Adaptive Explicit Magnus Numerical Method for Nonlinear Dynamical Systems
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摘要: 基于最近发展的矩阵李群上非线性微分方程的显式Magnus展式，给出了非线性动力系统的有效的数值算法，并且在数值求解过程中具有自适应的步长控制特点，可以显著地提高计算效率．最后，通过非线性动力系统典型问题Duffing方程和强刚性的Van derPol方程以及非线性振子的Hamilton方程的数值实验来说明方法的有效性．
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关键词:
- 非线性动力系统 /
- Hamilton系统 /
- 数值方法 /
- 步长控制
Abstract: Based on the new explicit Magnus expansion developed for nonlinear equation defined on matrix Lie group, an efficient numerical method was suggested for nonlinear dynamical system. To improve the computational efficiency, the integration step size can be controlled self adaptively. The validity and effectiveness of the method were proved by application to several nonlinear dynamical systems, including Duffing system, Van der Pol system with strong stiffness, and nonlinear Hamiltonian pendulum system. -
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