Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an effcient numerical method is proposed for nonlinear dynamical systems. To improve computational effciency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffng system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.
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