System of PDEs which is tricky for PDEPE
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I have a system of PDEs, mainly diffusion equations of the form:
Where a and d are constants and _t,_x represent partial differentiation w.r.t. t and x respectively. In terms of pdepe, I would have: f=0 for the third equation. Would this cause errors in the code?
I'm also struggling to see how I can input the boundary conditions.
Torsten on 23 May 2018
Edited: Torsten on 23 May 2018
"pdepe" is designed to solve systems of parabolic-elliptic pdes. Your third pde is hyperbolic in nature. Thus "pdepe" is not suited to solve your system.
You will have to discretize your equations in space and solve the resulting system of ordinary differential equations using ODE15S.
Look up "method-of-lines" for more details.
Torsten on 24 May 2018
You could try to use "pdepe" with the third equation differentiated:
with Dirichlet boundary condition
E = E0
at one end of the interval and
(epsilon*E)_x + b*c=0
at the opposite end.
Precise Simulation on 9 Jun 2018
Systems of PDEs might also be easier to solve with the FEATool FEM Toolbox which features a GUI and easy syntax for defining custom PDEs and equations. This example of heat transport and diffusion might be a good start, otherwise you could perhaps use the built-in convection and diffusion physics mode and modify it according to your equations.