Use weedkiller not wanting to seep into neighbours garden

Hi,

I have lots of weeds and wild grass growing through parts of 'my' garden some has gone through and started to grow into my neighbours garden. Its very tough and would take me ages to remove by digging it out. I do not want to use anything too strong and don't want anything in my neighbours garden ruined by me placing down weedkiller in my part which most likely will seep through into theirs.
Anyone suggest what i can do to get rid of it all.

Thanks for any tips.

Cisco

Weedkiller is fine , no risk to neighbour.

Any systemic killer will do....such as Roundup. After the weeds/grass has died cut off with a strimmer or leave to rot.

I use a very powerful paraffin burner because it leaves a nice clean finish but it can catch fire to the fence.

Thank you both will purchase some ‘Round up’. My concern was my sprayed weed killer along with the rain seep through the soil into my neighbour’s garden and ruins their plants.
Wrecked it - No wooden fence to catch fire just about 3 foot metal rails stuck in inch concrete block between their garden and mine.

Cheers!

Cisco