The Algorithm of Neural Networks on the Initial Value Problems in Ordinary Differential Equations

@article{Liying2007TheAO,
  title={The Algorithm of Neural Networks on the Initial Value Problems in Ordinary Differential Equations},
  author={Xu Li-ying and Wen Hui and Zeng Zhe-Zhao},
  journal={2007 2nd IEEE Conference on Industrial Electronics and Applications},
  year={2007},
  pages={813-816}
}
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. 

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