I am looking for a book (or any resource such as an article, website, etc.) for learning Similarity Transformation for transforming
differential equations. I would appreciate it if you let me know of any reference.
indeed, if he's working with black-scholes, the heat equation is the way to goBut perhaps the OP can start with Bluman & Cole's paper:
http://www.jstor.org/stable/24893142?se ... b_contents
that's maybe a little advanced for someone to for learn Similarity Transformation for transforming differential equations, but it's of historical interest in that george bluman essentially derived some of the formulas for barrier options a couple of decades before the math finance folk rediscovered them. And I doubt if they credited him for it.
I do not quite understand your statement. Are you saying Lie group/algebra and its representations have tenuous bearings on mathematical physics? Noether's theorem that gives all the conservation laws is but one example of its bearing. Many eigenvalue problems, for energy levels, in quantum mechanics either are too tedious or cannot be solved without Lie group or discrete group representations. I must have misunderstood your statement.I have Olver's book, I did Lie Groups and Lie Representations in undergrad and I don't understand what these PDEs deliver.
The link to classical mathematical physics (where all the interesting PDEs come from) is tenuous. Am I missing something?
I'm saying I don't understand how this stuff is useful in let's say Navier Stokes or Black Scholes PDE. Caveat: I haven't tried and wouldn't know where to start.I do not quite understand your statement. Are you saying Lie group/algebra and its representations have tenuous bearings on mathematical physics? Noether's theorem that gives all the conservation laws is but one example of its bearing. Many eigenvalue problems, for energy levels, in quantum mechanics either are too tedious or cannot be solved without Lie group or discrete group representations. I must have misunderstood your statement.I have Olver's book, I did Lie Groups and Lie Representations in undergrad and I don't understand what these PDEs deliver.
The link to classical mathematical physics (where all the interesting PDEs come from) is tenuous. Am I missing something?