A new based error approach to approximate the inverse langevin function

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 invers...

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Bibliographic Details
Published in:Rheologica acta 2014-08, Vol.53 (8), p.585-591
Main Authors: Nguessong, Alain Nkenfack, Beda, Tibi, Peyraut, François
Format: Article
Language:English
Subjects:
Approximation
Characterization and Evaluation of Materials
Chemistry and Materials Science
Complex Fluids and Microfluidics
Error correction
Food Science
Materials Science
Mathematical analysis
Mechanical Engineering
Original Contribution
Polymer Sciences
Polynomials
Soft and Granular Matter
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Summary: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).
ISSN:0035-4511
1435-1528
DOI:10.1007/s00397-014-0778-y