I am using the explicit finite backward difference scheme to discretize and calculate the price of an European call option in a discretization stencil.
My goal is to find the error at a given time step (e.g. at the 200th time step in a 360 time step model) evaluated at each spatial step (which represents the underlying asset price in this case) for the numerical solution, as compared to the analytical Black Scholes solution.
However, I don't understand how to supply the 200th time step parameter to the Black Scholes equation to calculate the option value at that time step for different asset prices. As far as my understanding goes, the BS equation only takes in the size of the time step, which is calculated by dividing the option duration into equal sizes. It then gives the option value at t=0.
How can I use the BS model to find the option value at, say, t = 200/360?