Material for learning finite difference solution to Hamilton-Jacobi equation
Hello, I have a homework of implementing finite difference solution of Hamilton-Jacobi equation using Matlab. The instructor is using her own set of notes. I'm a bit lost in details of the formulation (basically I want to learn more about the concept of characteristic curves, the merits of using central vs. backward differences. the intuition for entropy conditions, etc). I'd like to experiment few other things as well (other than the way she formulated the equations). And I would like to get a fair understanding as well; I'm planning to implement in Matlab, and Sage & Maple as well (Maple & Sage for my own good). Hamilton-Jacobi equations & finite differences sound pretty standard topic though (I'm a CS person; all about discrete structures and algebra. But I'm willing to cram some analysis in a short time given a good book). My question is: do you have any recommendation for a good book? I don't want to be skimming through 5 books or so (I compiled a collection from Google Books, course websites, lecture notes etc), but some here might know the best book to read & save me the hassle.
(BTW, the PDEs are for an image processing course. Also, my homework is about implementation & number crunching. It's NOT about discussion; so the topics I listed above are my own list of confusing terms.)