\(L_ 2\) estimates for Chebyshev collocation
Considering the numerical solution of symmetric hyperbolic systems with variable coefficients, the author proves a stability estimate for the following approach: From the hyperbolic system a system of ordinary differential equations is obtained by developing the solution into a Chebyshev series with N terms, projecting the spatial operator part and the right hand side in \(L_ 2\) onto the M-th degree Legendre polynomials \((M<N\) for smoothing), projecting then onto those polynomials which meet the boundary conditions. For \(N-M=cN^ r\), \(c>0\), \(1\geq r>0\) and for sufficiently smooth data the estimate converges to the estimate for the continuous system.
scientific article; zbMATH DE number 4082905
scientific article