Title :
The Algorithm of Neural Networks on the Initial Value Problems in Ordinary Differential Equations
Author :
Li-Ying, Xu ; Hui, Wen ; Zhe-Zhao, Zeng
Author_Institution :
Changsha Univ. of Sci. & Technol., Changsha
Abstract :
A new method for solving initial value problems in ordinary differential equations (ODES) is proposed in this paper. The algorithm of neural networks based on the cosine basis functions is studied in detail. The convergence theorem of neural networks algorithm is given and proved. The algorithm is validated by the simulation examples of ODES. The results show the proposed approach is more precise than modified Euler method and Heun´s method.
Keywords :
differential equations; initial value problems; neural nets; Heun method; convergence theorem; cosine basis functions; initial value problems; modified Euler method; neural networks; ordinary differential equations; Differential equations; Industrial electronics; Neural networks; Cosine Basis Functions; Neural Network; Ordinary Differential Equations; convergence theorem;
Conference_Titel :
Industrial Electronics and Applications, 2007. ICIEA 2007. 2nd IEEE Conference on
Conference_Location :
Harbin
Print_ISBN :
978-1-4244-0737-8
Electronic_ISBN :
978-1-4244-0737-8
DOI :
10.1109/ICIEA.2007.4318520
