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We present a straightforward and reliable continuous method for computing thefull or a partial Lyapunov spectrum associated with a dynamical systemspecified by a set of differential equations. We do this by introducing astability parameter beta>0 and augmenting the dynamical system with anorthonormal k-dimensional frame and a Lyapunov vector such that the frame iscontinuously Gram-Schmidt orthonormalized and at most linear growth of thedynamical variables is involved. We prove that the method is strongly stablewhen beta > -lambda_k where lambda_k is the k'th Lyapunov exponent indescending order and we show through examples how the method is implemented. Itextends many previous results.Comment: 14 pages, 10 PS figures, ioplppt.sty, iopl12.sty, epsfig.sty 44 k

Computing Lyapunov spectra with continuous Gram - Schmidt orthonormalization