Beat me to it kopes. 🙂  RoundUp is the go. Please make sure you read the instructions carefully. whatever you spray it onto will die, so make sure it's only the Ivy. 🙂 

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@kopenhagen5 wrote:

Using something as Round Up means it goes to the roots and kills the plant.

So if the neighbor doesn't want it either, that's a quick solution.

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For Ivy it's best to cut a heap back then cut a slit in cut ends & paint on NEAT Glyphosate ( Round up is fine). Do not mix with water and apply to each fresh cut  as the slit is completed.

Wear gloves.

Yes, as tuckcase says.  Paint  glyphosate undiluted.

Do not spray if it's windy,  you'll wear it.

The ivy roots are on the neighbours yard between the fence and their garage. 

There is a 10 inch gap there and the ivy is now coming through the spaces in the fence. 

It will be very hard to get to the roots without taking the palings off the fence.  The ivy was covering their back fence until they had the fence replaced and we thought that they had removed it all BUT it has now come back in a different spot.

Boiling water works wonders and so does neat white vinegar...............and both are cheap!