Hello everyone,

I suppose that this is more of a PDE question, but ultimately some numerical analysis will be used.

I have a 2nd order pde on my hands for a density in stock and interest rate in time. I need to step through this pde forward and update one of the coefficients.

The initial density is a delta function and I tried anothe transform so that I have a normal initially, but it is still too thin and steep. So, finite differences are difficult. I would need to integrate over this density, so I would need some specialized mesh.

So, I am turning to Green's functions and I will try to get a closed form. Does anyone know of a good book with many examples of Green's functions, especially applicable to finance? Or, if there is some work that has been done with Green's functions for 2nd order pdes (with 2 or more state variables), please let me know, so that I do not reinvent the wheel

Thanks,

Taras