A New Methodology for the Development of Efficient Multistep Methods for First–Order IVPs with Oscillating Solutions IV: The Case of the Backward Differentiation Formulae

Autor:	Theodore E. Simos
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	numerical solution initial value problems (IVPs) backward differentiation formulae (BDF) phase–fitting amplification–fitting multistep methods Mathematics QA1-939
Zdroj:	Axioms, Vol 13, Iss 9, p 649 (2024)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms13090649
Popis:	A theory for the calculation of the phase–lag and amplification–factor for explicit and implicit multistep techniques for first–order differential equations was recently established by the author. His presentation also covered how the approaches’ efficacy is affected by the elimination of the phase–lag and amplification–factor derivatives. This paper will apply the theory for computing the phase–lag and amplification–factor, originally developed for implicit multistep methods, to a subset of implicit methods, called backward differentiation formulae (BDF), and will examine the impact of the phase–lag and amplification–factor derivatives on the efficiency of these strategies. Next, we will show you the stability zones of these brand-new approaches. Lastly, we will discuss the results of numerical experiments and draw some conclusions about the established approaches.
Databáze:	Directory of Open Access Journals
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