非线性Klein-Gordon方程的Fourier谱方法

研究了更一般的非线性Ｋｌｅｉｎ－Ｇｏｒｄｏｎ方程ｕｔｔ－ｕｘｘ＝ｆ（ｕ）的周期初边值问题．构造了此问题的半离散和全离散的Ｆｏｕｒｉｅｒ谱格式，利用非线性函数的有界延拓法，讨论了这两种谱格式的误差估计，证明了Ｆｏｕｒｉｅｒ谱格式的收敛性，得到其收敛精度，从而避免了较难的先验估计，放宽了非线性项条件．

Fourier spectral methods for nonlinear Klein Gordon equation

The problem of the periodic initial value is examined, generalizing from the nonlinear Klein Gordon equation u tt -u xx =f(u) . For this purpose here are given the semi discrete Fourier spectral scheme and fully discrete Fourier spectral scheme. By the bound extensive method of nonlinear functions, error estimation of the two schemes is studied, the connergence of them is proved, and their convergence precision is obtained. Thus the complex prior extimates are avoided and nonlinear therms are softened under a more general condition.