Results from the Magnetic Induction Equation

I have a Fortran program called "rmagnet.f90" which aims to solve the Magnetic Induction Equation numerically.
I set the program's parameters to the following:
steps in timeloop=100

I wanted to make the magnetic field B appear to be cylindrical. To do this, I defined a radius in terms of the y & z axes and defined B such that it depended upon this radius in the x-direction only. My initial condition for B was:

I was limited to this form for B, since I intended to later solve this equation in terms of a vector potential A. With this in mind, I was satisfied that the modulus of my magnetic field will actually appear as 2 cylinders now.

In order to check that my results were as I hoped, I used another IDL program called, "" to plot a contoured cross-section, shown below.


My contour plot verified that the results from my code were as I had expected.