一种新型齐次扩容精细积分法

A method of homogenization of high precision direct integration

根据函数分段插值逼近的思想 ,在一个积分步长内用多项式近似表示方程的非齐次项 ,提出了一种原理简单、实施容易的求解非齐次线性微分方程组的新型齐次扩容精细积分法 ,该方法不涉及矩阵的求逆运算 ,不需要计算傅里叶级数展开系数的振荡函数积分 ,且在一个积分步长内只求解一个相应的齐次扩容微分方程组 ,因而本方法和已有的同类方法相比具有更高的计算精度和效率 。

A method to solve non homogeneous and linear differential equations by homogenization high precision direct integration (HHPD P) was proposed. Since the non homogeneous term can be expressed approximately by a polynomial form within an adequate integral interval, it is unnecessary to compute the inverse matrixes and the integral of oscillating functions due to Fourier series, and only homogeneous linear differential equations need to be solved. In comparison with some methods, the proposed one is much simpler, easier to compile the computer program and of higher accuracy and efficiency.