On 15/7/2017 at 0:10 PM, gamer9xxx said:

For the integration of cost field they are using Eikonal equation for traversing the areas.

No, the eikonal equation defines what is a shortest path. "Traversing the areas" is what algorithms that compute solutions of the eikonal equation, i.e. shortest paths, need to do somehow.  In the case of chapter 23 of Game AI Pro:

Quote

We are now ready for cost field integration. As with the LOS pass, we start with the active
wave front list. This active wave front comes from the list of “Wave Front Blocked” loca-
tions from the previous LOS pass. In this way we only integrate locations that are not
visible from the goal.
We integrate this wave front out until it stops moving by hitting a wall or a sector
border. At each grid location we compute the integrated cost by adding the cheapest cost
field and integrated cost field’s up, down, left, or right neighbors together. Then repeat this
Eikonal equation process again and again, moving the wave front outward toward each
location’s un-integrated, non-walled neighbors.

Maintaining a list of active wavefront cells looks definitely like a "brushfire" algorithm.

Are you confusing this basic building block of multiple source/single destination grid-based pathfinding with the full pathfinding solution described in the book (tile-based architecture, portals, caching, LOS special case, specific flags and data structures, etc.)?