A New Methodology for the Development of Efficient Multistep Methods for First-Order IVPs with Oscillating Solutions

In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams–Bashforth appro...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 12; no. 4; p. 504
Main Author: Simos, Theodore
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2024
Subjects:
Adams–Bashforth methods
Algebra
Algorithms
Bibliographic literature
Boundary value problems
Comparative analysis
initial value problems (IVPs)
Methods
multistep methods
numerical solution
Stability analysis
trigonometric fitting
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary:In this research, we provide a novel approach to the development of effective numerical algorithms for the solution of first-order IVPs. In particular, we detail the fundamental theory behind the development of the aforementioned approaches and show how it can be applied to the Adams–Bashforth approach in three steps. The stability of the new scheme is also analyzed. We compared the performance of our novel algorithm to that of established approaches and found it to be superior. Numerical experiments confirmed that, in comparison to standard approaches to the numerical solution of Initial Value Problems (IVPs), including oscillating solutions, our approach is significantly more effective.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math12040504