Work

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

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.17606

Author: Takács, Bálint

Institutions: Eötvös Loránd University, Budapest University of Technology and Economics, Hungarian Research Network

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6966675716

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