Some applications of Sigmoid functions

Iranian Journal of Numerical Analysis and Optimization

مقاله 12، دوره 11، شماره 1 - شماره پیاپی 19، خرداد 2021، صفحه 221-233  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.68901.1015

نویسندگان

M. A. Jafari؛ A. Aminataei

Department of Mathematical Finance, Faculty of Financial Sciences, Kharazmi University, Tehran, Iran.

چکیده

In numerical analysis, the process of fitting a function via given data is called interpolation. Interpolation has many applications in engineering and science. There are several formal kinds of interpolation, including linear interpolation, polynomial interpolation, piecewise constant interpolation, trigonometric interpolation, and so on. In this article, by using Sigmoid functions, a new type of interpolation formula is presented. To illustrate the efficiency of the proposed new interpolation formulas, some ap plications in quadrature formulas (in both open and closed types), numerical integration for double integral, and numerical solution of an ordinary differential equation are included. The advantage of this new approach is shown in the numerical applications section.

کلیدواژه‌ها

Sigmoid function؛ Interpolation؛ Numerical integration؛ Quadrature formula؛ Numerical solution of ordinary differential equation

مراجع

1. Costarelli, D. and Kyurkchiev, N. A Note on the smooth approximation to |x(1 − x) · · ·(n − 1 − x)| using Gaussian error function, Commun. Appl. Anal. 25(1) (2021), 1–10.
2. Eslahchi, M.R., Masjed-Jamei, M. and Babolian, E. On numerical improvement of Gauss-Lobatto quadrature rules, Appl. Math. Comput. 164(2005), 707–717.
3. Gautschi, W. Numerical analysis, Birkhauser, Boston, 1997.
4. Kyurkchiev, N., Iliev A. and Rahnev, A. A look at the new logistic models with “polynomial variable transfer”, LAP LAMBERT Academic Publishing, 2020.
5. Kyurkchiev, N. and Markov, S. Sigmoid functions: Some approximation and modelling aspects, LAP LAMBERT Academic Publishing, 2015.
6. Masjed-Jamei, M. and Dragomir, S.S. A new generalization of the Os trowski inequality and applications, Filomat, 25 (2011), 115–123.
7. Masjed-Jamei, M., Jafari, M.A. and Srivastava, H.M. Some applications of the Stirling numbers of the first and second kind, J. Appl. Math. Comput. 47 (2015), 153–174.
8. Masjed-Jamei, M., Milovanovic, G.V. and Jafari, M.A. Closed expressions for coefficients in weighted Newton-Cotes quadratures, Filomat 27(4)(2013), 649–658.
9. Stoer, J. and Bulirsch, R. Introduction to numerical analysis, Translated from the German by R. Bartels, W. Gautschi and C. Witzgall. Second edition. Texts in Applied Mathematics, 12. Springer-Verlag, New York,1993.