partial integro-differential equation

[xyysharon]

Dear Dr. Zwicker,
Thanks for this wonderful package! I really appreciate your work, but I just have some questions.
I am trying to solve a partial integro-differential equation in 1D which looks like:

How can I include the integral term in the PDE? I could not find example codes that include integral term.
Can you show demonstration code?
Thank you!

[david-zwicker]

This is not supported out-of-the box, but you could write a custom pde class, where you calculate the integral in each timestep.

[david-zwicker]

I just realized that it will be rather simple to support integrals over entire fields in the pde.PDE class. I started to work on this today and if nothing fails, this should be merged into the main branch tonight.

[xyysharon]

Thank you for your response! I'm really looking forward to it！

[david-zwicker]

The master branch now supports the following syntax:

eq = pde.PDE({'c': '-integral(c)'})

This is of course an oversimplified example, where the integral of the field c affects the evolution rate at each point. However, this should get you started to implement your own equation.

[xyysharon]

Thanks David! It works fine for my work!!! By the way, when I use matplotlib 3.5 for drawing, there was a flash back. So I switched to version 3.2 and it works.

[david-zwicker]

Good to hear that things work for you. Concerning the newer matplotlib, could you please open an Issue with a detailed description, so we can track and fix this problem?!

[xyysharon]

Okay, I'll open a new one.