I'm relatively new in numerical methods for PDEs, so I have a question about solving the following PDE numerically for $W(x,p)$ in the phase space:$$-p\frac{dW}{dx}+x\frac{dW}{dp}+\frac{d}{dx}\left(xW \right)+2 \frac{d}{dp}\left(pW \right) + \frac{d^{2}W}{dx^{2}} +\frac{d^{2}W}{dp^{2}}-\frac{d^{2}W}{dxdp} = 0.$$What is the simplest (yet reasonably accurate) numerical method to solve the equation above? I expect to see a Gaussian in $x,p$ and I wish to visualize the numerical solution in the window $(x,p,W(x,p))$.
Numerical method to find stationary solution of an PDE in the phase space
pde;numerical analysis;python