2-D simulation of a wave help

The goal of this project is to make a 2-D simulation of a wave reflecting off of an arbitrarily shaped surface via the finite difference time domain method. a) experimentally determine the numerical stability of your FDTD scheme, i.e. figure out how small the time step must be as a function of the space step in order for the solution to remain bounded. b) Implement metallic (i.e. perfectly conducting) boundary conditions, and submit a program that causes reflection of a plane wave from the edges of your space. c) Implement a lens with a spherical-shaped surface. Submit a program which shows that the lens focuses a plane wave. d) Implement a waveguide by exciting a wave inside a long dielectric with greater than that of surrounding