The PDE is as below:
$$ h(t, \alpha), t\in[0, 60], \alpha \in [-300, 300] $$ $$ \partial_th+0.04\alpha-200\alpha \partial_\alpha h+0.5\partial_{\alpha\alpha}h=0 $$ with terminal condition: $$ h(T, \alpha) = 0.02, \qquad \text{where}\qquad T=60 $$ what is $h(0, \alpha)$?
So I use a grid on t and $\alpha$ to back induct $ h(0, \alpha) $. Now the problem is the coefficient of $\partial_\alpha h$, which is $-200\alpha$, is very big. And after several steps, it will blow up.
Any suggestions on this?
Thanks for your help.