A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.
A NEW METHOD OF IMPOSING BOUNDARY-CONDITIONS IN PSEUDOSPECTRAL APPROXIMATIONS OF HYPERBOLIC-EQUATIONS / Funaro, Daniele; D., Gottlieb. - In: MATHEMATICS OF COMPUTATION. - ISSN 0025-5718. - STAMPA. - 51:(1988), pp. 599-613. [10.2307/2008765]
A NEW METHOD OF IMPOSING BOUNDARY-CONDITIONS IN PSEUDOSPECTRAL APPROXIMATIONS OF HYPERBOLIC-EQUATIONS
FUNARO, Daniele;
1988
Abstract
A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.
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