Can I solve more than two PDEs in 2D?

Hello,

I want to solve a system of several diffusion-equation reactions in 2D to simulate a gradient of proteins in a cell.

Something like:

du1/dt = D(d^2u1/dx^2+d^2u1/dy^2) + r1*u2 - r2u1

du2/dt = D(d^2u2/dx^2+d^2u2/dy^2) - r1*u2 + r3u3

...

I tried to solve it using the central difference method in space and the forward difference method in time, but I get negative concentration values... So I guess I did it wrong. I was wondering if I can use a solver like pde to solve more than two PDEs in 2D, but is it even possible? Which methods can I use?

Best,

Cecilia

Answer 1

[Torsten]

If you have a licence for the PDE Toolbox, you can apply it to solve your problem.

[Cécilia]

I find only tutorials to solve system of several PDEs in 1D or one equation in 2D... but not to solve system of several PDEs in 2D. Do you have resources to help me?

[Torsten]

https://uk.mathworks.com/help/pde/ug/nonlinear-system-with-cross-coupling-between-components.html

I think it's obvious how to solve such a system for more than 2 components in 2d.

The documentation can help:

https://uk.mathworks.com/help/pdf_doc/pde/index.html

[Cécilia]

Thank you!