Consider a $1$D space with discrete grid points represented by indices $i=1,2,3,$dots,$N.$ The electric field $E_z$ at each point is governed by the update equation:

$E_z^{n+1}(i)=E_z^n(i)+\frac{t}{lon}(H_y^n(i)-H_y^n(i-1)),$

where $n$ is the time index $t$ is the time step, and $lon$ is the permittivity of the medium. The magnetic field is updated as:

$H_y^{n+1}(i)=H_y^n(i)+\frac{t}{}(E_z^{n+1}(i+1)-E_z^{n+1}(i)),$

where $$ is the permeability of the medium.

Write a MATLAB script to simulate the propagation of an electromagnetic wave in a $1$D space using the FDTD method. Assume a sinusoinal source function $E_z^0(i)=sin(\frac{}{c}ix)$ at the center of the domain $)=(\frac{N}{2}$ at time $n=0.$

Parameters are as follows:

Number of grid points is $200$

Spatial step is $0\mathrm{.}1m$ and and time step is "obviously" related to this value.

Frequency of the source is $1Hz$

Permittivty and Permeability is $8\mathrm{.}854{10}^{-12}\frac{F}{m}$ and $4{10}^{-7}\frac{H}{m}$ respectively.

Simulate the wave propagation for $1000$ time steps and visualize the electric field $E_z$ and $H_y$ at different plots.

Your code must include explanation for every key steps and parameters used.