I am modelling a Klein-Gordon equation (similar to a wave equation), by mode decomposition, i.e. I need to solve the eigenvalue problem y_n'' = - omega_n ** 2 * y (This is of course a vast simplification).
This procedure involves many steps, but the main ones are

1. Calculate the solution for each of the modes (identified with an index n) up to a maximum index max_n. Save it to the nth element of a solution array of the class I am using to do all this (as this is all part of a bigger project).

for n in range(-max_n, max_n+1):
    self.solution_array[n+max_n] = scipy.integrate.solve_bvp(
        Klein_Gordon_differential_equation,
        boundary_conditions,
        ...,
        p=(eigenvalue_guess(n),),
        )

This is suboptimal as I am not doing any parallelization.

2. When all these modes are calculated, calculate some physical quantity regarding the full family of solutions, which changes the context of the problem.

3. With this new context, repeat step 1.

4. If some convergence is achieved, stop.

When trying to solve for the eigenvalue, SciPy raises a MemoryError: Not enough memory to perform factorization.

Is there anyway I change my method so that I do not get a MemoryError? For example, is it possible that since I am not using parallelization, SciPy ‘sees’ less memory than what it should be seeing? i.e. will parallelization solve something more than just runtime?

Note: Please tell me if I need to add more details. The process in itself its pretty simple, but the calculations I am doing involve a lot of subcalculations that I do not think are relevant for the question.

Edit: The traceback of the error:

Traceback (most recent call last):
  File "main.py", line 45, in <module>
    smoothing=smoothing,
  File "/home/sanz/MasterArbeit/computation/calculations/increase_lambda.py", line 84, in main
    plt.show()
  File "/usr/lib/python3/dist-packages/matplotlib/pyplot.py", line 254, in show
    return _show(*args, **kw)
  File "/usr/lib/python3/dist-packages/matplotlib/backend_bases.py", line 3266, in show
    cls.mainloop()
  File "/usr/lib/python3/dist-packages/matplotlib/backends/_backend_tk.py", line 1039, in mainloop
    managers[0].window.mainloop()
  File "/usr/lib/python3.7/tkinter/__init__.py", line 1283, in mainloop
    self.tk.mainloop(n)
KeyboardInterrupt

Edit: Other probably relevant information: The code breaks down due to physical reasons (when the eigenvalue of some mode goes to 0, due to the external electric field being too strong). When that happens, I understand that scipy tries to increase the number of nodes used with each iteration. I guess that is where the memory error is