计算物理 ›› 1997, Vol. 14 ›› Issue (2): 227-232.
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曾晓东, 齐翔林, 汪云九
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Zeng Xiaodong, Qi Xianglin, Wang Yunjiu
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摘要: 提出一种求解自治非线性常微分方程周期解的方法——谱展开法。它直接把解形式上写成Fourier级数,其频率和各谐波成份待定,而将原非线性常微分方程问题变换成求解相应的非线性代数方程组,还以van der Pol方程和神经元群平均场方程为例对该方法进行说明和讨论。
关键词: 极限环, 谱展开法
Abstract: A practical method,the spectral method,is developed to find the periodic solution of non linear ordinary differentical equations directly.By expanding the solution into its Fourier series with the frequency and the amplitudes of each harmonics to be determined,the problem of sloving the non linear ordinary differential equations is transformed into the solution of corresponding non linear algebraic equations.Two examples,the van der Plo equation and the mean field equations of the neuronal groups,are also presented to explain and discuss this algorithm.
Key words: Limit Cycle, Spectral Method
中图分类号:
O241
曾晓东, 齐翔林, 汪云九. 求解极限环的谱展开法[J]. 计算物理, 1997, 14(2): 227-232.
Zeng Xiaodong, Qi Xianglin, Wang Yunjiu. A SPECTRAL METHOD FOR SOLVING THE LIMIT CYCLE OF NON LINEAR ORDINARY DIFFERENTIAL EQUATION[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 14(2): 227-232.
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