On computational applications of the Levi-Civita field

DOI10.1016/j.cam.2020.113041zbMath1462.26034OpenAlexW3035261568MaRDI QIDQ2196020

Khodr Shamseddine, Darren Flynn

Publication date: 28 August 2020

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2020.113041

zbMATH Keywords

numerical integrationnumerical methodsnumerical differentiationBernoulli numbersLevi-Civita fieldnon-Archimedean analysis

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Numerical differentiation (65D25) Numerical integration (65D30) Non-Archimedean analysis (26E30)

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Uses Software

• Mathematica

Cites Work

• Analysis on the Levi-Civita field and computational applications
• Higher order numerical differentiation on the infinity computer
• Analytical properties of power series on Levi-Civita fields
• Conjugate-symplecticity properties of Euler-Maclaurin methods and their implementation on the infinity computer
• On integrable delta functions on the Levi-Civita field
• Intermediate value theorem for analytic functions on a Levi-Civita field
• A Comparison of Three High-Precision Quadrature Schemes
• Advances in Ultrametric Analysis
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