Material for learning finite difference solution to Hamilton-Jacobi equation

[amature83]

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.)
Thanks!

 

[mighty2000]

Dear student,

Thank you for reaching out for help with your homework on implementing finite difference solution of Hamilton-Jacobi equation using Matlab. I understand that you are struggling with some of the details and concepts involved in this topic and are looking for recommendations on a good book to help you gain a better understanding.

First of all, I would recommend checking with your instructor to see if they have any specific recommendations for books or resources that align with their course material. They may have a preferred text or other resources that they can share with you.

In addition, here are some general recommendations for books that cover Hamilton-Jacobi equations and finite difference methods:

1. "Numerical Solution of Partial Differential Equations" by G.D. Smith. This book provides a thorough introduction to finite difference methods for solving PDEs, including Hamilton-Jacobi equations. It also includes a chapter on the use of Matlab for numerical computations.

2. "Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems" by Randall J. LeVeque. This book covers a wide range of finite difference methods for both ordinary and partial differential equations, including Hamilton-Jacobi equations. It also includes Matlab code examples and exercises.

3. "Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods" by Sandip Mazumder. This book provides a comprehensive treatment of finite difference and finite volume methods for PDEs, including Hamilton-Jacobi equations. It also includes Matlab code examples and exercises.

4. "Numerical Partial Differential Equations: Finite Difference Methods" by J.W. Thomas. This book focuses specifically on finite difference methods for PDEs and includes a chapter on Hamilton-Jacobi equations. It also includes Matlab code examples and exercises.

I hope these recommendations will help you find a book that suits your needs and provides a clear understanding of the concepts involved in solving Hamilton-Jacobi equations using finite difference methods. Good luck with your homework!