A spectral method in space and a finite-difference scheme in time are employed to approximate the solution of the model equation: yt=yx. The operator ∂/∂x is discretized by the collocation method based on the Chebyshev nodes. The second order Runge-Kutta method is used for the operator ∂/∂t. It is known that the location, in the complex plane, of the eigenvalues of the collocation matrix is crucial for the stability. A simple way of computing the coefficients of the characteristic polynomial of that matrix is shown. An explicit computation of the roots gives indications on the choice of the time step. © 1987, Elsevier B.V.
Some results about the spectrum of the chebyshev differencing operator / Funaro, D.. - 133:C(1987), pp. 271-284. ((Intervento presentato al convegno International Symposium on Numerical Analysis tenutosi a Polytechnic University of Madrid, Madrid nel 17-19 October 1985 [10.1016/S0304-0208(08)71738-9].
Some results about the spectrum of the chebyshev differencing operator
Funaro D.
1987-01-01
Abstract
A spectral method in space and a finite-difference scheme in time are employed to approximate the solution of the model equation: yt=yx. The operator ∂/∂x is discretized by the collocation method based on the Chebyshev nodes. The second order Runge-Kutta method is used for the operator ∂/∂t. It is known that the location, in the complex plane, of the eigenvalues of the collocation matrix is crucial for the stability. A simple way of computing the coefficients of the characteristic polynomial of that matrix is shown. An explicit computation of the roots gives indications on the choice of the time step. © 1987, Elsevier B.V.
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