A variable step-size method for solving stiff Lyapunov differential equations

We propose a method for solving stiff Lyapunov differential equations. A feature of this method is that the step-size of integration can be adjusted automatically according to the magnitude of the difference between two computed solutions at two successive time steps. This approach can automatically keep increasing the step-size of integration when the transient part of the solution becomes less and less significant. We encoded this method in MATLAB/sup (R)/ and tested it on several Lyapunov differential equations with known analytic solutions. In each of the cases, the relative errors of the computed solutions near the steady state were small even for large step-sizes of integration.