Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficienc...Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, 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 Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.展开更多
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 d...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 der Pol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.展开更多
基金the National Natural Science Foundation of China (No. 10632030 and10572119)the Fundamental Research Foundation of NPUthe Scientific and Technological Innovation Foundation for teachers of NPU
文摘Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, 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 Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.
文摘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 der Pol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.
