Finite difference for 2nd order PDE

[juricab]

I need to solve the following PDE:
$$\frac{1}{2}F_{\eta \eta }\sigma _{\eta }^{2}\eta ^{2}+\frac{1}{2}F_{pp}\sigma _{p}^{2}+F_{p}k(m-p)+F_{\eta }a\eta -rF=0 \label{6}$$ where p goes from minus to plus infinity and eta goes from zero to plus infinity.

Here p and eta are state variables and all other variables are constants. I only have initial condition that F(p.0)=F(p), and I can calculate F(p). I am trying to solve this equation using finite difference with no luck. I am wondering if this can be solved at all using finite difference?

 

[gtoguy97]

Any help would be much appreciated. The PDE in \eqref{6} is a partial differential equation (PDE). It can be solved using finite difference methods, such as the method of lines or the finite element method. The initial condition given in the problem can be used to generate the initial values for the solution of the PDE. Once these initial values are known, the finite difference method can be used to solve the PDE.