A new based error approach to approximate the inverse langevin function

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TitreA new based error approach to approximate the inverse langevin function
Type de publicationJournal Article
Year of Publication2014
AuteursNguessong ANkenfack, Beda T, Peyraut F
JournalRHEOLOGICA ACTA
Volume53
Pagination585-591
Date PublishedAUG
Type of ArticleArticle
ISSN0035-4511
Mots-clésInverse Langevin function, Pade approximation, Taylor expansion
Résumé

In the present paper, we propose a new approximation of the inverse Langevin function. This new approximation is based on a two-step modification of the fractional formula introduced by (Cohen 1991). Our proposal is motivated by the minimization of the error between the Cohen formula and the inverse of the Langevin function. It results in two additional terms adopting a remarkable simple power and polynomial forms. The correction provides an excellent agreement with a maximum relative error equal to 0.046 % (against a maximum error of 4.94 % for the Cohen formula).

DOI10.1007/s00397-014-0778-y