Can I connect my iphone to my computer via a Wi-Fi WITHOUT a network?

I want to know if I can connect my iphone to my computer using the Wi-Fi dongle (or any other way of doing it), WITHOUT any internet access. I hope this makes sense!

Basically there's a program that I use for work which allows the use of an iphone app as an extra feature but it wants you to connect to your Wi-Fi network to be able to use it… I don't have a network on my work computer, its a mobile computer, so I would like to know if I can connect my iphone and computer so I can use this app.

Yes… You would need a router but you can have them communicate with each other without reaching the internet

Sometimes called an ad-hoc network.
Check out this article
http://www.logicinmind.com/en/support/iphone-ad-hoc-wireless-network/

Or google iphone ad-hoc networks

It depends on the app.

In theory, it ought to work an an ad-hoc network. But in practice, it may require DNS running. You may be able to just enter the ip address of the computer on ad-hoc. If not, and it wants a name, you might have to run a local network with local DNS and DHCP so that the iphone thinks it's on the internet and you can use a name.

For ad-hoc, you can create an ad-hoc network on your computer in the network settings. Then when you scan for Wi-Fi in the iphone, you should see it listed.
I've done that between a Linux laptop and a Nokia tablet, and saved the settings so it just shows up as one of the network choices.