Legendre and Chebyshev dual-Petrov–Galerkin methods for Hyperbolic equations
نویسندگان
چکیده
A Legendre and Chebyshev dual-Petrov–Galerkin method for hyperbolic equations is introduced and analyzed. The dual-Petrov– Galerkin method is based on a natural variational formulation for hyperbolic equations. Consequently, it enjoys some advantages which are not available for methods based on other formulations. More precisely, it is shown that (i) the dual-Petrov–Galerkin method is always stable without any restriction on the coefficients; (ii) it leads to sharper error estimates which are made possible by using the optimal approximation results developed here with respect to some generalized Jacobi polynomials; (iii) one can build an optimal preconditioner for an implicit time discretization of general hyperbolic equations. 2007 Elsevier B.V. All rights reserved. MSC: 65M70; 35L50; 65M12
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