Coefficients for Systems of PDEs

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

(cu)+au=f,

The notation (cu) means the N-by-1 matrix with (i,1)-component

j=1N(xci,j,1,1x+xci,j,1,2y+yci,j,2,1x+yci,j,2,2y)uj

Other problems with N > 1 are the parabolic system

dut(cu)+au=f,

the hyperbolic system

d2ut2(cu)+au=f,

and the eigenvalue system

(cu)+au=λdu.

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 question is how to express each coefficient: d, c, a, and f. For answers, see f for Systems, c for Systems, and a or d for Systems.

    Note:   If any coefficient depends on time or on the solution u or its gradient, then all coefficients should be NaN when either time or the solution u is NaN. This is the way that solvers check to see if the equation depends on time or on the solution.

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