# 基于泰勒展开的线性多步法构造方法的研究A Study on Construction for Linear Multi-Step Methods Based on Taylor Expansion

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Following the previous literature on multi-step formulae for initial value problems of ODEs (ordi-nary differential equations), we study the construction for linear multi-step methods based on Taylor expansion in this paper. We try the weighted average method and derive a new formula. Then we check this new method in an example, and compare the original two formulae and con-structed new formula. Via such numerical experiment, this method is reliable. Some constructed new formulae can have relatively high stability and small error while solving ODEs initial value problems.

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