Optimal one-stage and two-stage schemes for steady state solutions of hyperbolic equations

Abstract

Chiu, C., Optimal one-stage and two-stage schemes for steady state solutions of hyperbolic equations, Applied Numerical Mathematics 11 (1993) 475–496. In this paper, we consider finding steady state approximations to hyperbolic equations by solving the related ODE systems using spatial discretization. An optimal one-stage scheme is derived based on the particular distribution pattern of eigenvalues of the spatial discretization matrix. An optimal two-stage method is then designed based on a geometric closure of the eigenvalues and the results from the one-stage method. The applications of these methods include but are not limited to solving nonsymmetric linear systems.