Q.Living In Midwest With A Neighbor That Has A Pump In The Middle Of His Yard.
During heavy rains he floods my yard and the back end which slopes downward erodes at the grass. Is there a stronger grass to hold against the flooding?
Certified GKH Gardening Expert
Bahia grass, ryegrass, and rough stalk bluegrass tolerate wet soils. They perform best in shade, but you didn't mention whether the site was in sun or shade. This would be a good question for your local extension agent, who will know which grasses do well in your area.
https://www.gardeningknowhow.com/extension-search
You might consider adding a border of moisture loving perennials. This article will help:
https://www.gardeningknowhow.com/ornamental/water-plants/wgen/water-tolerant-plants.htm
https://www.gardeningknowhow.com/ornamental/trees/tgen/wet-soil-trees.htm
For other ideas about how to improve drainage (such as a French drain):
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/yard-drainage-problems.htm