一类非齐次线性常微分方程的精细积分方法

提出了一种求解一类非齐次线性常微分方程的精细积分方法，通过该方法可以得到逼近计算机精度的结果。首先，定义了一个函数类的集合，该集合中元素的导数可以由该集合中的元素线性表出；然后，在原来方程的基础上增加由该集合中的函数的导数构成的微分方程，得到封闭的齐次线性常微分方程组；最后利用经典的精细积分方法求解该方程组。该方法对非齐次项属于该类函数的线性常微分方程行之有效。方法扩大了经典精细积分方法的求解范围，编程实现简单，算例结果证明了方法的有效性。

Precise integration method for a kind of non-homogeneous linear ordinary differential equations

Precise integration method for a kind of non-homogeneous linear ordinary differential equations is presented. This method can give precise numerical results approaching the exact solution. First of all, a function set is defined, in which the derivative of the elements can be linearly represented by the elements; Then, on the basis of the original equation, new differential equations obtained by derivative of elements are increased, so the closed homogeneous linear ordinary differential equations are obtained; At last, those differential equations are solved by the classic precision integration method. This method is effective for linear ordinary differential equations whose non-homogeneous term belongs to the set described above. The scope of application of the classical precise integration method is expended by this method, and it can be very simple to program, and numerical results demonstrate the effectiveness of the method.