Solution of the second and fourth order differential equations using irbfn method
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:  Nam Mai-Duy, Thanh Tran-Cong. (2003): Approximation of function and its derivatives using radial basis function networks. Applied Mathematical Modelling, QLD 4350.  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.  T. Poggio, F. Girosi, Networks for approximation and learning, in: Proceedings of the IEEE 78, 1990, pp. 1481–1497.  S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, New Jersey, 1999.  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.  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. 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.
Copyright (c) 2022 Journal of Education for Pure Science- University of Thi-Qar
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The Authors submitting a manuscript do so on the understanding that if accepted for publication, copyright of the article shall be assigned to Journal of education for Pure Science (Jeds), University of Thi-Qar as publisher of the journal.
Copyright encompasses exclusive rights to reproduce and deliver the article in all form and media, including reprints, photographs, microfilms and any other similar reproductions, as well as translations. The reproduction of any part of this journal, its storage in databases and its transmission by any form or media, such as electronic, electrostatic and mechanical copies, photocopies, recordings, magnetic media, etc. , will be allowed only with a written permission from Journal of education for Pure Science (Jeds), University of Thi-Qar.
Journal of education for Pure Science (Jeds), University of Thi-Qar, the Editors and the Advisory International Editorial Board make every effort to ensure that no wrong or misleading data, opinions or statements be published in the journal. In any way, the contents of the articles and advertisements published in the Journal of education for Pure Science (Jeds), University of Thi-Qar are sole and exclusive responsibility of their respective authors and advertisers.