力学问题的分形级数解

Fractal Series Solution for Mechanics Problems

给出戴劳级数、三角级数等的推广———分形级数，并讨论力学问题的分形级数解。在戴劳级数、三角级数等级数中，各项的指数及角度的系数为非负整数，而在分形级数中，各项的指数及角度的系数为任意实数，或变量的函数。讨论了强非线性ＫｄＶ 方程的分形级数解。在确定分形级数时，可应用加权残数法（ 如最小二乘法） 。

This paper presents the fractal series generalized from Taylor series, Fourier series and the like, and discusses the fractal series solution for mechanics problem. In Taylor series, Fourier series and the like, the index of each term and the angular coefficient are all non negative integral numbers; while in the fractal series, they can be taken as any real numbers or functions of variables. Furthermore, this paper discusses the fractal series solution to the strongly non linear KdV equation. For the determination of its fractal series, the method of weighted residuals such as LSM can be used.