Abstract
An optimal two-stage Runge–Kutta time integration scheme is derived to compute steady-state approximations to hyperbolic equations. The analysis is general in the sense that it requires only that the eigenvalues of the derivative matrix lie in the right half of the complex plane. Thus it is applicable to spatial discretizations which do not have uniformly spaced points. As examples, the method is applied to two hyperbolic problems which have been discretized in space by Chebyshev spectral collocation.
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