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

B. Takacs

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 245, issue C, 337-365

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 counterpart — 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.

Keywords: Nonstandard finite difference; Multistep method; Positivity preservation; SSP linear multistep methods (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:245:y:2026:i:c:p:337-365

DOI: 10.1016/j.matcom.2026.01.015

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