i want to solve the followning second order non linear PDE :
$$\frac{\partial V}{\partial t}(t,x) + g(x)\frac{\partial V}{\partial x}(t,x) + q(x)\frac{\partial^{2} V}{\partial x^{2}}(t,x) + h(x) =0 $$
with boundary condition $V(T,x) = \Phi(x)$ where $t\le T$.
I heard that the method of characteristics can work in order to determine $V(t,x)$. However, i have never met this method before. Could someone give me a quick quide ?
thanks