the Fourier method unpractical in many cases. This work investigates...
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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...