Pinelli, AlfredoCouzy, W.Deville, M. O.Benocci, C.2023-06-202023-06-2019961064-827510.1137/S1064827593253835https://hdl.handle.net/20.500.14352/58576A new Chebyshev collocation algorithm is proposed for the iterative solution of advection-diffusion problems. The main features of the method lie in the original way in which a finite-difference preconditioner is built and in the fact that the solution is collocated on a set of nodes matching the standard Gauss-Lobatto-Chebyshev set only in the case of pure diffusion problems. The key point of the algorithm is the capability of the preconditioner to represent the high-frequency modes when dealing with advection-dominated problems. The basic idea is developed for a one-dimensional case and is extended to two-dimensional problems. A series of numerical experiments is carried out to demonstrate the efficiency of the algorithm. The proposed algorithm can also be used in the context of the incompressible Navier-Stokes equations.engjournal articlehttp://epubs.siam.org/doi/abs/10.1137/S1064827593253835http://www.siam.org/open access51advection-diffusioncollocationChebyshevpreconditioningfinite differencestaggered gridMatemáticas (Matemáticas)12 Matemáticas