线性多步法的通解和误差(英文)

The General Solutions and their Errors of Linear Multi-Step Method

线性多步法是求解微分方程的一种精度较高的方法,而目前用线性多步法得到的许多优美的公式既没有给出通解结构,也没有给出相应的局部截断误差。现在从Taylor展开式出发,给出线性多步法中几个公式的具体推导过程,导出通解的一般形式,在通解中对基础解系取特殊值得到一些著名公式,同时给出具体的局部截断误差。

Linear Multi-step Method is the way to precisely solve the differential equations. The current formulas derived from the linear multi-step method have been regarded as perfect one. However, in which the structure of general solutions as well as corresponding local truncation errors. With Taylor formula,the reasoning course do not be given,for some concrete formulas are given.It is shown that the general forms and their trunetion errors of common solutions.In common solutions,give some special values in basic solution systems,some famous formula may be obtained.