We have a hyperbolic pde (in fact the 1d wave equation) with indep vars X, T
We use the central difference approximations for the second derivatives wrt X, T to get
[phi(Xn, Tj+1) -2phi(Xn, Tj) + phi(Xn, Tj+1)]/(dT^2) = [c^2][phi(Xn-1, Tj) -2phi(Xn, Tj) + phi(Xn=1, Tj)]/(dX^2)
where dX...