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基于高振荡积分的数值算法

Numerical algorithm based on high oscillation integral

Study on Dynamical System / 2019,1(2)：43-51 / 2019-12-18 851 921

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• Authors: 盛辉     
• Information:

  西北工业大学，西安

• Keywords: 高振荡非齐次动力系统；高振荡积分；Magnus 积分；数值算法
• highly oscillatory nonhomogeneous dynamic system; highly oscillatory integral; Magnus integral; numerical algorithm
• Abstract: 为实现高振荡问题模型方程的有效数值求解，基于高振荡积分的渐进积分算法，针对随时间高频率振荡的非齐次线性动力系统给出有效的数值算法 .基于变分常数公式将非齐次动力系统重新表示为指数形式，利用 Magnus 积分方法求解指数部分，利用渐进积分算法求解高振荡的积分项 . 数值实验表明：该算法求解精度随振荡频率的增大而提高，且简单易用，也可以容易推广到多个方程的情形。
• To solve highly oscillatory model equations efficiently, based on asymptotic integral algorithm for highly oscillatory integrator, an efficient numerical algorithm is proposed for nonhomogeneous linear dynamic systems which has the characteristic of time-dependent high-frequency oscillations. The nonhomogeneous dynamic system is reformulated as a system of exponential form by variation-of-constants formula, the exponential part is solved by Magnus integrator, and highly oscillatory term is solved by asymptotic integral algorithm. The numerical examples indicate that the solution precision of the algorithm improves with the increase in oscillatory frequency, and it is easy to be used and easily extended to the case of multiple equations.
• DOI: https://doi.org/10.35534/sds.0102006c
• Cite: 盛辉．基于高振荡积分的数值算法［J］．动力系统研究，2019，1（2）：43-51．