Need a help at computational electromagnetics

[Ahmed123]

Hi dears

I study numerical electromagnetics , especially FDTD method , i reached to the point at where i introduce my sources then i get an understanding problem .. at this method ( as in the attached photo ) the electric field is defined at time (t) and magnetic field at (t+dt/2) and there is a space separation between them equals half of the cell .. so the electric field function is defined as g(t) and but magnetic field take that messy expression as in the picture can anyone help me how we got this expression ..

 

[Paul Colby]

I'm guessing only the drive term (at a point in the grid?) in the FDTD algorithm is being shown in the image. The grid is in space and time. Looks like they've included the propagation delay in $g(t)$ source term for the neighboring $H$-field point. For the FDTD algorithm to be stable, this time delay needs to be very small in comparison to $\frac{\Delta t}{c}$.