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

A new method for solving initial value problems in ordinary differential equations (ODE
_S
) 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 ODE
_S
. The results show the proposed approach is more precise than modified Euler method and Heun's method.