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A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations. (English) Zbl 0699.65079
Summary: 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.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
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