Tasks to carry out:

• Solve the diffusion equation
• Explore the evolution of the magnetic field magnitude and of the exponential decay rate
• Explore the evolution of the spatial solution for Br and Bφ, and of the pitch angle of the mean magnetic field p
• Explore how different boundary conditions affect the results
• Explore how different seed fields affect the results

A brief summary:

I solved the diffusion equation by considering a finite difference method of the 2nd order, and 4th order runge kutta time stepping. I considered different kinds of seed fields to study the time evolution of the fields. In my first attempt of this, I was only able to work with Dirichlet boundary conditions, but I was able to add it later.

A note to sir:

At the time to submitting Task 1, the file I uploaded was this one(pdf), but I was able to significantly improve the structure of my code by writing a general Runge Kutta function that works for any two variables and the user can specify the type of boundary conditions(Dirichlet or Neumann) as a parameter, and hence I decided to redo the calculations with the updated code, and I have uploaded it here. You may consider the updated file if that’s okay. You can also check the actual .ipynb files in this Github Repository.

For now, I reference the pdf of the .ipynb file, of the updated code, where I have explained the steps and process.

Task1_2.pdf