一个高精度收敛的变系数微分方程精确解析法*

文1]给出精确解析法,可用于求解任意变系数微分方程,所得到的解具有二阶收敛精度.在此基础上,本文以变截面梁弯曲为例,给出一个高精度的算法.不增加工作量的情况下可达到四阶收敛精度.具有计算快,简单等特点,文末给出算例,仅用很少的单元即可获得高的收敛精度,表明了本文理论的正确性.

A High Convergent Precision Exact Analytic Method for Differential Equation with Variable Coefficients

The exact analytic method was given byl]. It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high precision algorithm is given based on 1], through a bending problem of variable cross section beams. It can have "the fourth convergent precision without increasing computation work. The present computation method is not only simple but also fast. The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements. The correctness of the theory in this paper is confirmed.