What is the reference I should read to solve this PDE numerically ? $$\frac{\partial u}{\partial t} - r (\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2})+\sin(y)\frac{\partial u}{\partial x}=0$$ with the following periodic boundary conditions $$u(-\pi,y,t)=u(\pi ,y,t) \\ (u(x,-\pi,t)=u(x,\pi,t) \\ u_x(-\pi ,y,t)=u_x(\pi,y,t)\\ u_y(x,-\pi,t)=u_y(x,\pi,t) \\ u(x,y,0)=F(x,y) \\ r>0$$
Thank you.