A one-pass predictor-corrector algorithm for the inverse Langevin function

Date

2022-01-01

Author

BAŞDEMİR, SELÇUK
Dal, Hüsnü

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© The Author(s) 2022.Inverse Langevin function has an extensive use in statistical mechanics, polymer chemistry, and physics. Main struggle is that the inverse Langevin function cannot be expressed in an exact analytical form. To this end, many approaches to estimate the inverse Langevin function have been proposed. A trade-off can be observed between level of accuracy and mathematical complexity in the existing approximants in the literature. In the present contribution, a simple, yet efficient one-pass predictor-corrector algorithm is proposed for the accurate prediction of the inverse Langevin function. The predictor step uses the approximants yp(x) proposed in the literature. The corrector term is based on a single iteration applied to the error function (Formula presented.) (yp) – x. The correction term is based on the yp and has the same form irrespective of the specific approximant used in the predictor step. Hence, the additional computational cost is constant irrespective of the approximant used as predictor. In order to demonstrate the accuracy and efficiency of the approach, maximum relative error and the computational cost before and after corrector step are analysed for eight different approximants. The proposed one-pass predictor-corrector approach allows the use of relatively simpler approximants of the inverse Langevin function by improving their accuracy by at least an order of magnitude.

Subject Keywords

Inverse Langevin function, rubber elasticity, statistical mechanics, non-Gaussian statistics, Pade approximants, APPROXIMATION, BIREFRINGENCE, ELASTICITY, MOLECULES, NETWORK, MODEL, Inverse Langevin function, non-Gaussian statistics, Padé approximants, rubber elasticity, statistical mechanics

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85133402077&origin=inward
https://hdl.handle.net/11511/99051

Journal

Mathematics and Mechanics of Solids

DOI

https://doi.org/10.1177/10812865221102549

Collections

Department of Mechanical Engineering, Article

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Citation Formats

S. BAŞDEMİR and H. Dal, “A one-pass predictor-corrector algorithm for the inverse Langevin function,” Mathematics and Mechanics of Solids, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85133402077&origin=inward.