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Accelerated Solutions of Nonlinear Equations Using Stabilized Runge-Kutta Methods

In this paper we discuss the use of stabilized Runge-Kutta methods to accelerate the solution of systems of nonlinear equations. The general idea is to seek solutions as steady state solutions of an associated system of ordinary differential equations. A class of stabilized RungeKutta methods are derived that can be used to efficiently evolve the associated system to steady state. Computational results for a set of reaction-diffusion equations and a set of Schroediner-Poisson equations are presented.