There is a well-known book from 2006 by Daniel Duffy, which is Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. You may find it here on Wiley's:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118673447
On the other hand, he has a more recent book:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781119719731
Have anyone here checked on both? What are the main differences? What would you recommend for someone looking to go further in FDM?
Thanks a lot!