Abstract
Chebyshev spectral collocation methods for approximating the solution of Burgers' equation are defined and analyzed. Discretization in time by an implicit/explicit single step method is discussed. This method is shown to be stable under a very weak condition on the time step, for the (linear) diffusive part is dealt with implicitly. Besides, fast transform methods can be used to compute the explicit (non linear) convective term.
Optimal order error estimates are established in the weighted L2-norm.
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The research of this author has been partially supported by the U.S. Army through its European Research Office under contract No. DAJA-84-C-0035.
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Bressan, N., Quarteroni, A. An implicit/explicit spectral method for Burgers' equation. Calcolo 23, 265–284 (1986). https://doi.org/10.1007/BF02576532
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DOI: https://doi.org/10.1007/BF02576532