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$$
Hz^{n+1/2}_{i+1/2,j+1/2} = Hz^{n-1/2}_{i+1/2,j+1/2}
+ \frac{dt}{dy} (Ex^{n}_{i+1/2,j+1} - Ex^{n}_{i+1/2,j}) \\
- \frac{dt}{dx} (Ey^{n}_{i+1,j+1/2} - Ey^{n}_{i,j+1/2})
$$
$$
Ex^{n+1}_{i+1/2,j} = Ex^{n}_{i+1/2,j} + \frac{dt}{dy} ( Hz^{n+1/2}_{i+1/2,j+1/2} - Hz^{n+1/2}_{i-1/2, j-1/2} )
$$
$$
Ey^{n+1}_{i,j+1/2} = Ey^{n}_{i,j+1/2} - \frac{dt}{dx} ( Hz^{n+1/2}_{i+1/2,j+1/2} - Hz^{n+1/2}_{i-1/2, j+1/2})
$$
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