on iPhone there is a find my friends application, to show them on a map. Is there a similar application available that works on both Android and iPhone?
Glympse should be what you're looking for. It is available for Android, for iOS, and even for Windows Phone. And it cares for your privacy: you decide who can see you, and for how long. That other person then gets a kind of "Token" which expires after the set time.
Glympse on Android (source: Google Play; click images for larger variants)
You can not only see where your friends are, you can also let the app guide you to them (or the other way around).
Glympse is available for free, well rated, and pretty famous amongst those who are familiar with the field.
You can use Waze for this.
It is primarily a navigation app which runs on iPhone, Android and Windows Phone but you can use it to see where your friends are. You can also see your friends through the Waze website.
It is free to use. You can follow multiple friends simultaneously.