As Systems of PDEs describes, toolbox functions can address the case of systems of N PDEs. How do you represent the coefficients of your PDE in the correct form? In general, an elliptic system is
For 2-D systems, the notation represents an N-by-1 matrix with an (i,1)-component
For 3-D systems, the notation represents an N-by-1 matrix with an (i,1)-component
The symbols a and d denote N-by-N matrices, and f denotes a column vector of length N.
Other problems with N > 1 are the parabolic system
the hyperbolic system
and the eigenvalue system
To solve a PDE using this toolbox, you convert your problem into one of the forms the toolbox accepts. Then express your problem coefficients in a form the toolbox accepts.
The coefficients can be functions of location (x, y,
and, in 3-D, z), and, except for eigenvalue problems,
they also can be functions of the solution u or
its gradient. For eigenvalue problems, the coefficients cannot depend
on the solution
u or its gradient.
If any coefficient depends on time or on the solution u or
its gradient, then all coefficients should be