OPTIMAL ONE-STAGE AND 2-STAGE SCHEMES FOR STEADY-STATE SOLUTIONS OF HYPERBOLIC-EQUATIONS

In this paper, we consider finding steady state approximations to hype rbolic equations by solving the related ODE systems using spatial disc retization. An optimal one-stage scheme is derived based on the partic ular distribution pattern of eigenvalues of the spatial discretization matrix. An optimal two-stage method is then designed based on a geome tric closure of the eigenvalues and the results from the one-stage met hod. The applications of these methods include but are not limited to solving nonsymmetric linear systems.