Computing routing information to support pervasive applications is different from that on the Internet. When the user moves freely from one place to another, the frequently method of computation and communication of routing information on Internet is often a waste of resources. In order to improve the computation of routing information on Internet to support pervasive applications, we put forward a new model of wireless networks and use neural networks as a fast tool to compute shortest paths on-demand on a time-dependent wireless network. The high-speed and stability of the method is proved. It also makes a new study on solving the optimization, but not NP-hard problems by neural networks