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Numerical methods are developed to study various applications in electromagnetic wave propagation and scattering. Analytical methods are used where possible to enhance the efficiency, accuracy, and applicability of the numerical methods. Electromagnetic induction (EMI). A new numerical method is developed to obtain an accurate and fast solution of the early time EMI response in the transmittance of electromagnetic waves in the region from 0 to 2000 Km. The method is combined with the finite element method to provide the entire time domain response. To facilitate the solution, the Forward Backward and the Leap-frog method also is applied. To do this we assume the magnetic field is stored at each grid point. The electric field is stored at half intervals in order to allow central difference method as well as to simplify boundary condition. in order to evaluate these we use the number density of electron/ion depend on the altitude and time which is given by Ambipolar equation.