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Need a help for FDTD

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Ahmed-Mostafa

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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 any one help me how we got this expression ..
 

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