Radial basis function networks in the numerical solution of linear integro-differential equations

Applied Mathematics and Computation

Volumn 188, Issue 1, 2007, Pages 427-432

  Golbabai, A ^a   Seifollahi, S ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

Integro differential equation; Quasi Newton method; Radial basis function network

Indexed keywords

ERROR ANALYSIS; INTEGRODIFFERENTIAL EQUATIONS; NEWTON-RAPHSON METHOD; NUMERICAL METHODS; OPTIMIZATION;

APPROPRIATE ERROR FUNCTIONS; APPROXIMATE SOLUTIONS; QUASI-NEWTON METHOD;

RADIAL BASIS FUNCTION NETWORKS;

EID: 34248228330     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.10.004     Document Type: Article

References (16)

1. Berenguer M.I., Fortes M.A., Garralda Guillem A.I., and Ruiz Galan M. Linear Volterra integro-differential equation and Schauder bases. Appl. Math. Comput. 159 (2004) 495-507
2. Broomhead D.S., and Lowe D. Multivariate functional interpolation and adaptive networks. Complex Syst. 2 (1988) 321-355
3. Buhmann M.D. Radial basis functions. Acta Numer. 9 (2000) 1-38
4. Delves L.M., and Mohamed J.L. Computational Methods for Integral Equations (1985), Cambridge University Press, Cambridge
5. Derong L., Tsu-Shuan C., and Yi Z. A constructive algorithm for feedforward neural networks with incremental training. IEEE Trans. Circ. Syst. 49 12 (2002)
6. Fletcher R. Practical Methods of Optimization. second ed. (1987), Wiley, New York
7. Golbabai A., and Seifollahi S. Numerical solution of the second kind integral equations using radial basis function networks. Appl. Math. Comput. 174 (2006) 877-883
8. Haykin S. Neural Networks: A Comprehensive Foundation (1999), Prentice-Hall, New Jersey
9. L. Jianyu, L. Siwei, Q. Yingjian, H. Yaping, Interactive gradient algorithm for radial basis function networks, in: The Sixth International Conference on Signal Processing, 2002, pp. 1187-1190.
10. Jianyu L., Siwei L., Yingjian Q., and Yaping H. Numerical solution of elliptic partial differential equation using radial basis function neural networks. Neural Networks 16 (2003) 729-734
11. Lagaris I.E., Likas A., and Fotiadis D.I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Networks 9 (1998) 987-1000
12. Mai-Duy N., and Tran-Cong T. Approximation of function and its derivatives using radial basis function networks. Appl. Math. Modell. 27 (2003) 197-220
13. Maleknejad K., and Mahmoudi Y. Numerical solution of integro-differential equation by using hybrid Taylor and Block-Palse functions. Far East J. Math. Sci. (FJMS) 9 2 (2003) 203-213
14. Maleknejad K., and Mahmoudi Y. Taylor polynomial solution of high-order nonlinear Volterra Fredholm integro-differential equations. Appl. Math. Comput. 145 (2003) 641-653
15. Park J., and Sandberg I.W. Universal approximation using radial basis function networks. Neural Comput. 3 (1991) 246-257
16. Powell M.J.D. Radial basis functions for multivariable interpolation: a review. In: Mason J.C., and Cox M.G. (Eds). Algorithms for Approximation (1987), Clarendon, Oxford, UK 143-167