High-Order Adams–Bashforth Methods for First-Order IVPs with Oscillating Solutions

The theory for computing the phase-lag and amplification-factor for both explicit and implicit multistep approaches for first-order differential equations was recently established by one of the authors. The goal of this work is to design high order Adams–Bashforth algorithms that eliminate the phase...

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Bibliographic Details
Published in:Mediterranean journal of mathematics Vol. 22; no. 5; p. 115
Main Authors: Hong, Mei, Lin, Chia-Liang, Simos, Theodore E.
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.08.2025
Subjects:
Algebra
Differential equations
Methods
Phase lag
ISSN:1660-5446, 1660-5454
Online Access:Get full text
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Summary:The theory for computing the phase-lag and amplification-factor for both explicit and implicit multistep approaches for first-order differential equations was recently established by one of the authors. The goal of this work is to design high order Adams–Bashforth algorithms that eliminate the phase-lag, amplification-factor, and their respective derivatives. The stability zones of the recently developed approaches will also be presented. Additionally, we will discuss our findings from numerical experiments using the recently created techniques.
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ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-025-02876-5