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arXiv · 2505.17606

An insight on some properties of high order nonstandard linear multistep methods

Bálint Takács
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Abstract

In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard version of Taylor's series is constructed. The preservation of some qualitative properties (boundedness, the linear combination of the components, and a property similar to monotonicity) is also proven for all step sizes. The methods are applied to a one-dimensional equation and a system of equations, in which the numerical experiments confirm the theoretical results.

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Bálint Takács. 2025-05-23. An insight on some properties of high order nonstandard linear multistep methods. https://arxiv.org/abs/2505.17606

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