Black Scholes PDE explicit Scheme

I am currently working on the implementation of classic schemes to solve the BS PDE and it seems that I make a mistake in my code because the result looks far from the result of the BS formula. Here is the maths of the implicit scheme: Substituting $\tau = T - t$ into the Black-Scholes equation and using the chain rule, we get: $$-\frac{\partial V}{\partial \tau} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + rS\frac{\partial V}{\partial S} - rV = 0$$ To solve this equation using an