I'm trying to solve the below PDE using explicit finite difference method but it just never seems to converge. If i increase the timesteps and/or the spacesteps even by a little amount, the final value increases exponentially. I even tried solving it using separation of variables method but to no avail. I appreciate your tips.

Cheers.

Sankar.

∂V/∂t=(0.16+0.08Sin(t))∂²V/∂x² 0 < x <1

I.C. V(x,0)= x - x²

B.C. V(0,t)=0

B.C.V(1,t) =0

To find V (0.5,1)