Solution of the second and fourth order differential equations using irbfn method
DOI:
https://doi.org/10.32792/jeps.v11i2.130Abstract
In this paper we introduce presents a numerical approach, based on radial basis function networks (RBFNS), for the approximation of a function and its derivatives (scattered data interpolation), The proposed approach here is called the indirect radial basis function network (IRBFN) to solve second and fourth order differential equations the procedure can start with the second derivative. First, the second order derivative is approximated by a RBFN, then the first order derivative is obtained by integration. Finally the original function is similarly obtained, i.e. by integrating the first derivative function. This second method is here referred to as the second indirect method or IRBFN2 likewise fourth -grade derivative IRBFN4
References
References: [1] Nam Mai-Duy, Thanh Tran-Cong. (2003): Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modelling, QLD 4350. [2] Mai-Duy, N. and Tran-Cong, T. (2001) “Numerical solution of differential equations using multiquadric radial basis function networks”, Neural Networks, Vol 14 No 2, pp. 185-99.
J. Moody, C.J. Darken, Fast learning in networks of locally-tuned processing units, Neural Computation (1989) 281–294. [4] T. Poggio, F. Girosi, Networks for approximation and learning, in: Proceedings of the IEEE 78, 1990, pp. 1481–1497. [5] S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, New Jersey, 1999. [6] Divo, E.; Kassab, A. J. (2007): An efficient localized radial basis function meshless method for fluid flow and conjugate heat transfer. ASME Journal of Heat Transfer, vol. 129, pp. 124–136. [7] Mai-Duy, N.; Tanner, R. I. (2007): A Collocation Method based on One Dimensional RBF Interpolation Scheme for Solving PDEs. International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 (2), pp. 165–186. [8]Ngo-Cong, D., et al. (2012). "A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis." CMES: Computer Modeling in Engineering and Sciences 83(5): 459-498.
Downloads
Published
Issue
Section
License
Copyright Policy
Authors retain copyright of their articles published in the Journal of Education for Pure Science (JEPS).
By submitting their work, authors grant the journal a non-exclusive license to publish, distribute, and archive the article in all formats and media.
License
All articles published in JEPS are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
This license permits unrestricted use, distribution, and reproduction in any medium, provided that the original author(s) and the source are properly credited.
Author Rights
Authors have the right to:
-
Share their articles on personal websites, institutional repositories, and academic platforms
-
Reuse their work in future research and publications
-
Distribute the published version without restriction
Journal Rights
The journal retains the right to:
-
Publish and archive the articles
-
Include them in indexing and archiving systems such as LOCKSS and CLOCKSS
-
Promote and disseminate the published work
Responsibility
The contents of all articles are the sole responsibility of the authors. The journal, editors, and editorial board are not responsible for any errors, opinions, or statements expressed in the published articles.
Open Access Statement
JEPS provides immediate open access to its content, supporting the principle that making research freely available to the public enhances global knowledge exchange.
This work is licensed under a Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/
