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A MULTISTEP ALGORITHM FOR ODEs
TL;DR: In this article, the convergence of a linear implicit multi-step numerical method for ordinary difierential equations is proved following the Dahlquist theory, and the time stability is established too.
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Abstract: The objective of this paper is to prove the convergence of a linear implicit multi- step numerical method for ordinary difierential equations. The algorithm is obtained via Taylor approximations. The convergence is proved following the Dahlquist theory. As an additional topic, the time stability is established too. Comparative tests between some of the most known numerical methods and this method are presented. Keywords. Taylor approximation, multi-step method, stability, consistency, time regions stability. AMS (MOS) subject classiflcation: 65L06, 65P99.
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